ITS and traffic management

Full text

C. Barnhart and G. Laporte (Eds.), Handbook in OR & MS, Vol. 14
Copyright © 2007 Elsevier B.V. All rights reserved
DOI: 10.1016/S0927-0507(06)14011-6
Chapter 11
ITS and Traffic Management
M. Papageorgiou
Dynamic Systems and Simulation Laboratory, Technical University of Crete,
731 00, Chania, Crete, Greece
E-mail: markos@dssl.tuc.gr
M. Ben-Akiva
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology,
77 Massachusetts Ave., Cambridge, MA 02139, USA
E-mail: mba@mit.edu
J. Bottom
Charles River Associates, Inc., Boston, MA, USA
E-mail: jbottom@crai.com
P.H.L. Bovy
Transportation and Traffic Planning Section, Faculty of Civil Engineering and Geosciences,
Delft University of Technology, Delft, The Netherlands
E-mail: p.h.l.bovy@tudelft.nl
S.P. Hoogendoorn
Transportation and Traffic Planning Section, Faculty of Civil Engineering and Geosciences,
Delft University of Technology, Delft, The Netherlands
E-mail: s.p.hoogendoorn@tudelft.nl
N.B. Hounsell
Transportation Research Group, School of Civil Engineering and the Environment,
University of Southampton, Hants, SO17 1BJ, UK
E-mail: N.B.Hounsell@soton.ac.uk
A. Kotsialos
School of Engineering, University of Durham, South Road, Durham, DH1 3LE, UK
E-mail: apostolos.kotsialos@durham.ac.uk
M. McDonald
Transportation Research Group, School of Civil Engineering and the Environment,
University of Southampton, Hants, SO17 1BJ, UK
E-mail: M.Mcdonald@soton.ac.uk
1Introduction
The observed traffic conditions on road and highway networks result from
a quite complex-to-describe confrontation of supply and demand. Supply is
715

716 M. Papageorgiou et al.
mainly determined from the available road and highway infrastructure, most
notably its capacity. Demand is the collective outcome of individual driver de-
cisions regarding the effectuation (or not) of a trip, the choice of transportation
mode, of departure time, of the route to be followed, etc. Traffic congestion is
observed in increasing levels on road and highway networks around the world,
with detrimental consequences for traffic efficiency, safety as well as for the
environment. Traffic congestion affects the nominal capacity of the available
infrastructure leading to a vicious cycle of further congestion increase, fur-
ther infrastructure degradation, and so forth. In fact, the traffic throughput
measured in congested road or highway networks is usually well below the
nominal network capacity. Traffic control measures and strategies described
in this chapter aim at maintaining the available infrastructure capacity close
to nominal levels, protecting the traffic networks from the detrimental effects
of oversaturation and even gridlock. In this sense, traffic control is deemed to
mainly act on the supply side of the basic traffic equation. Other operational
measures have been employed in an attempt to reduce congestion by influenc-
ing the manifest traffic demand; this includes various forms of administrative
restrictions or of demand management (road pricing being the most promi-
nent), which, however, are not addressed in this chapter.
The chapter consists of 4 main overview sections, Section 2presenting an
overview of traffic flow modeling advancements, Section 3addressing the issue
of route guidance and information systems, while Sections 4and 5are con-
cerned with specific road and motorway network control systems, respectively.
2Trafficflowmodeling
2.1 Traffic flow modeling approaches
Understanding traffic flow characteristics (e.g., headway distributions, rela-
tion between density and speed, capacity distributions) and knowledge of the
associated analytical tools (e.g., queuing models, shockwave theory, simulation
models) to predict the dynamics of these characteristics under given demand,
supply and control conditions, is an essential requirement for the planning,
design and operation of a transportation system. For the analysis of a simple
arterial, on-ramp, or merge area, as well as for studying traffic flow operations
in urban or motorway networks, being able to predict the traffic performance
is an essential factor in the analysis of the system.
Traffic flow modeling research started when Lighthill and Whitham (1955)
presented their seminal paper on the wave dynamics of traffic flow. Their work
was based on the analogy of vehicles in traffic flow and particles in a fluid. Since
then, the mathematical description of traffic flow has been a lively subject of
research and debate for traffic engineers. This has resulted in a broad scope of
low-end and high-end models.

Ch. 11. ITS and Traffic Management 717
Before giving an overview of these models, we need to emphasize that
it is highly unlikely that traffic science will ever produce a complete theory
on the motion of individual cars. Despite of this, the last five decades have
provided tools to construct a framework of useful – albeit incomplete – theo-
ries from traffic observations and experimentation. These incomplete theories
are neither deductive (i.e., stemming from excellent theories), nor inductive
(black box), but rather intermediate; basic mathematical model structures are
adopted, after which specific flow properties are determined from empirical
or experimental data. Since the only accurate physical law in traffic flow the-
ory is the conservation of vehicle’s equation, the main challenge of traffic flow
researchers is to look for intuitive and useful theories of traffic flow.
2.1.1 Microscopic and macroscopic characteristics and models
A key distinction made in the study of traffic systems is that between mi-
croscopic and macroscopic variables. Microscopic characteristics (e.g., time
headways, individual speeds and distance headways) pertain to the individ-
ual driver–vehicle unit in relation to the other drivers in the flow. Microscopic
models describe the behavior of individual vehicles in relation to the infrastruc-
ture and other vehicles in the flow. On the contrary, macroscopic characteris-
tics pertain to the properties of the traffic flow as a whole (for instance at a
cross-section, or at a time instant). Examples of macroscopic characteristics are
flow, time-mean speed, density, and space-mean speed. Macroscopic models
describe traffic flow in terms of its macroscopic characteristics. The intermedi-
ate mesoscopic level is used to indicate the behavior of groups of drivers.
2.1.2 Properties of traffic flow
Microscopic and macroscopic characteristics of traffic flow have been stud-
ied for many years. Studies concern a large variety of aspects such as the dis-
tribution of headways, statistical relations between speed and density, capacity
of the infrastructure, propagation of shock-waves, etc. A lot of consideration
has been put into average behavior of drivers under the assumption of station-
ary flow conditions. Under these conditions, it is reasonable to assume that the
average behavior of drivers is the same for the same average conditions. That
is, drivers having a certain speed u, will on average maintain the same distance
headway s=1/k (where kdenotes the vehicular density, i.e., the mean num-
ber of vehicles per unit roadway length) with respect to the preceding vehicles.
This in turn implies that if we may assume that there exists some statistical (but
not necessarily causal!) relation among the density k(or equivalently, the mean
distance headway s), the (space) mean speed uand flow q=ku,thenitholds:
(1)q=Q(k) =kU(k)
Figure 1 shows an example of the three forms of this fundamental rela-
tion, showing some of its important properties (dU/dk<0, U(kj)=0,
Q(kj)=0, qc=maxkQ(k),etc.).Thefundamental relation will depend on

718 M. Papageorgiou et al.
Fig. 1. Examples of the fundamental relations between flow, density, and speed.
the different properties of the road (width of the lanes, grade), flow composi-
tion (percentage of trucks, fraction of commuters, experienced drivers, etc.),
external conditions (weather and ambient conditions), traffic regulations, etc.
Traffic flow observations however show that many data are not on the fun-
damental diagram. While some of these points can be explained by stochastic
fluctuations (e.g., vehicles have different sizes, drivers have different desired
speeds and following distances), a number of researchers have suggested that
these differences are structural and stem from the dynamic properties of traffic
flow. That is, they reflect so-called transient states (i.e., changes from conges-
tion to free flow (acceleration phase) or from free flow to congestion (deceler-
ation phase)) of traffic flow.
Several authors have studied the nonlinear or even chaotic-like behavior of
the traffic system (cf. Bovy and Hoogendoorn, 2000; Pozybill, 1998). Among
these behaviors are hysteresis and metastable or unstable behavior of traf-
fic flow. The latter implies that in heavy traffic a critical disturbance may be
amplified and develop into a traffic jam (spontaneous phase-transitions). In il-
lustration, empirical experiments performed in Forbes et al. (1958),andEdie
and Foote (1958, 1960) have shown that a disturbance at the foot of an upgrade
propagates from one vehicle to the next, while being amplified until at some
point a vehicle came to a complete stop. This instability effect implies that once
the density crosses some critical value, traffic flow becomes rapidly more con-
gested without any obvious reasons. More empirical evidence of this instability
and start–stop wave formation can be found in among others (Verweij, 1985;
Ferrari, 1989; Leutzbach, 1991). In Kerner and Rehborn (1997) and Kerner
(1999) it is empirically shown that local jams can persist for several hours, while
maintaining their form and characteristic properties. In other words, the sta-
ble complex structure of a traffic jam can and does exist on motorways.1These
findings show that traffic flow has some chaotic-like properties, implying that
1Apart from the formation of stop-and-go waves and localized structures, a hysteric phase-transition
from free-traffic to synchronized flow that mostly appears near on-ramps is described in Kerner and

Ch. 11. ITS and Traffic Management 719
microscopic disturbances in the flow can result in the on-set of local traffic jams
persisting for several hours.
Having said this, it should be clear that traffic flow shows some interesting
phenomena, which must be reflected correctly by the different models that
have been proposed. The remainder of this section focuses on these different
models, while discussing their most important properties.
2.1.3 Approaches to traffic flow modeling
Traffic flow models may be categorized using various dimensions (determin-
istic or stochastic, continuous or discrete, analytical or simulation, etc.), sto-
chastic. The most common classification is the distinction between microscopic
and macroscopic traffic flow modeling approaches. However, this distinction is
not unambiguous, due to the existence of hybrid models. This is why below,
models are categorized based on the following aspects:
1. Representation of the traffic flow in terms of flows (macroscopic), groups
of drivers (mesoscopic), or individual drivers (microscopic).
2. Underlying behavioral theory, which can be based on characteristics of the
flow (macroscopic), or individual drivers (microscopic behavior).
The remainder of this section uses this classification to discuss some important
flow models. Table 1 presents an overview of these models and the relevant
sections.
2.1.4 Microscopic traffic flow models
A microscopic model provides a description of the movements of individ-
ual vehicles that are considered to be a result of the characteristics of drivers
and vehicles, the interactions between driver–vehicle units, the interactions be-
tween driver–vehicle units and the road characteristics, external conditions,
and the traffic regulations and control. In general, two types of driver tasks
are distinguished: longitudinal tasks (acceleration, maintaining speed, distance
keeping relative to leading vehicle) and lateral tasks (lane changing, overtak-
ing). With respect to the longitudinal movement, most microscopic simulation
Ta b l e 1 .
Overview of traffic flow model classification
Representation Behavioral rules
Microscopic Macroscopic
Vehicle-based Microscopic flow models (2.1.4) Particle models (2.1.5)
Flow-based Gas-kinetic models (2.1.7) Macroscopic models (2.1.6)
Rehborn (1997). In addition, transitions from synchronized flow to the jammed traffic state occur in
congestion, upstream of the bottleneck.

720 M. Papageorgiou et al.
models assume that a driver will only respond to the one vehicle (the leader)
that is driving in the same lane, directly in front of her.
When the number of driver–vehicle units on the road is very small, the driver
can freely choose her speed given her preferences and abilities, the roadway
conditions, curvature, prevailing speed-limits, etc. In any case, there will be
little reason for the driver to adapt her speed to the other road-users. The
target-speed of the driver is the so-called free speed. In real life, the free
speed will vary from one driver to another, but also the free speed of a sin-
gle driver may change over time. Most microscopic models assume however
that the free speeds have a constant value that is driver-specific. When traf-
fic becomes denser, drivers will no longer be able to choose the speed freely,
since they will not always be able to overtake a slower vehicle. The driver will
need to adapt her speed to the prevailing traffic conditions, i.e., the driver is
following. In the remainder, we will discuss some of these car-following mod-
els. Models for the lateral tasks, such as deciding to perform a lane-change
and gap-acceptance, will not be discussed in this section in detail; a concise
framework of lane changing modeling is provided by Ahmed et al. (1996).
Safe-distance models. The first car-following models were developed in Pipes
(1953) and were based on the assumption that drivers maintain a safe distance:
a good rule for following vehicle i−1 at a safe distance siis to allow at least the
length S0of a car between vehicle iand the vehicle ahead for every ten miles
perhourofspeedviat which iis traveling:
(2)si=S(vi)=S0+Tr·vi
where S0is the effective length of a stopped vehicle (including additional
distance in front), and Trdenotes a parameter (comparable to the reaction
time). A similar approach was proposed in Forbes et al. (1958). Both theo-
ries were compared to field measurements. It was concluded that according to
Pipes’ theory, the minimum headways are slightly less at low and high velocities
than observed in empirical data. However, considering the models’ simplicity,
agreement with real-life observations was amazing (cf. Pignataro, 1973).
In Leutzbach (1988) a more refined model describing the spacing of con-
strained vehicles in the traffic flow was proposed. Considering an overall re-
action time Tr, the distance needed to come to a full stop given the initial
speed vi, the friction coefficient μ, and gravity g,equals
(3)S(vi)=S0+Tr·vi+v2
i
2μg 
Stimulus-response models. Stimulus-response models are dynamic models
that describe the reaction of drivers as a function of changes in distance,
speeds, etc., relative to the vehicle in front. These models are applicable to
relatively busy traffic flows, where the overtaking possibilities are small and
drivers are obliged to follow the vehicle in front of them. Drivers do not want

Ch. 11. ITS and Traffic Management 721
the gap in front of them to become too large, so that other drivers might en-
ter it. At the same time, the drivers will generally be inclined to keep a safe
distance.
Stimulus-response models assume that drivers control their acceleration.
The well-known model proposed in Chandler et al. (1958) is based on the in-
tuitive hypothesis that a driver’s acceleration is proportional to the relative
speed vi−1−vi:
(4)ai(t +Tr)=˙
vi(t) =αvi−1(t ) −vi(t)
where Tragain denotes the overall reaction time, and αdenotes the sensitivity.
Based on field experiments, conducted to quantify the parameter values for
the reaction time Trand the sensitivity α, it was concluded that αdepended on
the distance between the vehicles: when the vehicles were close together, the
sensitivity was high, and vice versa. The following specification was proposed
by
(5)α=α0
xi−1(t) −xi(t ) 
One of the main aspects of a dynamic model is its stability, i.e., whether
small disturbances will damp out or be amplified. For the stimulus-response
model (4), two types of stability can be distinguished, namely local stability
(stability of response of a driver on the leading vehicle i−1), and asymptotic
stability (propagation of disturbances along a platoon). Asymptotic stability is
of more practical importance than local stability. If a platoon of vehicles is as-
ymptotically unstable, a small disturbance in the movement of the first vehicle
is amplified as it is passed over to the next vehicle, which in turn can lead to
dangerous situations. Let us briefly consider both kinds of stability. The local
and asymptotic stability of the model depends on the sensitivity αand the re-
action time Tr, i.e., the model is locally stable if C=αTr<π/2. Asymptotic
stability requires C=αTr<1/2. Note that local stability is less critical than as-
ymptotic stability because the stimulus-response model becomes unstable only
for (unrealistically) large response times or large sensitivity values.
This simple model has several undesirable and unrealistic properties. For
one, vehicles tend to get dragged along when the vehicle in front is moving at
a higher speed. Furthermore, when the distance si(t) is very large, the speeds
can become unrealistically high. To remedy this deficiency, sensitivity αcan be
defined as a decreasing function of the distance. In more general terms, the
sensitivity thus can be defined as follows
(6)α=α0(vi(t +Tr))m
(xi−1(t) −xi(t ))l
Equation (6) implies that the following vehicle adjusts its speed vi(t) propor-
tionally to both distances and speed differences with delay Tr. The extent to
which this occurs depends on the values of α,l,andm. Combining Equations
(4) and (6), and integrating the result, relations between the speed vi(t +Tr)

722 M. Papageorgiou et al.
and the distance headway xi−1(t) −xi(t ) can be determined. Assuming station-
ary traffic conditions, the following relation between the equilibrium speed U
and the density kresults
(7)U(k) =U01−k
kj(l−1)1/(1−m)
for m= 1andl= 1; k=1/(xi−1−xi)denotes the density (average number
of vehicles per unit roadway length); kjis the so-called jam-density (density at
which U=0); U0is the mean free speed (at k=0). We refer to Leutzbach
(1988) for a more general expression of (7).
An alternative approach was proposed in Helly (1959), which includes an
additional term describing the tendency of drivers to maintain a certain desired
following distance Si(t):
(8)ai(t +Tr)=α1vi−1(t) −vi(t )+α2xi−1(t) −xi(t) −Si(t)
where
(9)Si(t) =β0+β1vi(t ) +β2ai(t) where βj0
Car-following models have been mainly applied to single lane traffic (e.g.,
tunnels, cf. Newell (1961)) and traffic stability analysis (Herman et al., 1959;
May, 1990). The parameters of the model (7) have been estimated using
macroscopic and microscopic data by a large number of researchers. It should
be noted that no generally applicable set of parameter estimates has been
found so far, i.e., estimates are site-specific. An overview of parameter esti-
mates can be found in Brackstone and McDonald (1999).
Optimal speed models. So far, the models considered mainly describe the car-
following task where the follower (in time) will aim to drive at the speed of the
leader, at a certain distance gap. Of course, there can be choices of the desired
speed other than the speed of the leader. In Bando et al. (1995) it is assumed
that the desired speed is a function of the distance between the vehicles under
consideration, i.e.,
(10)ai(t) =Udes(xi−1(t) −xi(t)) −vi(t)
Tr
where Udes(xi−1−xi)=U0tanh(xi−1−xi).
Psycho-spacing models. The car-following models discussed so far have
a mechanistic character. The only human element is the presence of a finite
reaction time Tr. However, in reality a driver is not able to:
•observe a stimulus lower than a given value (perception threshold);
•evaluate a situation and determine the required response precisely, for
instance due to observation errors resulting from radial motion obser-
vation;

Ch. 11. ITS and Traffic Management 723
•manipulate the gas and brake pedal precisely.
Furthermore, due to the need to distribute her attention to different tasks,
a driver will generally not be permanently occupied with the car-following task.
This type of considerations has inspired a different class of car-following mod-
els, namely the psycho-spacing models. The first psycho-spacing models were
based on theories borrowed from perceptual psychology provided in Michaels
(1963);cf.Leutzbach and Wiedemann (1986). In these models, car-following
behavior is described using a plane with relative speed and headway distance
as axes. The model is illustrated in Figure 2.
It is assumed that the vehicle in front has a constant speed and that the
potential car-following driver catches up with a constant relative speed v
r=
vi−1−vi. As long as the headway distance xi−1−xiis larger than sg, there is no
response. If the absolute value of the relative speed is smaller than a boundary
value vrg, then there is also no response because the driver cannot perceive the
relative speed. The threshold value is not a constant but depends on the speed
difference. If the vehicle crosses the boundary, it responds with a constant pos-
itive or negative acceleration. This happens in Figure 2 first at point A, then at
point C, then point B, etc. The term pendeling (the pendulum of a clock) for
the fact that the distance headway varies around a constant value, even if the
vehicle in front has a constant speed, has been introduced in Leutzbach (1988).
In this action-point model the size of the acceleration is arbitrary in the first
instance, whereas it was the main point of the earlier discussed car-following
models.
Action point models form the basis for a large number of contemporary
microscopic traffic flow models. In Brackstone and McDonald (1999) it is con-
cluded that it is hard to come to a definitive conclusion on the validity of these
models, mainly because the calibration of its elements has not been successful
so far.
Fig. 2. Basic action-point car-following model.

724 M. Papageorgiou et al.
Submicroscopic simulation models. In addition to describing the time–space
behavior of the individual entities in the traffic system, submicroscopic simula-
tion models describe the functioning of specific parts and processes of vehicles
and driving tasks. For instance, a submicroscopic simulation model describes
the way in which a driver applies the brakes, considering among other things
the driver’s reaction time, the time needed to apply the brake, etc. These sub-
microscopic simulation models are very suited to predict the impacts of driver
support systems on the vehicle dynamics and driving behavior. Examples of
submicroscopic models are SIMONE (Minderhoud, 1995), MIXIC (van Arem
and Hogema, 1995), and PELOPS (Ludmann, 1998). For a review on micro-
scopic and submicroscopic simulation models, we refer to Ludmann (1998) and
Minderhoud (1995).
Cellular Automaton (CA) or particle hopping models. CA-models aim to com-
bine advantages of micro-simulation models, while remaining computationally
efficient by use of efficient storage and computation algorithms. The car-
following rules generally lack intuitive appeal and their exact mechanisms are
not easily interpretable from the driving-task perspective. These models de-
scribe the traffic system as a lattice of cells of equal size (typically 7.5 m).
A CA-model describes in a discrete way the movements of vehicles from cell
to cell (cf. Nagel, 1996, 1998). The size of the cells are chosen such that a ve-
hicle driving with a speed equal to one, moves to the next downstream cell
during one time step. The vehicle’s speed can only assume a limited number of
discrete values ranging from zero to vmax.
The process can be split-up into three steps:
•Acceleration. Each vehicle with speed lower than its maximum speed
vmax, accelerates to a higher speed, i.e., v←min(vmaxv+1).
•Deceleration. If the speed is greater than the distance gap dto the pre-
ceding vehicle, then the vehicle will decelerate: v←min(v d).
•Dawdling (“Trödeln”). With given probability pbrake, the speed of a ve-
hicle decreases spontaneously: v←max(v −10).
Using this minimal set of driving rules, and the ability to apply parallel com-
puting,2the CA-model is very fast, and can consequently be used both to sim-
ulate traffic operations on large-scale motorway networks, as well as for traffic
assignment and traffic forecasting purposes. The initial single-lane model of
Nagel (1996) has been generalized to multilane multiclass traffic flow. In Wu
et al. (1999) time-oriented car-following rules have been proposed, instead of
the traditional space-oriented heuristic rules. It is argued that the resulting
model describes drivers’ behavior more realistically.
2When one relaxes the parallel update requirement, we generally do not speak of Cellular Automata
models. However, the term particle hopping model still applies (cf. Nagel, 1998).

Ch. 11. ITS and Traffic Management 725
Verification of CA-models for car traffic on German and American motor-
ways and urban traffic networks (Wu et al., 1999; Esser et al., 1999), shows
fairly realistic results on a macroscopic scale, especially in the case of urban
networks in terms of reproduction of empirical speed-density curves.
Fuzzy logic-based models. The first application of fuzzy logic systems is due
to Kikuchi and Chakroborty (1992), aiming at fuzzifying the stimulus-response
model. The model was used to illustrate how a fuzzy logic system can be used
to describe car-following and local instability. More recent developments are
reported in Rekersbrink (1995) and Henn (1995).
2.1.5 Particle models
Particle models can be considered as a specific type of numerical solution
approach (so-called particle discretization methods;cf.Hockney and Eastwood,
1988), applied to mesoscopic or macroscopic continuum traffic flow models.
These models distinguish individual vehicles, but their behavior is described by
aggregate equations of motion, for instance a macroscopic traffic flow model.
An example of a particle model is INTEGRATION (van Aerde, 1994).
2.1.6 Continuum traffic flow models
Continuum traffic flow models deal with traffic flow in terms of aggregate
variables, such as flow, densities and mean speeds. Usually, the models are
derived from the analogy between vehicular flow and flow of continuous me-
dia (e.g., fluids or gasses), complemented by specific relations describing the
average macroscopic properties of traffic flow (e.g., the relation between den-
sity and speed). Continuum flow models generally have a limited number of
equations that are relatively easy to handle.
Most continuum models describe the dynamics of density k=k(x t),space
mean speed u=u(x t),andflowq=q(x t). The density k(x t ) describes
the expected number of vehicles per unit length at instant t.Theflowq(x t)
equals the expected number of vehicles flowing past cross-section xduring per
time unit. The speed u(x t) equals the mean speed of vehicles defined ac-
cording to q=ku. Some macroscopic traffic flow models also contain partial
differential equations of the speed variance θ=θ(x t) or the traffic pressure
P=P(xt) =kθ.
Conservation of vehicles and the kinematic wave model. Assuming that the de-
pendent traffic flow variables (density, flow, speed) are differentiable functions
of time tand space x, the following partial differential equation represents the
fact that on a roadway, vehicles cannot be lost or created:
(11)
∂k
∂t +∂q
∂x =r(x t) −s(x t)
describing that the number of vehicles on a small part of the roadway of length
dxincreases according to the balance of inflow and outflow at the boundaries

726 M. Papageorgiou et al.
(interfaces) xand x+dx, respectively, and the inflow r(xt) and outflow
s(x t) at on-ramps and off-ramps, respectively (source and sink terms). To-
gether with the fundamental relation q=ku,Equation(11) constitutes a
system of two independent equations and three unknown variables. Conse-
quently, to get a complete description of traffic dynamics, a third independent
model equation is needed.
In combining the fundamental relation Equation (1) with Equation (11),
a nonlinear first-order partial differential equation results: the kinematic wave
model (Lighthill and Whitham, 1955):
(12)
∂k
∂t +∂q
∂x =∂k
∂t +c(k)∂k
∂x =0where c(k) =dQ
dk
Here c(k) denotes the so-called kinematic wave speed, describing the speed at
which small disturbances propagate through the traffic flow.
Generalized solutions to the kinematic wave model can be determined by
the method of characteristics, see, e.g., Logghe (2003). For the kinematic wave
model, it can be shown that characteristic curves are straight lines in the
(x t)-plane with slope c(k) that emanate from the boundary (i.e., at x=x0or
t=t0) of the considered time–space region. Along the characteristics, den-
sities are conserved and are thus equal to the density at the point on the
boundary from which the characteristic emanates. When on this boundary
∂c(k)/∂x < 0, the characteristic curves will in time intersect ( focusing)and
ashockwave will result. The shock wave speed ωcan be determined from the
shock wave equation (May, 1990):
(13)ω=q2−q1
k2−k1
where (k1q
1)and (k2q
2)respectively denote the traffic conditions down-
stream and upstream of the shock S. Besides shockwaves, acceleration fans are
formed in case of discontinuities in the density, characterized by k(x t) >
k(y t ) for x<y. These acceleration fans describe the way vehicles drive
away from a high-density region into a low-density region. A typical situation
in which this occurs, is a traffic light turning to green, where the acceleration
fan describes the way vehicles drive away from the formed vehicle queue.
The kinematic wave model can be solved efficiently either analytically or nu-
merically, and its properties and limitations are well understood. Amongst the
drawbacks of the model is the formation of shocks irrespective of the smooth-
ness of the initial conditions. Moreover, the kinematic wave model assumes
that the traffic speeds adapt to the stationary speed U(k) immediately (no
fluctuations around the equilibrium speed), and thus does not respect the fi-
nite reaction times and bounded acceleration possibilities of its constituent
elements. The latter drawback has been remedied in Lebacque (2002),byim-
posing additional constraints on the solutions of the kinematic wave model
prescribing the maximum acceleration of the cars. The kinematic wave model
is not able to predict stop-and-go waves with amplitude-dependent oscillation

Ch. 11. ITS and Traffic Management 727
times, which are quite common in real-life traffic flow (Verweij, 1985), nor is
traffic hysteresis (average headways of vehicles approaching a jam are smaller
than vehicles driving out of a jam, see Treiterer and Myers, 1974) described.
Traffic instability is also not captured by the kinematic wave model.
Recent improvements in the model are reported in Daganzo (1997, 2002a,
2002b), considering multiple lanes, as well as dividing the driver population
into different user-classes showing different driving characteristics. The con-
cept of motivation, indicating that passing drivers will temporarily accept
smaller headways, is also introduced.
Payne-type models. To relax the assumptions that the speeds cannot differ
from the stationary speed u=U(k), the latter expression has been replaced by
a dynamic equation for the speeds alongside the conservation of vehicle equa-
tion (Payne, 1971). Payne-like models can be derived from car-following laws.
Considering a driver at location xi(t),looking ahead to location
(14)xε
i=(1−ε)(xi−1−xi)+ε(xi−2−xi−1) where 0 ε1
In Zhang (2003) the following expression for the speed viof vehicle iis used
vi(t +Tr)=Ukxε
i(t) t +βvε
i(t) −vi(t )
(15)where vε
i(t) := uxε
i(t) t 
Udenotes the equilibrium speed as a function of the density, Trdenotes the
reaction time, and βis a dimensionless parameter. Using Taylor series expan-
sions (Zhang, 2003), the following dynamic expression for the mean speed
v(x t) is derived
(16)
∂u
∂t +u+2βc∗(k)∂u
∂x +c2(k)
k
∂k
∂x =U(k) −u
Tr+μ(k)∂2u
∂x2
where
(17)c∗(k) =kdU
dkand μ(k) =2βTrc2(k)
denote the sound speed and the traffic viscosity, respectively.
From Equation (16), different factors can be identified that can be inter-
preted from driver behavior. The term (c2(k)/ k)(∂k/∂x) denotes the effect
of driver anticipation, showing how drivers anticipate on downstream condi-
tions: in regions of increasing density, drivers will anticipate and reduce their
speeds accordingly. The relaxation term (U(k) −u)/Trdescribes the smooth
adaptation of the speed uto an equilibrium state U(k), given the relaxation
time Tr; under stationary conditions, we have u=U(k). The viscosity term
μ(k) ∂2u/∂x2reflects the influence of higher-order anticipation, i.e., the way
drivers react to changes in relative speeds vε
i(t) −vi(t ).
For specific parameter choices, the general expression (16) can be reduced
to other models: the original model of Payne (1971) can be derived by choosing

728 M. Papageorgiou et al.
β=0 (no higher-order anticipation). For a constant sound speed c∗(k) =c0,
the viscous model of Kühne (1991) results.
It can be shown that the model is unstable in a certain density range (small
perturbations in the density grow into traffic jams), and that the model is able
to (qualitatively) describe stop-and-go traffic. Moreover, small perturbations
in the stable flow will dissipate. In general, solutions to the model are smooth.
As a result, the model does backward smoothing to a sharp concentration/speed
profile, thus possibly predicting negative driving speeds. We can therefore con-
clude that the model may violate the anisotropic character (traffic mainly reacts
to downstream traffic conditions) of traffic flow. This nonanisotropic nature
manifests itself prominently in the workings of shock and expansion waves: in
contrast to the kinematic model, which has only one family of kinematic waves,
Payne-type models have two, associated with the characteristic curves ξ12de-
fined by
(18)
dξ12
dt=λ12=u+β±1+β2c(k)
The waves in the first characteristic ξ1field travel with a speed less than the
speed u, and are qualitatively identical to the kinematic waves in the kinematic
wave model. The waves in the second characteristic field travel faster than the
average traffic flow, implying that in this field, information reaches vehicles
from behind. In Zhang (2003) it is argued that for β<1, this will never occur,
since the speed of the second characteristic ξ2approaches u.
Extensions are reported in Hoogendoorn and Bovy (1999),Hoogendoorn
et al. (2002),andHelbing et al. (2001), which pertain to the modeling of mul-
ticlass and multilane traffic flow in networks, including nonlocal, forwardly
directed interactions, effects of vehicle space requirements. It is important to
note that these models are based on gas-kinetic models (see Section 2.1.7),
rather than on car-following models like equation (15).
2.1.7 Gas-kinetic flow models
Starting point of the gas-kinetic models, is the so-called phase-space density
(PSD),
(19)κ(x t v) =k(x t ) ·f(v|x t)
where κdescribes the mean number of vehicles k(x t) per unit roadway length
and f(v) the speed distribution at that location and instant. Prigogine and
Herman (1971) were the first to use the notion of the PSD to derive a model
describing the behavior of traffic flow. They achieved this by assuming that the
PSD changes according to the following processes:
1. Convection ∂(vk)/∂x. Vehicles with a speed vflow into and out of the
roadway segment [x x +dx), causing a change in the PSD κ(x t  v).
2. Acceleration towards the desired speed (V 0(v) −v)/Tr,whereV0(v)
denotes the expected desired speed of vehicles driving with speed v;
Trdenotes the acceleration time.

Ch. 11. ITS and Traffic Management 729
3. Deceleration when catching up with a slower vehicle, while not being able
to immediately overtake (1−p(k))κ(x t v) (w −v)κ(x t w) dw=
(1−p(k))κ(x t v)(u(x t ) −v).
Their deliberations yielded the following partial differential equation (PH-mo-
del):
∂κ
∂t +∂(vk)
∂x
(20)=∂
∂v V0(v) −v
Tr+1−p(k)κ(x t v)u(x t ) −v
where the density kand the mean speed uare defined according to
k(x t) =κ(x t v) dvand
(21)u(x t) =vf ( v |x t) dv
The most complex process here is probably the interaction process. Let us
briefly discuss how this term is determined from the following, simple behav-
ioral assumptions:
1. The “slow-down event” is instantaneous and occurs with a probability of
(1−p(k)),wherepdenotes the so-called immediate overtaking prob-
ability, reflecting the event that a fast car catching up with a slow car
can immediately overtake to another lane, without needing to reduce its
speed.
2. The speed of the slow car is not affected by the encounter with the fast
car, whether the latter is able to overtake or not.
3. The lengths of the vehicles can be neglected.
4. Only two vehicle encounters are to be considered, multivehicle encoun-
ters are excluded.
The model of Prigogine and Herman has been criticized and improved by
Paveri-Fontana (1975). He considers a hypothetical scenario where a free-
flowing vehicle catches up with a slow moving queue, and considers two ex-
treme cases:
1. The incoming vehicle passes the whole queue as if it were one vehicle.
2. It consecutively passes each single car in the queue independently.
In Paveri-Fontana (1975) it is shown that the Prigogine and Herman formalism
reflects the second case, while the real-life situation falls between these two ex-
tremes. He also shows that the term reflecting the acceleration process yields
a desired speed distribution that is dependent on the local number of vehicles.
This is in contradiction to the well-accepted hypothesis that driver’s personality
is indifferent with respect to changing traffic conditions (the so-called person-
ality condition;cf.Daganzo, 1995). To remedy this deficiency, Paveri-Fontana

730 M. Papageorgiou et al.
generalized the PSD κ(x t v) by also including the distribution of the desired
speeds
(22)˜κ(x t v v0)=k(x t ) ˜
f(vv
0|x t)
where ˜
f(vv
0|x t) denotes the joint probability density function of speed v
and free speed v0.
Other researchers have objected to the validity of the vehicular chaos as-
sumption underlying the expression for the effects of vehicle interactions. In
Munjal and Pahl (1969) it is argued that the interaction term “corresponds to
an approximation in which correlation between nearby drivers is neglected”,
being only valid in situations where no vehicles are platooning. This issue has
been remedied explicitly in Hoogendoorn and Bovy (1999) by distinguishing
between platooning and nonplatooning vehicles.
In Nelson et al. (1997) it is argued that plausible speed-density relations can
only be determined from the Prigogine–Herman model, based on the nontriv-
ial assumption that the underlying distribution of desired speeds is nonzero for
very small speeds. The situation when this assumption does not hold is investi-
gated in Nelson and Sopasakis (1998). It is found that at concentrations above
some critical value, there is a two-parameter family of solutions, and hence
a continuum of mean velocities for each concentration. This result holds for
both constant values of the passing probability and the relaxation time, and for
values that depend on concentration in the manner assumed by Prigogine and
Herman. It is hypothesized that this result reflects the well-known tendency
toward substantial scatter in observational data of traffic flow at high concen-
trations.
Paveri-Fontana model generalizations are reported in Hoogendoorn and
Bovy (1999),Hoogendoorn et al. (2002),andHelbing et al. (2001),where
gas-kinetic models for multiclass and multilane traffic flow including nonlo-
cal, forwardly directed interactions, effects of vehicle space requirements are
presented. These gas-kinetic models serve as the starting point to derive con-
tinuum models by application of the so-called method-of-moments. Another
multilane gas-kinetic model was proposed in Klar and Wegener (1999a, 1999b).
In Tampére et al. (2002) adaptive driver behavior is introduced into the gas-
kinetic modeling approach.
2.1.8 Model application
Traffic flow and microsimulation models designed to characterize the behav-
ior of the complex traffic flow system have become an essential tool in traffic
flow analysis and experimentation. The application areas of these tools are very
broad, e.g.:
•Evaluation of alternative treatments in (dynamic) traffic management.
•Design and testing of new transportation facilities (e.g., geometric de-
signs).

Ch. 11. ITS and Traffic Management 731
•Operational flow models serving as a submodule in other tools (e.g.,
traffic state estimation, model-based traffic control and optimization,
and dynamic traffic assignment).
•Training of traffic operators.
Which or even if a model should be used, depends largely on the type of
problem at hand. Important issues are the purpose of the study, the required
level-of-detail (is the individual driver behavior and changes therein impor-
tant), what kind of data is available for model calibration and validation, and
the type of network considered (urban, motorway).
Nevertheless, some general remarks can be made. For one, the application
of microscopic (simulation) models will in general be more time-consuming,
both in the sense of computation time needed to perform the simulations (long
computation time per simulation due to detailed representation of dynamic
processes) and requirement to do multiple runs to get statistically valid results
in case of stochastic microsimulation models.
Moreover, calibration and validation of microscopic models may be a labo-
rious task. This can be explained by noticing that these models aim to mimic
human behavior in real-life traffic (not in contrived “car-following experi-
ments”), which is hard to observe, measure and validate (cf. Daganzo, 1994).
This is problematic, given the observed nonlinear behavior of the collective
traffic flow: the microscopic details have to be just right for the simulation to
realistically describe and predict for instance stop–start waves in traffic flow.
In Brackstone and McDonald (1999) it is convincingly argued that suitable
data (e.g., pair-wise vehicle trajectories collected by instrumented vehicles,
or remote-sensing; cf. Hoogendoorn et al., 2002)mustbeusedinthemodel
calibration, and that the models are to be disassembled and tested in a step-by-
step fashion. In general, the lack of “microscopic” data results in macroscopic
calibration that cannot produce the optimal parameters since the number of
degrees of freedom is too large.
Macroscopic models are generally suited for large scale, network-wide ap-
plications, where macroscopic characteristics of the flow are of prime interest.
Macroscopic models are generally too coarse to correctly describe microscopic
details and impacts, for instance caused by changes in roadway geometry.
Macroscopic models are assumed to describe macroscopic characteristics of
traffic flow more accurately. Calibration of macroscopic models is relatively
simple (compared to microscopic models), for instance using loop detector
data (see Cremer and Papageorgiou, 1981; Helbing, 1997). Mostly, speed-
density relations derived from observations are required. In a recent paper,
Kerner et al. (2000), it is shown that traffic jam dynamics can be described and
predicted using macroscopic models that feature only some characteristic vari-
ables, which are to a large extent independent on roadway geometry, weather,
etc. This implies that macroscopic models can describe jam propagation reli-
ably, without the need for in-depth model calibration.

732 M. Papageorgiou et al.
3 Route guidance and information systems
3.1 Introduction
Advances in data processing, sensor and communications technologies have
made it possible to provide travelers with information on network conditions
based on real-time measurements. Better information should enable indi-
viduals to make better travel decisions. Moreover, as significant numbers of
travelers respond to such information, network conditions will themselves be
affected. Of particular interest here are systems intended to improve route
choice decisions, either by providing data on network conditions or by recom-
mending specific routes to a destination. These are called Route Guidance and
Information Systems (RGIS). A number of factors justify interest in these sys-
tems.
To begin with, travelers are frequently unaware of all the options available to
them. This is clearly the case for those unfamiliar with an area; the increasing
popularity of GPS-based navigation systems that provide turn-by-turn direc-
tions to a destination, attests to the value of basic way-finding information.
In addition, there is considerable evidence that even individuals who con-
sider themselves familiar with an area, have only a limited knowledge of travel
options. In Jeffery (1981), for example, it is estimated that, with better infor-
mation on travel options and conditions, even habitual drivers in an area could
reduce their average distance and travel time by around 7 percent.
Moreover, congestion is to a significant extent an unpredictable phenom-
enon. It has been estimated, for example, that roughly 60 percent of congestion
delays on US urban highways result from specific unpredictable events such as
accidents, vehicle breakdowns, and the like (Lindley, 1987). Recurrent con-
gestion, resulting from traffic levels that are systematically high relative to
available roadway capacity over a particular time period, also has a random
component that derives from variability in travel demand levels and network
performance. Because of the randomness in travel conditions, prior experience
can be an imperfect basis for travel decisions, and supplementing it with more
up-to-date information could result in better individual decisions as well as,
perhaps, improved network conditions.
A number of researchers have assessed the likely network-level impacts
and benefits of RGIS. Notable studies include Koutsopoulos and Lotan
(1989),Mahmassani and Jayakrishnan (1991),Al-Deek and Kanafani (1993),
Emmerink et al. (1995),andHall (1996). Under a variety of assumptions and
approaches, these studies have investigated the likely reduction in total travel
time, the distribution of travel time savings between guided and unguided
drivers, and the variation of these benefits as a function of the RGIS market
penetration rate (fraction of drivers receiving guidance).
On the other hand, operational experiences with RGIS to date have gen-
erally been on too limited a scale and for too brief a time to allow strong

Ch. 11. ITS and Traffic Management 733
empirical conclusions about its network level impacts to be drawn. Possible ex-
ceptions include high-volume corridors equipped with variable message signs,
and urban areas with real-time traffic condition reports. For example, using
data from the Washington, DC traffic information system (Wunderlich et al.,
2001) travelers with and without access to information on prevailing link tra-
versal times were simulated. Travelers were assumed to have a desired arrival
time at their destination, and to determine their path and departure time ac-
cordingly. The simulated travel experiences, in terms of travel times, on-time
arrival reliability, risk of lateness, and early and late schedule delays were com-
piled. It was found that guidance improved the various measures of travel time
reliability without significantly affecting average travel time itself.
This section reviews current knowledge about route guidance and informa-
tion systems. Although a distinction is sometimes made between prescriptive
guidance and descriptive information, both kinds of data will generally be re-
ferred to here as guidance. A particular set of guidance data disseminated at
a particular time will be called a message. Objectives and technological con-
straints that influence message content are discussed in Section 3.2.
Messages may be derived from static or dynamic information about the net-
work. Static systems provide fixed information about the network and may be
of use in tasks such as way-finding or preliminary trip planning; however, they
do not recognize actual traffic conditions. Static systems will not be further con-
sidered here. Dynamic RGIS can be classified as nonpredictive and predictive
systems. The former base the messages provided to drivers on measurements
or estimates of prevailing network conditions, while the latter derive messages
from forecasts of future network states. The two kinds of system can involve
quite different issues, and will be discussed separately in Sections 3.3 and 3.4.
Data on the effects of guidance on individual traveler behavior are available
from laboratory experiments with driving simulators and, to a more limited
extent, from surveys and observations of travelers who use RGIS. Knowledge
of these effects is important to develop predictive guidance, and ultimately to
evaluate the economic benefits of RGIS. Current knowledge of traveler re-
sponse to information is discussed in Section 3.5.
Finally, Section 3.6 identifies some areas of current research.
3.2 Overview of route guidance and information systems
3.2.1 Guidance objectives
In traffic networks subject to congestion, a flow pattern that optimizes
a system-level objective is not generally the same as one that results when each
driver independently chooses her preferred route. For example, the flow pat-
tern that minimizes the total travel time of all vehicles on the network generally
differs from the pattern obtained when each driver attempts to minimize her
individual travel time. The two types of pattern are referred to as system and
user optimal flow patterns, respectively.

734 M. Papageorgiou et al.
It is sometimes suggested that network operators could use route guidance
as a tool to force the network towards a system optimal flow pattern. This may
be an appropriate policy in exceptional circumstances such as emergency evac-
uation situations, but it is unlikely to be successful in the long run for routine
situations. Drivers are free to ignore any guidance messages that they per-
ceive as incompatible with their own decision criteria. Moreover, systematic
attempts to influence drivers’ decisions by providing misleading information,
even if well intentioned, are likely to lead over time to large scale driver rejec-
tion of the RGIS.
The focus here will be on guidance derived from user optimality objectives.
As argued in Hall (1996), such guidance can be usefully viewed as a way of
correcting the dis-equilibrium travel behavior that results from lack of infor-
mation. However, it may not be feasible to provide individual drivers with
messages precisely matched to their particular route choice decision criteria.
A common alternative approach is to base messages solely on travel times,
i.e., to report link or path traversal times (descriptive information) or to rec-
ommend minimum travel time paths (prescriptive guidance). Traversal times
prevailing at the time of guidance generation are often used for this purpose;
these are called instantaneous travel times. However, in a dynamic network,
with link traversal times that vary over time, instantaneous times may be dif-
ferent from the experienced times that drivers incur when making a trip. While
guidance based on experienced times is arguably closer to drivers’ own choice
criteria, generating such guidance requires the use of a predictive model, and
is considerably more complex than simply measuring and reporting the pre-
vailing traversal times.
Guidance is an attempt to improve the information available to drivers for
their route choice decision, yet the guidance itself will rarely be perfect. Data
collection, processing, and communications systems constrain the quality and
quantity of data that can be generated and transmitted, and humans are limited
in their ability to process information, in particular while driving. These factors
affect the type of guidance that an RGIS can provide. A poorly designed RGIS
can exacerbate rather than improve congestion. In Ben-Akiva et al. (1991) and
Kaysi et al. (1995) RGIS design issues are discussed including possible counter-
productive effects of poorly-designed systems. These include concentration,in
which guidance reduces the normal dispersion of driver behaviors and leads to
increased congestion on a smaller number of routes; and overreaction,inwhich
drivers’ response to guidance shifts congestion or leads to oscillations in flows
on different routes.
3.2.2 RGIS functional characteristics
The principal features that characterize different RGIS designs are briefly
identified here. Although the features are presented separately, many of them
are, in fact, interrelated in the sense that a choice for one constrains the feasi-
ble options for others.

Ch. 11. ITS and Traffic Management 735
Basis for guidance. As was indicated above, a major distinction is between
nonpredictive systems that generate guidance based on measurements or es-
timates of prevailing network conditions, and predictive systems that utilize
forecasts for this purpose.
Local/area-wide focus. Guidance generation may focus on either a local or
a wide area traffic network. A local focus considers conditions on individual or
perhaps small contiguous groups of network elements (road segments or junc-
tions); the guidance will typically be disseminated only over that area. A wide
area focus considers conditions throughout the network in determining the
messages to disseminate.
Transmission range. The RGIS dissemination technology determines the
distance from a guidance source over which the messages may be received.
Line-of-sight, small area and wide area technologies are possible. In the case
of short- and medium-range technologies, the locating of the guidance dissem-
ination sources, and the resulting coverage of the network and its flows, are
important system design decisions.
Collective/individual dissemination. The RGIS dissemination technology also
determines whether messages can be received by all vehicles in transmission
range, or only by vehicles equipped with suitable receivers. Examples of the
former include roadside variable message signs and highway advisory broad-
casts over standard radio frequencies; examples of the latter include coded
infrared, microwave, FM sub-carrier, and cellular packet radio transmissions.
One-way/two-way communications. In an one-way communication system,
drivers receive messages from the RGIS but do not provide any informa-
tion to the system. In a two-way system, drivers notify the system about their
travel desires and receive messages that are tailored to their specific trip needs.
Moreover, the data acquired about travel times and drivers’ trip intentions and
choices can be incorporated in the system’s state estimates and forecasts.
Pre-trip/en-route access to guidance. Guidance received prior to beginning
a trip may influence the decision to travel or not, the destination(s), the time
of departure, the mode of travel as well as the particular route to follow. Guid-
ance received while en-route will generally only affect the subsequent choice of
path. Driver response to messages may also be different in the two situations:
a pre-trip decision is a choice without immediate antecedent, whereas the en-
route decision to switch routes may involve a reluctance to abandon a prior
choice and so exhibit hysteresis or a threshold effect.
Message dissemination and guidance update intervals. Guidance messages
generally relate to a period of time rather than to a single instant, and so are
maintained or retransmitted during that period. The message dissemination in-
terval is the period of time during which a disseminated guidance message does
not change. The length of this period may be dictated by technological con-
straints or by human factors. The guidance update interval refers to the time
between successive computations of the messages to disseminate. In a com-
plex guidance system, messages cannot be continually recomputed because of

736 M. Papageorgiou et al.
delays inherent in collecting and processing data, and in generating and dis-
seminating the messages.
Message design. The final issue concerns the syntax and semantics of the
guidance messages themselves, including their medium of delivery, format,
content, and precision. The distinction between prescriptive guidance and de-
scriptive information was mentioned above. Visual or audio messages intended
for direct reception by drivers cannot be overly complex because of the diffi-
culty of assimilating them while driving. Messages that will be processed by an
in-vehicle unit and conveyed to the driver in a schematic visual form might per-
haps have a higher data content. The available communications bandwidth or
message display capabilities may also constrain message complexity and preci-
sion.
3.3 Nonpredictive and related systems
In a nonpredictive dynamic RGIS, messages are derived from estimates of
the network conditions that prevail at or before the time the guidance is gen-
erated. To the extent that these instantaneous conditions are a good indication
of what a driver will actually encounter during a trip, then route choice deci-
sions made using nonpredictive guidance should be well founded. Conversely,
the potential limitation of nonpredictive guidance is that network conditions
may change significantly during a trip and so invalidate decisions based solely
on conditions around the time of departure.
Descriptive nonpredictive guidance consists of information on estimated
prevailing traffic conditions, by processing measurements collected from var-
ious kinds of traffic sensors. Details of such data collection and processing
methods are beyond the scope of this paper. Prescriptive nonpredictive guid-
ance consists of route recommendations based on estimated prevailing condi-
tions. Numerous methods have been proposed for generating such guidance.
In Papageorgiou (1990),Bolelli et al. (1991),andCharbonnier et al. (1991),
for example, nonpredictive route guidance approaches based on methods from
control engineering have been proposed.
Most currently operational dynamic RGIS are nonpredictive. They typically
disseminate messages using variable message signs, public radio and televi-
sion, or telephones. In-vehicle dynamic nonpredictive RGIS have mostly been
limited-scale experimental prototypes. For example, the TravTek system (Rilett
et al., 1991), deployed in Orlando, Florida, included an in-vehicle unit that re-
ceived by radio coded updates of prevailing link travel times and computed the
minimum time path to destinations selected by the driver.
3.4 Predictive systems
3.4.1 Predictive guidance and consistency
Predictive route guidance and information systems base guidance on fore-
casts of future network conditions. The messages disseminated to a driver

Ch. 11. ITS and Traffic Management 737
reflect expectations of what conditions will be at network locations at the
time the driver will actually be there, and so are arguably closer to driver’s
actual decision criteria than nonpredictive messages based on prevailing or
historical conditions. In Ben-Akiva et al. (1996) the conditions under which
nonpredictive and predictive guidance result in the same flow patterns were
analyzed. In Pavlis and Papageorgiou (1999) it was showed that, in densely
meshed networks, nonpredictive guidance can have the same effects as predic-
tive guidance. In general, however, nonpredictive and predictive guidance will
be different and will have different impacts on network conditions.
Predictive guidance messages are derived from forecasts of future network
conditions. However, when these messages are disseminated and drivers re-
act to them in some way (for example, by changing departure times or paths),
future conditions are likely to be affected, possibly invalidating the forecasts
and rendering the messages irrelevant or worse. Within the context of a model
system, predictive guidance is said to be consistent if the forecasts on which
it is based are the same, within the limits of modeling accuracy, as those pre-
dicted to result after drivers receive the guidance and react to it. Consistency
is a generalization of the concept of traffic equilibrium. Unlike conventional
equilibrium, which assumes that travelers are perfectly informed about net-
work conditions, consistency accounts for the specific characteristics of avail-
able travel information and driver response to it.
3.4.2 Approaches for predictive guidance generation
One approach to generating predictive guidance simply ignores the con-
sistency issue. Guidance messages are based on condition forecasts that are
extrapolations from prevailing and historical conditions. The limitation of this
approach is that it does not take account of the effects of the guidance itself
on future network conditions: it does not ensure guidance consistency. This
may not be important at low levels of driver participation in the RGIS, but
is likely to lead to incorrect guidance messages when the number of vehicles
responding to guidance is sufficient to affect network flows and conditions.
Computation of consistent predictive route guidance requires application of
a dynamic traffic network model in order to forecast network conditions. Such
models are high-dimensional nonlinear systems; they can be quite complex and
require considerable amounts of data to identify. (Again, the necessary data
collection and processing tasks are not considered here.) They take the form
of mathematical models when analytical tractability is important, and of sim-
ulation models when the involved relationships defy convenient mathematical
expression.
Such a model is driven by exogenous time-dependent origin–destination
(OD) demands. The model includes components that predict how these de-
mands will choose paths and propagate along them. (Some models also predict
travelers’ choice of departure times.) The propagation of demand over its cho-
sen paths is determined by time-dependent link traversal times, and these

738 M. Papageorgiou et al.
traversal times are in turn affected by the congestion that results from the
movement of demand along the links.
Conventional (nonguidance) dynamic traffic assignment models compute
time-dependent equilibrium flows and traversal times under the assumption
that demand has perfect information about present and future congestion lev-
els and chooses paths accordingly. Guidance-oriented traffic network models,
on the other hand, must explicitly consider the availability and nature of travel
information, as well as driver behavior in the presence and absence of such
information. In Ben-Akiva et al. (1991) and Watling and van Vuren (1993) the
features that dynamic network models require for route guidance applications
are considered.
Guidance-oriented traffic models have been less studied than conventional
traffic assignment models. A high-level formal representation of a network
model for predictive guidance generation can be obtained using three time-
dependent problem variables and three maps (that are implemented as models
and algorithms) that relate them. The variables are: C, the network conditions;
M, the guidance messages; and P, the path splits (fraction of trips going to
a particular destination via each available path or subpath) at trip origins and
en-route decision points. The maps are:
•the network loading map S:P→C, which determines the network con-
ditions that result from the movement of exogenous time-dependent
OD demands over the network in accordance with a particular set of
path splits;
•the routing map D:M→P, which determines the path splits that
result from a particular set of guidance messages. The routing map gen-
erally incorporates a model of driver response to guidance messages;
and
•the guidance map G:C→M, which represents the response of the
RGIS, in the form of guidance messages, to a given set of network
conditions. (Note that messages output by this map for a given set of
conditions are not necessarily consistent, since driver reaction to the
messages may result in network conditions different from the inputs.)
Composite problem maps can be obtained by combining the network load-
ing, routing and guidance maps in different sequences. Each composite map
transforms an element of one problem variable into another element of the
same variable. There are three such maps (the symbol ∗denotes functional
composition):
•a composite map D∗G∗S:P→Pfrom the domain of path splits into
itself;
•a composite map S∗D∗G:C→Cfrom the domain of link conditions
into itself; and
•a composite map G∗S∗D:M→Mfrom the domain of messages into
itself.

Ch. 11. ITS and Traffic Management 739
In terms of these composite problem maps, predictive guidance consistency
means that a map’s time-dependent inputs (i.e., the time trajectory of a prob-
lem variable) coincide with its time-dependent outputs. Equality of the map’s
input and output values means that the value is a fixed point of the map. (If
T:X→Xis a one-to-one map, x∗∈Xis a fixed point of Tif x∗=T(x
∗).)
Thus, consistency in the context of predictive route guidance can be computed
and studied in terms of fixed points of the problem maps, or of approximations
to them.
Fixed point approaches under perfect information assumptions have been
investigated in Kaufman et al. (1998) as a basis for dynamic traffic assignment
and in Engelson (1997) in the context of driver information systems. In Yan g
(1998) and Bovy (1999) guidance models using fixed point approaches were
also considered. In Bottom (2000) additional details on the predictive guidance
generation formulation presented here are provided.
3.4.3 Operational predictive guidance systems
Operational experience with predictive systems is currently very limited.
The LISB system in Berlin (Hoffman, 1991) and the Autoguide system in
London (Catling, 1989) were early prototypes of systems with in-vehicle and
infrastructure-based components. Communications between the two compo-
nents served to establish travel times as well as to disseminate guidance. The
guidance consisted of next turn recommendations derived from minimum path
calculations using simple link traversal time predictions. These predictions,
in turn, were derived from historical link traversal time patterns and recently
measured traversal times. The usage of these systems did not attain levels that
would create consistency issues.
In the Netherlands, dynamic route information panels (DRIPs) can display
route recommendations for simple network topologies based on traffic predic-
tions and optimal control laws (Hoogendoorn and Bovy, 1998).
At least one traffic data company in the US sells network condition pre-
dictions that are based on extrapolations that take account of current traffic
measurements, typical patterns of link condition variations over time, and
other factors such as weather and special events. The details of the extrapo-
lation method are considered secret.
Systems that provide consistent predictive guidance at the level of an urban
or regional network are not yet operational. There have been limited experi-
mental deployments in traffic control centers of software systems (for example,
DYNASMART-X and DynaMIT) that are designed to generate such guidance.
The guidance generation logic in DynaMIT is explicitly based on the fixed
point approach described in the preceding section.
3.5 Driver response to RGIS
Understanding driver response to RGIS is required to develop effective
guidance systems that meet drivers’ information needs and contribute to con-

740 M. Papageorgiou et al.
gestion relief. Predictive guidance, in particular, requires the ability to forecast
driver responses to different possible messages in order to ensure guidance
consistency. Moreover, the economic evaluation of guidance systems also re-
quires a knowledge of the range of traveler responses to travel information.
Data on driver response to RGIS come from laboratory experiments with
travel choice simulators and, to a lesser extent, from observations of trav-
eler interactions with operational systems. The following paragraphs briefly
summarize what is currently known and not known regarding the impacts of
information on various travel-related decisions.
RGIS awareness and access decisions. Awareness, willingness to pay, and us-
age rates can be obtained by conducting travel surveys in areas where RGIS
services are available (Polydoropoulou and Ben-Akiva, 1999). The large-scale
panel surveys conducted every 3 years in Seattle-area by the Puget Sound Re-
gional Council provide data on the evolution over time of awareness and usage
decisions for different RGIS types (Peirce and Lappin, 2002).
Decision to travel or not. Relatively little information is available regard-
ing the effects of RGIS on the decision to travel or not; however, it is not
inconceivable that information about sufficiently bad travel conditions could
induce travelers to cancel their intended trips, particularly discretionary trips.
In Khattak et al. (1999) evidence are cited for this effect among noncommuters
from surveys carried out as part of the San Francisco-area TravInfo project.
Choice of destination or destinations. Similarly, relatively little information is
available in the literature regarding the effects of RGIS on destination choice,
or on the decision to visit several destinations and accomplish several purposes
in one trip through trip-chaining. Trips offering a choice among multiple des-
tination alternatives are likely to be for shopping (see, for example, Kraan et
al., 2000) or personal purposes. Opportunities to group multiple purposes and
destinations into a single trip-chain are more varied and difficult to character-
ize.
Departure time choice.InMannering et al. (1994) results from Seattle-area
surveys about commuters who receive travel information from radio, televi-
sion, and telephone services are presented. Of the commuters surveyed, 40%
indicated that they had some flexibility in scheduling and selecting the route
for their morning commute trip; 23% indicated no flexibility. However, 64%
responded that they rarely changed their departure time because of pre-trip
information.
Mode choice. Little detailed information is available about the mode choice
impacts of RGIS, although there is some evidence for this effect. As reported
in Yim and Miller (2000), less than 1% of the early callers to San Francisco’s
TravInfo service asked to be rerouted to the transit menu after learning about
bad traffic conditions from the traffic menu. However, as experience with the
system increased over the duration of the TravInfo field test deployment, it was
found that up to 5% of the callers asked to be rerouted to the transit menu. Of
those who accessed transit information, 90% ultimately chose transit for their
travel mode.

Ch. 11. ITS and Traffic Management 741
Route choice. Many surveys and travel choice simulator studies have demon-
strated the ability of RGIS to influence route choice. Based on analysis of
driver route choice responses to both VMS and radio information, it has been
suggested in Emmerink et al. (1996) that some people have an innate propen-
sity to use traffic information of any kind and from any source. Nonetheless,
there is considerable evidence that the nature of the guidance information, and
the conditions experienced prior to its dissemination, can strongly affect driver
route choice response to it.
Drivers’ perceptions of the accuracy and reliability of the messages is a key
determinant of their response. It has been found (Kantowitz et al., 1997) that
there exists an accuracy “threshold”, beneath which drivers will simply ignore
RGIS messages. Factors that increase drivers’ confidence in the accuracy of
the messages tend to increase the likelihood that the drivers will react to them.
In the context of route choice, such factors include observation of congestion
prior (and particularly just prior) to receiving the message, and favorable expe-
riences with the RGIS in prior uses. Drivers appear to be tolerant of a certain
amount of error in RGIS messages, although drivers familiar with an area will
expect a higher degree of accuracy from the information system.
Some drivers express a strong preference for descriptive information
on traffic conditions, while others prefer prescriptive recommendations of
a particular route to take (Khattak et al., 1996; Polydoropoulou et al., 1996).
Combining a prescriptive recommendation to change routes with descriptive
information justifying the recommendation has been found in some travel
choice simulator experiments to result in the highest route switching compli-
ance rates (Bonsall and Palmer, 1999).
A number of generally idiosyncratic factors condition a driver’s route choice
response to RGIS messages. For example, a motorway bias has been observed
in several studies. Because of this bias, drivers receiving messages that suggest
diverting from a nonmotorway to a motorway facility are considerably more
likely to comply than those who receive the opposite message, other things
being equal. As mentioned above, habit also plays a significant role in travel
decisions.
Learning. The day-to-day dynamics of commuter pre-trip departure time
and route choices as well as en-route path switching for morning commutes
were analyzed in Mahmassani and Liu (1999). Factors affecting route choice
behavior include: (1) arrival time flexibility, (2) user characteristics, and (3) in-
formation reliability. In Ozbay et al. (2001) the use of a stochastic learning
algorithm to analyze drivers’ day-to-day route choice behavior is proposed.
This model addresses the learning behavior of travelers based on experienced
travel time and day-to-day learning.
3.6 Areas of current research
Further development of route guidance and information systems will re-
quire better understanding of a number of issues, many of which have only

742 M. Papageorgiou et al.
recently begun to receive attention. This section describes ongoing research in
RGIS architecture, real-time computing, stochasticity and driver behavior.
System architecture. Nonpredictive guidance systems are relatively simple in
conception and robust in operation. Although they use data on instantaneous
network conditions, these systems may sometimes succeed in attaining objec-
tives based on experienced conditions, but need not do so in general. Basing
guidance on instantaneous conditions may sometimes exacerbate rather than
improve traffic problems. Predictive systems, based on experienced conditions,
depend on the availability and reliability of complex models of traveler be-
havior and network performance. Furthermore, they may be sensitive to high
levels of noise in model predictions, and are computationally demanding. Is
there a guidance system architecture that combines the better features of the
two approaches while avoiding their drawbacks? For example, multilevel con-
trol system designs have been developed for traffic control systems, but have
been less investigated in the context of RGIS.
Real-time response. Predictive guidance generation for a realistic network
requires considerable amounts of computation, yet it must be done quickly and
accurately enough for the guidance to be timely and of use to drivers. Parallel
and distributed computation environments are of interest in this regard, as are
fixed-point solution heuristics.
Stochasticity. Any of the individual maps involved in the predictive guidance
generation problem may be stochastic. The composite problem map will then
be stochastic as well, and its output when evaluated will be a realization of
a stochastic process rather than the deterministic time trajectory of a problem
variable. Nonetheless, the fixed-point interpretation of guidance consistency
continues to apply in this case, with the understanding that consistency now
means that problem map inputs and outputs are both stochastically equiva-
lent realizations of the same stochastic process. Markov chain Monte Carlo
techniques such as Gibbs sampling may be used to compute problem variable
statistics to any desired degree of accuracy. However, this approach is very
computationally demanding.
In practice, most stochastic guidance modeling efforts have adopted a “noisy
map” approximation to address the effects of stochasticity in the computation
of guidance solutions. Implicitly or explicitly, these approaches treat model
outputs not as a realization of a general stochastic process but rather as a time
trajectory of deterministic values affected by noise. Stochastic approximation
procedures are then applied to compute the fixed point. No rigorous justifica-
tion has yet been provided for this approach.
Driver behavior modeling. Applications of RGIS require the development
of reliable models of driver behavior and, in particular, of their response to
guidance messages. An important aspect of this is the development of better
models of the ways in which travelers form new perceptions from their most
recent experience, the guidance they received and their earlier experiences.
These efforts will benefit from advances in the understanding of the psycholog-
ical and cognitive processes involved in decision-making. Of particular interest

Ch. 11. ITS and Traffic Management 743
are studies of decision-making under the time pressure of driving situations,
and studies of the ways in which spatial and network knowledge affect driver
response to RGIS.
4 Urban network traffic control
4.1 Introduction
Optimum management and control of traffic in urban networks is an impor-
tant requirement for city authorities as they seek efficient, safe and sustainable
transport. In addition there is an increasingly wide range of demanding objec-
tives for transport policy makers to achieve, such as public transport priority,
improved conditions for vulnerable road users, real-time traffic information;
emergency and incident management and restraining traffic in sensitive ar-
eas. As a response to these issues, Urban Traffic Management and Control
(UTMC) systems have been introduced in many cities around the world to pro-
vide the tools to support efficient and effective network management to meet
needs of current and future traffic problems. Fundamentally UTMC systems
are conceived as modular, open systems that incorporate and build on existing
functionalities of existing signal control and other traffic management systems
as illustrated in Figure 3. An important point to note is that the Urban Traffic
Control (UTC) systems are often at the heart of UTMC and provide a better
migration path so that improvements in UTC are utilized to the full in UTMC.
UTC refers to the control of traffic in urban areas using traffic signals, which
are linked to operate in a coordinated way. Such linked signal systems may
be used to achieve a variety of policy objectives, which relate to efficiency of
traffic operations, improved safety, reduced atmospheric pollution, priority for
specific road user groups, access control to maintain or enhance urban envi-
ronments, and to mitigate the effects of irregular events such as accidents or
road closure. UTC systems use historic or (more commonly) real-time knowl-
edge of network conditions to determine the control strategy most appropriate
for the conditions, and signal infrastructure to inform and control road users.
4.2 UTC systems: general requirements
Early systems in the 1950s and 1960s were based on fixed-time traffic control
providing signal coordination or progression for traffic on an arterial, through
the optimization of offsets between adjacent sets of signals. UTC was therefore
justified on there being a sufficient density of traffic signals to make signal co-
ordination worthwhile, compared to the alternative of operating traffic signals
in isolation. Whilst relatively effective for traffic co-ordination in “predictable”
conditions, the inability of fixed-time systems to adjust to changing traffic con-
ditions has been a drawback in this approach. The desire for traffic signaling

744 M. Papageorgiou et al.
Fig. 3. Schematic illustration of a UTMC system (Source: Department of the UK Environment, Trans-
port and the Regions (1999))
to be more responsive to changing traffic conditions has led to the develop-
ment of a range of semi or fully traffic responsive UTC systems. The improved
performance of these systems has generally justified their additional cost (e.g.,
detection, maintenance, etc.).
A variety of methods for UTC have evolved over the last decades, re-
sponding to the needs of individual cities/countries, the existing research and
development base and advances in detection, communications and control
technology. These traffic-responsive UTC systems are continuously upgraded
to meet with current requirements. Quality attributes of a UTC system play
a major role in its architecture. These may include attributes such as the
speed of system response to recurring congestion and incidents (i.e., respon-
siveness), feedback philosophy, ability of integration, functional and spatial
extendability, wider range of control strategies, robustness, installation and
maintenance costs, etc. Flexibility of the system to incorporate enhancements
as policies/technologies advance is a further key attribute.
Criteria for installing a real-time UTC system are now much wider than the
need for efficient signal coordination for traffic. For example, the UTC com-
munications infrastructure and processing capabilities give a powerful tool for

Ch. 11. ITS and Traffic Management 745
the network manager, including such functions as traffic information, auto-
matic incident detection (AID), and congestion management.
4.3 Fundamentals of UTC
4.3.1 Principles of traffic signal control
Traffic signals operate by giving sequential priority to movements, including
pedestrian/cycling stages and other priorities. Sufficient separation of stages is
essential to ensure that conflicts between movements do not occur and there
are a variety of regulations and guidance documents provided by government
agencies. The regulations are similar across many countries, and differences re-
flect local driver behavior/expectation, enforcement regimes, and national atti-
tudes to guidance, regulation, and safety. In general, the smaller the amount of
time lost to road users when changing signal priority, the greater the capacity
and hence the shorter the delay.
Traffic signal controlled intersections may operate in isolation or be linked
to one or more adjacent intersections as part of a coordinated approach,
i.e., UTC. An isolated traffic signal is usually set by estimating an optimum
cycle time and green splits (the green times allocated to each separate move-
ment), i.e., those which minimize the delay. The optimum times are deter-
mined from a knowledge of traffic demand and the maximum (or “saturation”)
flows, also taking account of the time lost to traffic movements when the signals
are red to all traffic and the time lost as flows build up and fall from maximum
discharge rates. Usually delay is minimized when the degree of saturation (i.e.,
the ratio of demand to capacity, for the key movement) is about 0.85. Capacity
is a key parameter affecting performance and is determined as the saturation
flow multiplied by the effective green time per hour available for that flow.
When linking signals, the offset (i.e., the time delay in the start of the down-
stream cycle) is the crucial third variable to be considered with green splits
and cycle time. The need for linking signals usually relates to their proximity
to each other and the extent to which linking allows “platoons” of traffic to
proceed through adjacent junctions more efficiently.
For any specific condition of traffic demand a range of algorithms may be
used to optimize signal settings. In the early UTC systems, the database of
traffic demand was assumed fixed and signal timings were determined off-line.
However, traffic demand exhibits substantial short-term variability as well as
longer term changes in levels of flow and movement patterns. This has led to
increasingly sophisticated approaches to UTC which rely on substantial de-
tector input. Broadly, UTC systems may be categorized as fixed-time using
historic databases or demand responsive using on-line traffic data inputs. The
latter may be subdivided into centralized or decentralized systems. The char-
acteristics of these systems are outlined below in Sections 4.3.2 and 4.3.3 and
further details of specific systems are given in Section 4.4.

746 M. Papageorgiou et al.
4.3.2 Fixed-time systems
In fixed-time systems, off-line optimization is undertaken using demand lev-
els which are assumed constant for the period over which each fixed-time plan
is intended to run. Up to 10–15 plans may be developed to represent the com-
plete set of traffic conditions to be found on the network at different times.
A network is considered to operate as a series of different regions of groups of
linked signals, within each of which different signal plans will run. To ensure
that the arrival patterns of successive platoons of vehicles arrive consistently at
the downstream signals:
(1) a single cycle time must apply across the region and
(2) time offsets of the starts of successive cycles at one intersection from the
next must be the same.
The regional cycle time is based on that required for the busiest intersection.
Thus, a region may be bounded either by road links along which the benefits
of linking are small or where a common cycle time is very inappropriate.
Fixed-time plans may be readily used to create green waves, give pre-
determined priorities, and respond to special events which can be predicted,
such as football matches. They cannot respond to unplanned incidents such as
traffic accidents or unplanned road works. Plans may be set to change at pre-
determined times or changes may be triggered by flow or queue measurements
taken at key locations. There are also several systems which generate new plans
on-line, i.e., using very recent historic data.
Fixed-time systems require a considerable amount of traffic data to be col-
lected to set up and to keep up-to-date. Fixed-time plans can age rapidly,
particularly where traffic growth is high, and the benefits of linking may be lost
in three to four years if the plans are not updated. A further problem occurs
when plans change and discontinuities in flow patterns occur. This limits the
number of plans which can be used. Both the above points can be addressed
using traffic-responsive systems.
4.3.3 Traffic-responsive systems
Traffic-responsive systems use on-line detector measurements to optimize
signal timings on a cycle-to-cycle basis to better meet demand. Such sys-
tems may be coordinated largely from a central computer, e.g., SCOOT
(Bretherton, 1998) or have distributed intelligence and be coordinated largely
at a local level, e.g., UTOPIA (Donati et al., 1984). Centrally controlled sys-
tems use less intelligent local controllers, whilst with decentralized systems
each controller is more capable of taking local decisions, with some coordina-
tion between adjacent controllers. A wide range of traffic responsive systems
are now available with varying degrees of central and local control and key
systems are described in Section 4.4.
If a system is to respond to changes in traffic conditions, comprehensive de-
tection must be available. Detectors must be accurate, located appropriately
for the characteristics of the UTC system, and the information must be reli-
ably sent to the appropriate control center. In general, the more sophisticated

Ch. 11. ITS and Traffic Management 747
the system the more comprehensive the detector requirements and the more
susceptible it is to detector failure. Many systems have default values for the
controllers based on time of day which are implemented if loss of detectors or
communication occurs.
Increasingly, a wide range of detectors are available. Traditionally, ground-
based systems using inductive loops to measure the presence of a vehicle have
formed the basis of most UTC detection. Other ground-based systems include
magnetometers which measure changes in the earth’s magnetic field brought
about by the presence of a vehicle. Above ground detectors include microwave
systems, radar, infra-red, video, and laser systems. Each has specific charac-
teristics to capture different aspects of vehicle behavior. Image-based systems
can be installed without costly and disruptive installation works, but have yet
to reach their full potential. Using vehicles themselves as detectors is an ap-
plication being considered for the future. Overall, the quality, quantity, and
reliability of future information will encourage more sophisticated UTC con-
trol strategies.
Ta b l e 2 provides a summary of the main advantages and disadvantages of
different types of UTC systems.
4.4 System summaries
4.4.1 Fixed-time systems
TRANSYT (TRAffic Network StudY Tool). TRANSYT (Robertson, 1997)is
the most well-developed and widely-used fixed time UTC system. It is an off-
line program for calculating optimum coordinated signal timings in a network
of traffic signals. For each distinct traffic stream it assumes that the flow rate
averaged over a specified period is known and constant and that the saturation
flows for each link are also known. TRANSYT consists of two main elements
called the “traffic model” and the “signal optimizer”, as shown in Figure 4.
The traffic model represents traffic behavior in a highway network and pre-
dicts a performance index (PI) for the network for a given fixed-time plan and
average set of flows on each link. The PI measures the overall cost of traffic
“congestion”, which is usually a weighted combination of the total delay and
the number of stops made by vehicles.
Cyclic Flow Profiles (CFP’s) showing the distribution of flows entering each
link are used with a “platoon dispersion” model to estimate patterns of vehicle
arrivals at the downstream junction. “Uniform” delay is calculated in a similar
way as for SCOOT, illustrated in Figure 5, supplemented by formulae to repre-
sent random delays and oversaturated delays when the junction is over-loaded
(i.e., the queue does not clear in the green period). Signal optimization involves
an iterative “hill climbing” process to adjust the signal timings to achieve an op-
timum PI. Specific links may be given extra weighting by the user to implement,
for example, green waves on a corridor. Other city/country specific fixed-time
UTC systems are used around the world, but are not as widespread nor as well
documented as TRANSYT, so they are not described further here.

748 M. Papageorgiou et al.
Ta b l e 2 .
Summary of advantages and disadvantages of different types of UTC systems
UTC system Advantages Disadvantages
Fixed-time 1. Cheaper to install and
maintain.
1. Large amount of data to
be collected and updated.
2. Can be implemented using
noncentrally controlled
equipment.
2. Signal plans may require
updating.
3. Familiarity with settings
for regular users.
3. Disruption of plan
changing.
4. Green waves more easily
implemented.
4. Operator reaction to
incidents required.
5. Can favor specific vehicle
types easily.
5. Can not deal with
short-term traffic
fluctuations.
Responsive plan
selection
1. Can deal with some day to
day fluctuations.
1. Requires more data than
fixed-time systems.
2. Plan change time could be
more appropriate.
2. Detector failures possible.
3. Might be valuable on
arterial routes.
3. Needs discussions on
thresholds for plan change.
4. Cheaper than fully
responsive systems.
4. Plan may change for a
wrong reason.
5. Difficult to foresee all plan
needs.
Fully responsive 1. Less data needed to be
collected in advance.
1. Detector failures possible.
2. Plan evolves, so avoids
problems with plan changing
and updating.
2. More expensive to install
and maintain.
3.Candealwithshortand
long term traffic fluctuations.
3. Requires some central
control.
4. Automatic reaction to
incidents.
4. Maintenance critical.
5. Monitors traffic situation
throughout the area.
4.4.2 Traffic-responsive systems: Centralized
With centralized control, traffic detector information is sent to the UTC
center where it is processed and “optimum” timings are calculated for all the
traffic signals within the UTC system. These timings are then sent back to each
traffic signal controller on-street. Intelligence is therefore retained at one lo-
cation (the UTC center). The costs of on-street controllers can then be less,
although communication costs will usually be higher than decentralized sys-
tems with distributed intelligence. Five such systems are summarized below.

Ch. 11. ITS and Traffic Management 749
Fig. 4. Traffic model and signal optimizer in TRANSYT.
Fig. 5. Principles of the SCOOT traffic model (Source: Department of the UK Environment, Transport
and the Regions (1999)).

750 M. Papageorgiou et al.
SCOOT (Split Cycle Offset Optimization Technique). SCOOT (Hunt et al.,
1981; Bretherton, 1998) was developed in the United Kingdom and is op-
erational in many cities around the world. It operates based on three main
principles, namely the measurement of cyclic flow profiles (CFP), the updat-
ing every 4 seconds of its on-line traffic model of queues and delays on each
link and incremental optimization of signal timings. SCOOT uses detectors at
the upstream end of links to measure demand and CFP’s in real time. The up-
stream detection also allows any congestion on the link to be monitored (i.e.,
when the queue reaches the upstream detector) and the possible exit block-
ing effects of this congestion on upstream links. The SCOOT model predicts
downstream arrival patterns using a calibrated link cruise speed with some dis-
persion. The saturation flow rate for each signal stop line is validated when the
system is commissioned; this allows the growth and clearance of queues to be
estimated accurately. The on-line traffic model is used in real time by the signal
optimizer. SCOOT has three optimization procedures by which it adjusts sig-
nal timings (Department of the UK Environment, Transport and the Regions,
1999). These are the cycle time, green splits, and offsets, each optimized using
a different procedure at different frequencies. By the combination of relatively
small changes to traffic signal timings, SCOOT can respond to both short-term
local peaks in traffic demand, as well as following trends over time and thus
maintain a constant coordination of the signal network.
In addition to the optimization from the basic SCOOT model, the operation
has considerable flexibility to override values and set parameters for different
regions and different times. These may include gating strategies to protect an
area from excessive levels of traffic, bus priorities, etc. In addition to network
management, SCOOT has a substantial data base facility for storing, manipu-
lating, and presenting traffic data including flows, journey times, and queues.
Further facilities have been included in the latest releases (Bretherton et al.,
2003) with further research ongoing (Bretherton et al., 2004).
SCATS (Sydney Coordinated Adaptive Traffic System). SCATS (Lowrie, 1982)
was developed in Australia and has been implemented in many cities around
the world. It operates at two basic levels known as the “upper” level, which in-
volves offset plan selection and the “lower” level, which involves optimization
of junction parameters. The upper level generates offset plans by time of day
from historic data while the lower junction level optimizes green splits, cycle
times, and offsets between signalized junctions using an incremental feedback
process based largely on detectors situated at the stop lines. SCATS calculates
green splits based on the flow in the previous cycle and so is not fully respon-
sive to unpredictable arrival flows. It differs from systems such as SCOOT and
UTOPIA in that it does not have a traffic model and uses stop line detectors
to estimate departure rates, rather than arrival rates modeled from upstream
detectors.
SCATS is basically a modular system largely run by regional computers ca-
pable of handling a large number of intersections, with significant intelligence

Ch. 11. ITS and Traffic Management 751
within local controllers. A central computer may also be used to improve man-
agement functions. SCATS differs from many other systems in that the network
manager has a more direct involvement in setting up the system, i.e., it does not
have a model. The degree of operator understanding increases with the level
of simplicity of a system and this would lead to corridor operations being ad-
dressed most beneficially.
RHODES (Real-Time Hierarchical Optimized Distributed and Effective System).
RHODES (Head et al., 1992) was developed in United States. The RHODES
architecture is based on three levels of hierarchy. The highest level assigns
traffic to the network to determine base levels of traffic across the network
which takes into account both evolving traffic demand and current network
geometry. At the next level down, RHODES operates as a more typical UTC
system based on predicted platoon arrival patterns. At the intersection level
the movements of individual vehicles are modeled.
Basically there are two processes in RHODES namely “estimation and pre-
diction” and “decision system”. The first process takes the upstream detector
data and estimates the actual flow profiles in the network and the subsequent
propagation of these flows. On the other hand, the second process is where
the phase durations are selected to optimize a given objective function (min-
imization of average delay per vehicle, average queue lengths, numbers of
stops, etc.), the optimization being based on dynamic programming and de-
cision trees. Recently RHODES has been updated for the integration of bus
priority measures (Mirchandani et al., 2001).
MOTION (Method for the Optimization of Traffic Signals in Online Controlled
Networks). MOTION (Busch, 1996) is a recent UTC system developed
in Germany, with some limited implementation in some European cities.
MOTION is basically based on four functional levels namely “data acquisition
and pre-processing”, “traffic modeling and analysis”, “optimization of control
variables”, and “decision and transfer of signal programs”. The first module
receives the dynamic information from detection equipment via the central
traffic computer and may perform some data processing functions like deter-
mination of origins and destinations. The second module uses most important
individual traffic streams to determine actual O–D streams within the network
and turning movements at intersections, which is necessary to calculate green
splits and minimum cycle times for each intersection. Selection of a common
network cycle time for coordination, determination of link progression speeds,
and optimal offsets between individual intersections to minimize delay and
stops are determined in the third module. On the fourth level new signal pro-
grams are evaluated and transferred via the central traffic computer.
TUC (Traffic-Responsive Urban Control). TUC (Diakaki et al., 2000)has
been developed recently in Greece and has also been implemented in a few
other European cities, particularly in the context of EC-funded demonstration

752 M. Papageorgiou et al.
projects. TUC operates by modifying nominal signal timings using a multivari-
able regulator on-line. Nominal starting values for signal timings are based
on historic levels of demand. The regulator is based on the formulation of the
urban traffic control operation as a linear–quadratic control problem. The con-
trol objective is to minimize and balance link queues taking into account link
storage capacity. This formulation is potentially particularly useful in dealing
with oversaturated conditions. TUC has been expanded in recent years to allow
for public transport priority (Diakaki et al., 2003).
4.4.3 Traffic-responsive systems: decentralized
With decentralized (distributed) control, more intelligence for signal op-
timization is distributed to local traffic signal controllers. This can increase
flexibility and reduce communications costs, but controllers are usually more
costly. Three distributed systems are summarized below.
UTOPIA (Urban Traffic Optimization by Integrated Automation). UTOPIA
(Donati et al., 1984) was originally developed in Italy. The system is structured
as a hierarchical system organized on three levels known as the local level, the
area level and the town supervisor level. UTOPIA’s intelligent local controllers
can communicate with each other as well as with a central computer. The local
outstation level applies a microscopic model to estimate the state of the inter-
section directly collecting data from detectors located at the start of each link.
Local queue and turning percentage estimation, saturation flows and delay cal-
culations are performed by the local “observer”. The next level uses a historic
traffic database to validate the local detection, checking changes in the traffic
data or making comparisons of data upstream and downstream of the con-
gested links. The final level integrates the congestion information with data
from other systems like public transportation. The macroscopic model used at
this level has the advantage of collecting different sources of information and
having the coverage of the whole city.
PRODYN. PRODYN (Farges, 1990) was developed in France and has been
implemented in some other European cities. It uses an intersection open-loop
optimal feedback algorithm for traffic signal control. As with SCOOT and
UTOPIA, detectors are located at the upstream end of each link and where
appropriate at 200 m and 50 m upstream. The detectors collect occupancy
data. The system operates in 5 sec steps and the demand for each period is
estimated from that in the previous period. A time horizon for prediction is
75 sec. Optimization seeks to minimize the sum of the delays over the horizon.
A forward dynamic programming procedure is used for optimization. Intersec-
tion controllers simulate the outputs over the horizon using the link outputs
and off-line determined turning proportions. Intersection controllers commu-
nicate with each other to achieve a better arrival forecast for the downstream
intersection. The control structure at the network level is a decentralized one.

Ch. 11. ITS and Traffic Management 753
OPAC (Optimization Policies for Adaptive Control). OPAC (Gartner, 1991)
was first developed in the United States using dynamic programming to gen-
erate optimal control strategies. It provides the computation of signal timing
without requiring fixed cycle time, split, and offset in the conventional sense,
and it is constrained only by minimum and maximum green times. OPAC cal-
culates, in real time, near-optimal signal timings using on-line data that is
typically readily available from upstream detectors at local level and OPAC
supports system-wide coordination at the network level. Many developments
have been carried out over the years (Valdes and Paz, 2004).
4.4.4 Performance
A variety of studies have been undertaken in different locations seeking
to compare the performance of alternative control systems. Early compar-
isons were between isolated and coordinated forms of control. Results would
be expected to be highly dependent on network characteristics, so that, co-
ordination should be most favorable on arterial routes with closely spaced
traffic signals. Probably the most detailed surveys were undertaken in Glas-
gow, where fixed time co-ordination was found to reduce vehicle journey times
by some 16% on average compared to isolated control (Holroyd and Hillier,
1979).
Further comparisons by the UK Transport Research Laboratory have found
that the SCOOT UTC system offers delay savings of around 12% compared to
up-to-date fixed-time plans and up to 40% in peak periods in networks oper-
ating under isolated vehicle actuated control (McDonald and Hounsell, 1991).
A 4% annual increase in delay has also been reported for fixed-time plans
if not updated (Bell and Bretherton, 1986), so that the potential benefits of
traffic-responsive systems would then be higher.
Performance of the other systems described in Sections 4.4.1 and 4.4.2 have
also generally been evaluated through “before-and-after” studies. For exam-
ple, surveys of UTOPIA in Turin gave reductions in journey times of 20% for
public transport vehicles and 10–15% for other vehicles. Good results have
also been reported for SCATS and PRODYN. However, there is very little ev-
idence of the comparative performance of the systems described on the same
network.
4.5 Discussion
4.5.1 Operational Research (OR) techniques
The significant increase in real-time information availability on traffic states
in recent years, driven by advances in technology for detection, communica-
tions, and data processing, opens up exciting opportunities for further OR
applications. It is beyond the scope of this paper to discuss these in detail,
but opportunities are evident even from a sample of OR-related techniques
already being used, such as:
•Short-term prediction/forecasting (e.g., evolution of traffic states).

754 M. Papageorgiou et al.
•Data fusion (data increasingly available from different sources).
•Closed and open-loop control theory applications.
•Dynamic programming for optimization.
•Advanced control theory applications.
•Prediction methods for platoon dispersion, time-dependent queuing,
etc.
•Real-time simulation modeling and network analysis.
•Optimization methods (e.g., for signal timings to optimize against in-
creasingly diverse objective functions).
•Applications of fuzzy-logic for modeling/optimization.
•Artificial intelligence and “expert” systems.
Perhaps a key challenge in the coming years will be how to select and use
OR techniques most effectively against a background of changing optimiza-
tion criteria and data provision which, whilst rich, will be inevitably variable in
quantity, quality, and coverage.
4.5.2 Concluding comments
The optimum use of traffic signals for urban network traffic management
and control will continue to be a key issue for City Authorities. This section
therefore concludes with some comments on some of the opportunities and
challenges which can be identified for the coming years.
•Accurate and timely data will remain a key requirement of UTC sys-
tems: In general, the less timely the data, the poorer the control
(Bretherton et al., 2004). However, this can impose a considerable cost
burden on detection/communications, and advantage is yet to be fully
taken of new above-ground systems. Good real-time modeling of con-
gested situations remains an important component of effective UTC
(Jhaveri et al., 2003). This would seem to be a priority area for scien-
tific research, given the increase in congestion occurring in many towns
and cities.
•UTC systems will increasingly have to provide flexibility in control
strategy selection, including priorities for public transport, pedestrians,
and other road user groups. This will have an implication for optimiza-
tion methods and criteria.
•Integration of UTC with other physical and ITS-related urban traffic
management systems can offer significant benefits for the network and
will be a key requirement for the coming years.
5 Motorway traffic control
5.1 The control loop
Controlling the motorway traffic flow process is a highly complicated task
which may involve a variety of spatially distributed control measures such as

Ch. 11. ITS and Traffic Management 755
ramp metering, route guidance, variable speed limits, etc. The way the con-
trol measures behave and act on the traffic process stems from the specific
design of the control strategy used. The control strategy employed determines
the control actions, and the specific response to the prevailing traffic condi-
tions, through the available control actuators, is based on its design and on
pre-specified goals.
Figure 6 depicts the general control loop for the motorway network traffic
process which includes all technical and physical phenomena that should be
influenced according to the specific goals. The evolution of the traffic process
depends upon the control inputs and the process disturbances. The control in-
puts are directly related to corresponding control devices such as traffic lights,
variable message signs, variable direction signs, etc., and may be selected from
an admissible control region subject to technical, physical, and operational
constraints. The process disturbances cannot be manipulated, but may pos-
sibly be measurable (e.g., demand) or detectable (e.g., incident) or predictable
over a future time horizon with appropriate algorithms. Typical disturbances in
motorway traffic are traffic demands, origin–destination patterns, the drivers’
compliance to variable message signs, environmental conditions, and incidents.
The process outputs are quantities chosen to represent the performance as-
pects of interest, e.g., total time spent, queue lengths, etc. The estimation of the
traffic state and the prediction of the various traffic quantities are performed
based on real-time measurements taken from the traffic process, and are sub-
sequently fed to the control strategy. The control strategy determines, based
Fig. 6. Motorway traffic flow process under control.

756 M. Papageorgiou et al.
on the measured, estimated, and predicted quantities, the appropriate control
inputs which are fed to the traffic process so as to meet the specified goals
despite the impact of various disturbances.
5.2 Control strategy design
5.2.1 Ramp metering control strategies
General remarks. Ramp metering is the most direct and efficient way to con-
trol and upgrade motorway traffic. Various positive effects are achievable if
ramp metering is appropriately applied:
•Increase in mainline throughput due to avoidance or reduction of con-
gestion.
•Increase in the served volume due to avoidance of blocked off-ramps
or motorway interchanges.
•Utilization of possible reserve capacity on parallel arterials.
•Improved traffic safety due to reduced congestion and safer merging.
Fixed-time ramp metering strategies. Fixed-time ramp metering strategies are
derived off-line for particular times-of-day, based on constant historical de-
mands, without the use of real-time measurements. They are usually based on
simple static models (Wattleworth, 1965; Schwartz and Tan, 1977).
As an objective criterion, one may wish to maximize the number of served
vehicles (which is equivalent to minimizing the total time spent), or to max-
imize the total travel distance, or to balance the ramp queues. These formu-
lations lead to linear programming or quadratic programming problems that
may be readily solved by use of broadly available computer codes. An exten-
sion of these methods that renders the static model dynamic by introduction of
constant travel times for each section was suggested in Papageorgiou (1980).
The main drawback of fixed-time ramp metering strategies is that their set-
tings are based on historical rather than real-time data. This may be a rude
simplification because:
•Demands are not constant, even within a time-of-day.
•Demands may vary at different days, e.g., due to special events.
•Demands change in the long term leading to “aging” of the optimized
settings.
•Turning movements are also changing in the same ways as demands; in
addition, turning movements may change due to the drivers’ response
to the new optimized signal settings, whereby they try to minimize their
individual travel times.
•Incidents and further disturbances may perturb traffic conditions in
anonpredictableway.
In addition, fixed-time ramp metering strategies may lead (due to the ab-
sence of real-time measurements) either to overload of the mainstream flow
(congestion) or to underutilization of the motorway.

Ch. 11. ITS and Traffic Management 757
5.2.2 Reactive ramp metering strategies
Reactive ramp metering strategies are employed at a tactical level, i.e., in
the aim of keeping the motorway traffic conditions close to pre-specified set
values, based on real-time measurements.
Local ramp metering. Local ramp metering strategies make use of traffic mea-
surements in the vicinity of a ramp to calculate suitable ramp metering values.
The demand-capacity strategy (Masher et al., 1975), quite popular in North
America, reads
(23)r(k) =qcap −qin(k −1)if oout(k) ocr
rmin else
where (Figure 7)kis the discrete time index, qcap is the motorway capacity
downstream of the ramp, qin is the motorway flow measurement upstream of
the ramp, oout is the motorway occupancy measurement downstream of the
ramp, ocr is the critical occupancy (at which the motorway flow becomes maxi-
mum), and rmin is a pre-specified minimum ramp flow value. The strategy (23)
attempts to add to the measured upstream flow qin(k −1)as much ramp flow
r(k) as necessary to reach the downstream motorway capacity qcap.If,how-
ever, for some reason, the downstream measured occupancy oout(k) becomes
overcritical (i.e., a congestion may form), the ramp flow r(k) is reduced to the
minimum admissible flow rmin to avoid or to dissolve the congestion.
Comparing the control problem in hand with Figure 6, it becomes clear that
the ramp flow ris a control input, the downstream occupancy oout is an output,
while the upstream motorway flow qin is a disturbance. Hence, (23) does not
really represent a closed-loop strategy but an open-loop disturbance-rejection
policy (Figure 7(a)) which is generally known to be quite sensitive to various
further nonmeasurable disturbances.
The occupancy strategy (Masher et al., 1975) is based on the same philos-
ophy as the demand-capacity strategy, but it relies on occupancy-based esti-
mation of qin, which may, under certain conditions, reduce the corresponding
implementation cost.
An alternative, closed-loop ramp metering strategy (ALINEA) (Figu-
re 7(b)), suggested in Papageorgiou et al. (1991),reads
(24)r(k) =r(k −1)+KRˆ
o−oout(k)
where KR>0 is a regulator parameter and ˆ
ois a set (desired) value for the
downstream occupancy (typically, but not necessarily, ˆ
o=ocr may be set, in
which case the downstream motorway flow becomes close to qcap). In field ap-
plications, ALINEA has not been very sensitive to the choice of the regulator
parameter KR.
Note that the demand-capacity strategy reacts to excessive occupancies oout
only after a threshold value (ocr) is exceeded, and in a rather crude way, while
ALINEA reacts smoothly even to slight differences ˆ
o−oout(k), and thus it
may prevent congestion by stabilizing the traffic flow at a high throughput level.

758 M. Papageorgiou et al.
(a)
(b)
Fig. 7. Local ramp metering strategies. (a) Demand–capacity, (b) ALINEA.
The set value may be changed any time, and thus ALINEA may be embedded
into a hierarchical control system with set values of the individual ramps being
specified in real time by a superior coordination level or by an operator.
Comparative field trials have been conducted in various countries to as-
sess and compare the efficiency of local ramp metering strategies (see, e.g.,
Papageorgiou et al., 1998), such as the demand-capacity, ALINEA, and the
occupancy strategy. The field results clearly show ALINEA’s superiority for all
employed performance criterions.
Multivariable regulator strategies. Multivariable regulators for ramp metering
pursue the same goals as local ramp metering strategies: they attempt to op-

Ch. 11. ITS and Traffic Management 759
erate the motorway traffic conditions near some pre-specified set (desired)
values. While local ramp metering is performed independently for each ramp,
based on local measurements, multivariable regulators make use of all avail-
able mainstream measurements oi(k),i=1n, on a motorway stretch, to
calculate simultaneously the ramp volume values ri(k),i=1m,forall
controllable ramps included in the same stretch (Papageorgiou et al., 1990).
This provides potential improvements over local ramp metering because of
more comprehensive information provision and because of coordinated con-
trol actions. Multivariable regulator approaches to ramp metering have been
reported in Yuan and Kreer (1968),Young et al. (1997),andBenmohamed
and Meerkov (1994). The multivariable regulator strategy METALINE may
be viewed as a generalization and extension of ALINEA, whereby the metered
on-ramp volumes are calculated from
(25)r(k) =r(k −1)−K1o(k) −o(k −1)+K2
O−O(k)
where r=[r1r
m]is the vector of mcontrollable on-ramp volumes,
o=[o1o
n]is the vector of nmeasured occupancies on the motorway
stretch, O=[O1O
m]is a subset of othat includes moccupancy lo-
cations for which pre-specified set values 
O=[

O1
Om]may be given.
Note that for control-theoretic reasons the number of set-valued occupancies
cannot be higher than the number of controlled on-ramps. Typically one bottle-
neck location downstream of each controlled on-ramp is selected for inclusion
in the vector O. Finally, K1and K2are the regulator’s constant gain matrices
that must be suitably designed via an LQ procedure, see Papageorgiou et al.
(1990),andDiakaki and Papageorgiou (1994),fordetails.
Nonlinear optimal ramp metering strategies. Reactive ramp metering strategies
may be helpful to a certain extent, but, first, they need appropriate set values,
and, second, their character is more or less local. What is needed for motorway
networks or long stretches is a superior coordination level that calculates in
real time optimal set values from a proactive, strategic point of view. Such an
optimal control strategy should explicitly take into account:
•Demand predictions over a sufficiently long time horizon.
•The current traffic state both on the motorway and on the on-ramps.
•The limited storage capacity of the on-ramps.
•The ramp metering constraints regarding maximum queues allowed.
•The nonlinear traffic flow dynamics, including the infrastructure’s lim-
ited capacity.
•Any incidents currently present in the motorway network.
Based on this comprehensive information, the control strategy should deliver
set values for the overall motorway network over a future time horizon so as
•to respect all present constraints,
•to minimize an objective criterion such as the total time spent in the
whole network including the on-ramps.

760 M. Papageorgiou et al.
Such a comprehensive dynamic optimal control problem may be formulated
and solved with moderate computation time by use of suitable solution algo-
rithms. The nonlinear traffic dynamics may be expressed by use of suitable
dynamic models in state space form, where the state vector comprises all traffic
densities and mean speeds of motorway segments, as well as all ramp queues;
the control vector comprises all controllable ramp volumes; the disturbance
vector comprises all on-ramp demands and turning rates at bifurcations. The
problem’s constraints include the ramp metering constraints and the queue
constraints, see Section 5.3.
Thus, for given current (initial) state from corresponding measurements and
given demand predictions, the problem consists in specifying the ramp flows
r(k),k=0K−1, where Kis the considered horizon, so as to minimize
the total time spent (or some other criterion) subject to the nonlinear traffic
flow dynamics and the constraints, see Section 5.3.
This problem or variations thereof was considered and solved in various
works (Blinkin, 1976; Kotsialos et al., 2002). Although simulation studies indi-
cate substantial savings of travel time and substantial increase of throughput,
advanced control strategies of this kind have not been implemented in the field
as yet. Section 5.3 contains a simulation study for such an advanced coordi-
nated ramp metering control strategy.
5.2.3 Link control strategies
Link control may include one or a combination of the following actions:
•Variable speed limitation.
•Changeable message signs with indications for “keep lane”, or conges-
tion warning, or environmental warning (e.g., information about the
pavement state).
•Lane control.
•Incident warning.
•Reversable flow lanes (tidal flow).
There are many motorway stretches, particularly in Germany and in the
Netherlands, employing a selection of these measures. It is generally thought
that control measures of this kind lead to a homogenization of traffic flow (i.e.,
more homogeneous speeds of cars within a lane and of average speeds of dif-
ferent lanes) which is believed to reduce the risk of falling into congestion at
high traffic densities and to increase the motorway’s capacity. Very few sys-
tematic studies have been conducted to quantify the impact of these control
measures (see, e.g., Zackor, 1972; Smoulders, 1990) and corresponding val-
idated mathematical models are currently lacking. This is one of the reasons
why the corresponding control strategies of operating systems are of a heuristic
character (e.g., Bode and Haller, 1983; Zackor and Balz, 1984).
5.2.4 Route guidance control strategies
A route guidance system may be viewed as a traffic control system in the
sense of Figure 6. Based on real-time measurements, sufficiently interpreted

Ch. 11. ITS and Traffic Management 761
and extended within the surveillance block, a control strategy decides about
the routes to be recommended (or the information to be provided) to the road
users. This, on its turn, has an impact on the traffic flow conditions in the net-
work, and this impact is reflected in the performance indices. Because of the
real-time nature of the operation, requirements of short computation times
are relatively strict (for more details see Section 3).
5.2.5 Integrated motorway network traffic control
As mentioned earlier, modern motorway networks may include different
types of control measures. The corresponding control strategies are usually de-
signed and implemented independently, thus failing to exploit the synergistic
effects that might result from coordination of the respective control actions. An
advanced concept for integrated motorway network control results from suit-
able extension of the optimal control approach outlined above. More precisely,
the dynamic model of motorway traffic flow may be extended to enable the
inclusion of further control measures, beyond the ramp metering rates r(k).
Formally r(k) is then replaced by a general control input vector u(k) that
comprises all implemented control measures of any type. Such an approach
was implemented in the integrated motorway network control tool AMOC
(Advanced Motorway Optimal Control) in Kotsialos et al. (1999), where ramp
metering and route guidance are considered simultaneously with promising re-
sults, see also Moreno-Banos et al. (1993),Ataslar and Iftar (1998),Bellemans
(2003),Hegyi et al. (2003),andHegyi (2004).
5.3 An advanced example
5.3.1 The motorway network traffic model
The efficiency and the amelioration potential of nonlinear optimal ramp
metering strategies may be demonstrated by means of simulation for a large-
scale network with the use of the AMOC generic motorway network control
tool. In this case AMOC does not consider routing control measures, but only
ramp metering control actions.
The network is represented by a directed graph whereby the links of the
graph represent motorway stretches. Each motorway stretch has uniform char-
acteristics, i.e., no on-/off-ramps and no major changes in geometry. The nodes
of the graph are placed at locations where a major change in road geometry oc-
curs, as well as at junctions, on-ramps, and off-ramps.
The time and space arguments are discretized. The discrete-time step is
denoted by T. A motorway link mis divided into Nmsegments of equal
length Lm. Each segment iof link mat time instant t=kT ,k=0K,is
characterized by the macroscopic variables traffic density (see also Section 2)
ρmi(k) (veh/lane-km), mean speed vmi (k) (km/h), and traffic volume or
flow qmi(k) (veh/h). The basic equations used for their calculation for each
segment iof link mat each time step, are (this is a time-space discretized

762 M. Papageorgiou et al.
Payne-like model, see Section 2.1.6)
(26)ρmi(k +1)=ρmi (k) +T[qmi−1(k) −qmi (k)]
Lmλm

(27)qmi(k) =ρmi (k)vmi (k)λm
vmi(k +1)=vmi (k) +T{V[ρmi (k)]−vmi(k)}
τ
+T[vmi−1(k) −vmi(k)]vmi (k)
Lm
(28)−νT
τLm
ρmi+1(k) −ρmi(k)
ρmi(k) +κ
(29)Vρmi(k)=vfm exp −1
amρmi(k)
ρcrm am
where vfm denotes the free-flow speed of link m,ρcrm denotes the critical
density per lane of link m(the density where the maximum flow in the link
occurs), λmits number of lanes, and amis a parameter of the fundamental
diagram (Equation (29))oflinkm. Furthermore, τ, a time constant, ν,anan-
ticipation constant, and κ, are constant parameters same for all network links.
Additionally, it is assumed that the mean speed resulting from (27) is limited
from below by the minimum speed in the network vmin.
In order for the speed calculation to take into account the speed decrease
caused by merging phenomena and the speed reduction due to weaving phe-
nomena, resulting from lane drops in the mainstream, two additional terms are
added to (27),seeMessmer and Papageorgiou (1990).
For origin links, i.e., links that receive traffic demand and forward it into the
motorway network, a simple queue model is used.
(30)wo(k +1)=wo(k) +Tdo(k) −qo(k)
where wo(k) is the queue length (veh) in origin oduring period k,do(k) is the
demand (veh/h) at oat the same period, and qo(k) is the flow (veh/h) that en-
ters the mainstream. The outflow qo(k) is determined by the traffic conditions
on the mainstream link and possible ramp metering control measures applied.
If ramp metering is applied, then the outflow ˆ
qo(k) that is allowed to leave o
during period kis a portion po(k) of the outflow that would leave owithout
control.
(31)qo(k) =po(k) ˆ
qo(k)
where po(k) ∈[pmino1]is the metering rate for the origin link o, i.e., a con-
trol variable. If po(k) =1, no ramp metering is applied, else po(k) < 1. For
ˆ
qo(k) we have
(32)
ˆ
qo(k) =min ˆ
qo1(k) ˆ
qo2(k)

Ch. 11. ITS and Traffic Management 763
with
(33)
ˆ
qo1=do(k) +wo(k)
T
(34)
ˆ
qo2=Qoif ρμ(k) < ρcrμ
Qo1−ρμ1(k)−ρcrμ
ρmax−ρcrμ if ρμ(k) ρcrμ 
where Qois the on-ramp’s capacity (veh/h), and ρmax (veh/lane-km) is the
maximum density in the network. Thus the maximum outflow ˆ
qo(k) is deter-
mined by the current origin demand if ˆ
qo1<ˆ
qo2(see (32), (33)), or the
geometrical ramp capacity Qoif the mainstream density is undercritical, i.e.,
ρμ1(k) < ρcrμ (see (34)), or the reduced capacity due to congestion of the
mainstream, i.e., ρμ1(k) > ρcrμ (see (34)).
Motorway bifurcations and junctions (including on-ramps and off-ramps)
are represented by nodes. Traffic enters a node nthrough a number of input
links and is distributed to the output links according to
(35)Qn(k) =
μ∈In
qμNμ(k)
(36)qm0(k) =βm
n(k)Qn(k) ∀m∈On
where Inis the set of links entering node n,Onis the set of links leaving n,
Qn(k) is the total traffic volume entering nat period k,qm0(k) is the traffic
volume that leaves nvia outlink m,andβm
n(k) is the portion of Qn(k) that
leaves the node through link m.βm
n(k) are the turning rates of node nand
are assumed to be known for the entire time horizon. Equations (35) and (36)
provide qm0(k) required in (26) for i=1.
The upstream influence of density and the downstream influence of speed at
network nodes are taken under consideration by appropriate static models that
provide the required terms in (26) and (27) for i=1andi=Nm(Messmer
and Papageorgiou, 1990).
5.3.2 The constrained optimal control problem
The coordinated ramp metering control problem is formulated as a dy-
namic optimal control problem with constrained control variables which can
be solved numerically over a given time horizon. The general discrete-time
formulation of the optimal control problem reads:
(37)minimize J=ϑ[K]+
K−1

k=0
ϕx(k) u(k) d(k)
subject to
(38)x(k +1)=fx(k) u(k) d(k)x(0)=x0
(39)uimin ui(k) uimax ∀i=1m

764 M. Papageorgiou et al.
where Kis the considered time horizon, x∈
nis the state vector, u∈
m
is the vector of control variables, dis the vector of disturbances acting on the
traffic process, and ϑ,ϕare arbitrary, twice differentiable, nonlinear cost func-
tions.
Based on the previous section, it may be seen that by substituting (27), (35),
and (36) into (26);(29) into (27);(31)–(34) into (30), the traffic flow model
equations take the form of Equation (38). In this case the state vector xconsists
of the densities ρmi, the mean speeds vmi of every segment iof every link m,
and the queues wofor every origin o. The control vector uconsists of the ramp
metering rates poof every on-ramp ounder control, with pomin po(k) 
10 according to (39). Finally, the disturbance vector consists of all demands at
each origin of the network and all turning rates at the network’s bifurcations.
The chosen cost criterion aims at minimizing the Total Time Spent (TTS)
of all vehicles in the network (including the waiting time experienced in the
network queues). The cost criterion is as follows.
J=T
k
m
i
ρmi(k)Lmλm+
o
wo(k)
(40)
+af
opo(k) −po(k −1)2+aw
o
ψwo(k)2
with
(41)ψwo(k)=max 0w
o(k) −womax
where the first two term in (40) account for the TTS while af,aware weighting
factors. The term with weight afis included in the cost criterion to suppress
high-frequency oscillations of the control trajectories. The last additional term
is a penalty term included in the cost criterion in order to enable the control
strategy to limit the queue lengths at the origins if and to the level desired. The
parameters womax are pre-determined constants and express the maximum
permissible number of vehicles in origin o’s queue.
A powerful numerical solution algorithm is used to solve this constrained
discrete-time optimal control problem, see Papageorgiou and Marinaki (1995).
5.3.3 Application results
The previously described approach to network-wide optimal ramp metering
has been applied to the Amsterdam ring-road with the use of AMOC.
The Amsterdam Orbital Motorway (A10) is shown in Figure 8.TheA10si-
multaneously serves local, regional, and inter-regional traffic and acts as a hub
for traffic entering and exiting North Holland. There are four main connec-
tions with other motorways, the A8 at the North, the A4 at the South-West, the
A2 at the South, and the A1 at the South-East. The A10 contains two tunnels,
the Coen Tunnel at the North-West and the Zeeburg Tunnel at the East.
For the purposes of our study only the counter-clockwise direction of the
A10, which is about 32 km long, is considered. There are 21 on-ramps on

Ch. 11. ITS and Traffic Management 765
Fig. 8. The Amsterdam ring-road.
this motorway, including the connections with the A8, A4, A2, and A1 mo-
torways, and a total number of 20 off-ramps, including the junctions with A4,
A2, A1, and A8. It is assumed that ramp metering may be performed at each
on-ramp, whereby the maximum permissible queue length for the on-ramps
is set to 20 vehicles, while storage of 100 vehicles is permitted on each of the
motorway-to-motorway ramps of A8, A4, A2, and A1.
The model parameters for this network were determined from validation
of the network traffic flow model against real data taken from the motorways
(Kotsialos et al., 1998).
The ring-road was divided in 76 segments with average length 421 m. This
means that the state vector is 173-dimensional (including the 21 on-ramp
queues). Since ramp metering is applied to all on-ramps, the control vector
is 21-dimensional, while the disturbance vector is 43-dimensional. With a time
step T=10 s we have, for a horizon of 4 h, K=1440 which results in a large-
scale optimization problem with 279,360 variables.
5.3.4 The no-control case
The ring-road was studied for a time horizon of 4 hours, from 16:00 un-
til 20:00, using realistic historical demands from the site. This time period
includes the evening peak hour. In absence of any control measures, the ring-
road is subject to recurrent congestion that is formed downstream of the
junctions of A10 with A2 and A1 in A10-South. This congestion propagates
backwards causing severe traffic delays in the A10-West. Figure 9(a) depicts
the density propagation along the motorway segments (segment 0 is the first
segment of A10-West after the junction of A10 with A8). The formation of
large queues at the on-ramps can be seen in Figure 9(b) (on-ramp 0 corre-
sponds to A8). As a result, the total time spent over the 4-h-horizon is equal to
13,226 veh h.

766 M. Papageorgiou et al.
(a)
(b)
Fig. 9. No control: (a) Density, (b) on-ramp queues.
5.3.5 The control case
When ramp metering is performed at all on-ramps, the congestion is vir-
tually lifted from the network (Figure 10(a)). The control strategy succeeds
in establishing optimal uncongested traffic conditions on the A10-South and
A10-West by applying ramp metering mainly at A1 and A2 at an early stage.
In Figure 10(b), the queues are mainly occurring at A2 and A1 because these
ramps have larger maximum permissible queues (100 vehicles). The control
trajectories are depicted in Figure 10(c). The resulting total time spent is
8833 veh h, which is a 33.2% improvement compared to the no-control case.
A further improvement to the total time spent could be reached with larger
maximum permissible queues. Had there been no queue constraints at all, the
density profile of Figure 10(a) would be completely flat. In fact, the control
strategy performs a trade-off between the queue lengths and the existence
of congestion inside the network. Stricter queue constraints result in more
degraded traffic conditions inside the motorway due to accordingly reduced
control maneuverability.

Ch. 11. ITS and Traffic Management 767
(a)
(b)
(c)
Fig. 10. Optimal control. (a) Density, (b) on-ramp queues, (c) optimal ramp metering rates.
The computation time required to obtain the optimal solutions is moderate
and depends upon the search method used. The main part of the improvement
is typically achieved very fast. The computation time for the 4-h-horizon is
20 min for the bulk of the 33.2% improvement (more than 30.6%) on a Sun
Ultra5 with a Sparc IIi-360 MHz processor workstation.

768 M. Papageorgiou et al.
5.4 Future directions
As in many other engineering disciplines, only a small portion of the signif-
icant methodological advancements in motorway network control have really
been exploited in the field. It is beyond our scope to investigate and discuss the
reasons behind this theory–practice gap, but administrative inertia, little com-
petitive pressure in the public sector, the complexity of traffic control systems,
limited realization of the improvement potential behind advanced methods by
the responsible authorities, and limited understanding of practical problems
by some researchers may have a role in this. Whatever the reasons, the major
challenge in the coming decade is the deployment of advanced and efficient
traffic control strategies in the field.
Regarding motorway networks, operational control systems of any kind are
the exception rather than the rule. With regard to ramp metering, the main
focus is frequently not on improving efficiency but on secondary objectives of
different kinds. Most responsible traffic authorities and the decision makers
are far from realizing the fact that advanced real-time ramp metering systems
(employing optimal control algorithms) have the potential of changing dra-
matically the traffic conditions on today’s heavily congested (hence strongly
underutilized) motorways with spectacular improvements that may reach 50%
reduction of the total time spent.
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