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Optimizing Signalized Intersections Performance under
Conventional and Automated Vehicles Traffic
Mahmoud Pourmehraba,∗
, Lily Elefteriadoua, Sanjay Rankab, Marilo Martin-Gasullaa
aUniversity of Florida, 365 Weil Hall, PO Box 116580, Gainesville, FL 32611, United States
bDepartment of CISE, University of Florida, Gainesville, FL 32611, United States
Abstract
Automated vehicles, or AVs (i.e. those that have the ability to operate without a driver
and can communicate with the infrastructure) may transform the transportation system.
This study develops and simulates an algorithm that can optimize signal control simulta-
neously with the AV trajectories under undersaturated traffic flow of AV and conventional
vehicles. This proposed Intelligent Intersection Control System (IICS) operates based on
real-time collected arrival data at detection ranges around the center of the intersection.
Parallel to detecting arrivals, the optimized trajectories and signal control parameters
are transmitted to AVs and the signal controller to be implemented. Simulation experi-
ments using the proposed IICS algorithm successfully prevented queue formation up to
undersaturated condition. Comparison of the algorithm to operations with conventional
actuated control shows 38 – 52% reduction in average travel time compared to conven-
tional signal control.
Keywords: Automated Vehicle, V2I Communication, Trajectory Optimization,
Adaptive Signal, VISSIM
1. Introduction
The term autonomous or self-driving refers to the class of vehicles capable of per-
forming the driving task without human intervention. While an autonomous vehicle
is only concerned with operating itself, an Automated Vehicle (AV) also communicates
with other vehicles, infrastructure, or cloud to enhance the transportation system's per-
formance. A connected vehicle (CV) also exchanges information, but a human driver
controls the vehicle. Fig. 1 distinguishes these classes of vehicles based on their general
functionality and level of autonomy.
NHTSA (2016) recently adopted the SAE International definitions for six levels of
automation ranging from SAE level 0, being a conventional vehicle, to SAE level 5, being
a fully autonomous vehicle. Intermediate levels share responsibilities between the driver
and the automation system. In this study, the traffic stream consists of conventional
vehicles as well as communicative vehicles—those which comply with SAE levels 0 to 5
and capable of receiving instructions on their movement.
Recent attention has focused on designing signal control algorithms to incorporate
advanced vehicle technologies into the transportation system. In one of the first studies
that consider intersections, Dresner & Stone (2004) set up an agent-based algorithm to
∗Corresponding author, e-mail: mpourmehrab@ufl.edu
Preprint submitted to Transportation Research Part C: Emerging Tech. July 7, 2017
arXiv:1707.01748v1 [cs.SY] 1 Jul 2017
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Autonomous Automated Connected Conventional
Figure 1: Vehicles'classification based on their functionality.
accept incoming requests from AVs to reserve a set of tiles to complete their maneuver
within the intersection's conflict zone. Their algorithm assigns the right-of-way by grant-
ing the reservations with no conflict based on first-come-first-serve order in each lane.
The research assumes a fully automated environment with no conventional signal indi-
cation. Several other studies have also explored different options to prioritize vehicles'
crossing sequence under a variety of settings. (Ahmane et al. (2013); Elhenawy et al.
(2015); Feng et al. (2015); He et al. (2012); Levin & Boyles (2016); Li & Wang (2006); Li
et al. (2013); Tachet et al. (2016); Wu et al. (2013); Xie et al. (2012); Yan et al. (2008);
Zhong et al. (2015)).
Li et al. (2014) proposed a rolling-horizon procedure to make joint decisions on vehi-
cles'trajectory and signalization at an isolated intersection with AVs only and with two
conflicting through movements. Their algorithm uses the arrival information at a detec-
tion distance to compute a four-component trajectory for every vehicle. The algorithm
enumerates a set of binary signal decisions and selects the trajectories with the lowest
average travel time delay. Several studies proposed algorithms to improve on adaptive
signal control logic using the high-resolution data brought by automated/connected ve-
hicle technology (Lee & Park (2012); Lee et al. (2013); Goodall et al. (2013); Feng et al.
(2016); Yang et al. (2016); Le Vine et al. (2016)). Beyond isolated intersections, He et al.
(2015) proposed a real-time speed advisory algorithm that reduces the fuel consumption
of a connected vehicle traveling along an arterial with coordinated signals. Priemer &
Friedrich (2009) developed a signal phase control algorithm that reduces the queue length
at a signal network using V2I communication.
This study develops a trajectory-based optimization algorithm applicable to an iso-
lated intersection under mixed-traffic. The algorithm optimizes both the signal control
and the trajectories of AVs assuming there is no lane changing past the point of initial
communication of the vehicle and the intersection controller. The algorithm assumes the
traffic is undersaturated, i.e., there is no need to track vehicles over more than one cycle.
We develop a recursive model to establish the follower-lead dependency among vehicles
in each incoming lane. Depending on the type and position of each vehicle, we solve
either a trajectory optimization (for automated vehicles) or trajectory estimation (for
conventional vehicles) to obtain the respective trajectory. Due to the pivotal role of an
AV lead trajectory on the movement of its followers, we formulate and solve a non-convex
optimization problem that minimizes the travel time delay of vehicles within the available
detection range. The control algorithm also adjusts the signal control settings.
The following section reviews the literature on AVs and intersection management. The
third section provides an overview of the proposed methodology, while the fourth section
2
presents numerical results of the simulation experiments implementing our new approach,
along with comparisons to conventional actuated control simulated in VISSIM. The final
section discusses the performance of the algorithm, proposes potential improvements, and
poses questions for future research.
2. Literature Review
This section reviews published studies on integrating AVs with intersection operations.
Depending on the control logic, we classify the literature into two broad groups: (1)
reservation-based, i.e., models that allocate the right of way of the intersection based
on a set of pre-defined rules (2) trajectory-based, i.e., models that jointly optimize AV
trajectories and signal control.
Under the first category, Dresner & Stone (2004) developed the Autonomous Inter-
section Management (AIM) system, an algorithm that either rejects or grants requests
of automated vehicles to reserve a block of space-time in the intersection. They designed
AIM to replace traffic lights and stop signs. The paper indicates that the AIM sys-
tem can coordinate vehicles'crossing sequence more efficiently than conventional traffic
lights. In subsequent publications, the AIM was extended to: make the control policy
compatible with communicative semi-autonomous vehicles, (Au et al. (2015); Dresner &
Stone (2006a,b)); manage priorities for side traffic under unbalanced demand, (Au et al.
(2011)); improve estimation of vehicle arrivals to the stop bar, (Au & Stone (2010)); and
coordinate a network of multiple interconnected intersections, (Hausknecht et al. (2011)).
Several other studies also supported intersection control logics without the presence of
the traditional signal (Elhenawy et al. (2015); Tachet et al. (2016); Wu et al. (2013);
Yan et al. (2009)). These types of algorithms may have limitations on minimizing delay
because of: (1) frequent switches of right-of-way may disrupt platoons resulting in higher
total travel time for the intersection; (2) eliminating traffic signal heads makes the system
less expectable for conventional vehicles; (3) they do not consider the additional benefit
stemming from optimizing AV trajectories.
Feng et al. (2015) adopted a broader perspective of reservation-based models after
they formulated and solved a bi-level problem that feeds the connected vehicle data
into an adaptive signal control logic. Their algorithm predicts spatial information of
conventional vehicles using the connected vehicles'real-time data. Compared to a fully-
actuated control simulated in VISSIM, the proposed signalization reduced total delay
by 16% under higher rates of CVs. Despite addressing responsiveness to conventional
vehicles, their approach limits decision-space to determining priorities within the conflict
zone of an intersection.
Under the second category, trajectory-based optimization algorithms expand the deci-
sion space to improve intersection performance. Li et al. (2014) proposed a rolling-horizon
process to solve a trajectory-based optimization for an intersection with two conflicting
through movements assuming only AV traffic. The algorithm estimates the trajectory of
an AV as a function of its speed and position in the traffic stream. An upper level control
algorithm enumerates all the feasible switches between two conflicting movements within
a certain time interval. Their algorithm implements the combination of signal and tra-
jectory decisions that yield the least average delay. However, the signal control problem
was solved supposing only two straight movements which makes it feasible to enumerate
all timing options. Moreover, their methodology does not take into account presence of
conventional vehicles with no communication capabilities.
3
Guler et al. (2014) devised and simulated an algorithm to enumerate sequences to serve
connected vehicles at an intersection with two through movements. Promoting platoons,
they associated higher delay reduction with higher penetration rate of connected vehicles
in traffic. Recently, Yang et al. (2016) also evolved this work of Guler et al. (2014) to
solve a trajectory-based optimization for various types of AV/CV approaching an isolated
intersection. Once a vehicle arrived at a communication range from center of intersection,
an upper level algorithm provided departure sequence of vehicles through a branch and
bond tree search. Next, the lower level algorithm obtains the set of piecewise-linear
trajectories to obtain the least amount of average delay and number of stops. Through
simulation experiments, the method improved on actuated signal control with at least
50% penetration rate of automated and connected vehicles in traffic stream. Besides
considering an over-simplified intersection with two through movements, a piece-wise
linear trajectory form fails to address the deceleration/acceleration behavior of vehicles
which can lead to underestimating overall delay.
In summary, there are two types of algorithms that mainly differ in the extend of con-
trol decisions, i.e. signal scheduling and trajectory planning. The family of reservation-
based algorithms mostly focuses on obtaining the optimal sequence of serving lanes by
sorting incoming requests from AVs. Trajectory-based algorithms, however, further bene-
fit the connectivity and programmability of AVs to prepare them for the optimal departure
far ahead from the stop bar. On the other hand, considering the real-time execution of
the algorithms, the additional complexity in trajectory-based models could necessitate
more computational resources to be operational.
This study considers a mixed vehicle environment, aims to enhance adaptive signal
control, and takes advantage of AV presence to adjust their trajectories and further
minimize the overall travel time.
3. Methodology Overview
In this section, we develop models and sub-models to optimize intersection perfor-
mance using arrival information of AVs and conventional vehicles. We devise an algo-
rithm to process the arrival data at a lane-specific detection range on a real-time basis.
The traffic composition of (AVs, with two-way V2I connectivity, and conventional vehi-
cles, with no ability to communicate) is an input to the algorithm. The algorithm aims
to minimize travel time delay of arriving AVs by preventing unnecessary stops within
the communication range. This goal is achievable by synchronizing the signal control pa-
rameters only for undersaturated condition as queues are inevitable beyond that. Fig. 2
schematically shows the proposed Intelligent Intersection Control System (IICS).
Initially, the central computer, marked as 1 in Fig. 2, receives each vehicle's arrival
information, marked as 2 and 3, from a detection distance—the center line distance from
detection range to the stop bar—in each lane. Next, the algorithm computes the param-
eters associated with the movement of vehicles toward the intersection. The proposed
trajectory model minimizes the travel time delay of the automated and estimates the
movement of the conventional vehicles. The algorithm implements a modified adaptive
control logic based on computed trajectories, marked as 4. Finally, the algorithm pro-
vides two sets of outputs: (1) the signalization pattern, marked as 4; (2) the trajectory
of each AV to optimize travel time from the detection location to the stop bar, marked
as 5. The procedure is repeated each time a new vehicle arrives.
The next subsections present the proposed model to describe the movement of detected
vehicles. In this section, we model the movement of approaching vehicles. The trajectory
4
IntelligentIntersection
ControlAlgorithm
OptimalSignalDecision
Signal
Controller
Devicetocollectand
fusevehiclearrivals
information
Camera/Radarto
obtainconventional
vehiclearrivals
OptimizedTrajectories
Arrivalinformation:
(Lane,Speed,Location,Length,
Maxacceleration,Maxdeceleration,
Destination)
VehicleArrivals
Arrivalinformation:
(Lane,Speed,Location)
ConventionalVehicles SignalHeads
Automated/ConnectedVehicles
1
2
3
4
5
Figure 2: Intelligent Intersection Control System (IICS).
computation's state equation involves sub-models to predict trajectory of a conventional
vehicle or optimize trajectory of an automated vehicle. The adaptive signal control logic
is described in section. 3.2.
3.1. Algorithms for Trajectory Optimization/Estimation
The vehicle type, i.e. conventional or automated, and its position on the lane deter-
mine the trajectory computation process. We define a lead vehicle as a vehicle that moves
free from influence of others. Any vehicle's movement can affect its follower depending on
a variety of factors. Considering the cumulative effect in a lane, the lead vehicles have a
key role in intersection delay. Finally, we will formulate and solve a specific optimization
problem to minimize the travel time delay of an automated lead vehicle. We formulate an
equation to address the follower–lead dependencies among a set of vehicles in each lane.
The Automated vehicle Trajectory Optimization (ATO) reflects this effect by recursion.
A solution to ATO model guarantees that trajectory of all the k−1 first vehicles can
affect the trajectory of kth vehicle.
Data:
Lthe set of incoming lanes, l∈ L
Klthe ordered set of vehicles in lane l,∀l∈ L
typekl the type of vehicle kon lane l,typek l ∈ {AV :automated/connected vehicle, CV :
conventional vehicle},∀l∈ L,∀k∈ Kl
sptkl spatial information of vehicle kon lane l, including detection time stamp t0, location
dkl(t0), speed Vkl (t0), and movement of AVs m∈M={lef t, straight, right}
attkl set of attributes for vehicle kon lane lincluding maximum acceleration rate amax+
kl ,
maximum deceleration rate amax−
kl , vehicle longitudinal length Lkl , desired speed
Vdes
kl
spdmset of speed limits Vmax
mand Vcross
mwithin the detection range and at the stop bar
for movement m∈M
Φset of active phases to serve all available movements at the intersection, φ∈Φ
5
∆the phase-lane incident matrix ∆ = [δφl ∀l∈ L,∀φ∈Φ], where δφl is 1 if lane l
belongs to phase φ, 0 otherwise
sig the array that contains signal control events, sigφ= (tsφ, Gφ, Yφ, ARφ)
tsφthe time when the green interval for phase φbegins
Gφthe duration of green interval for phase φ
Yφthe duration of yellow interval for phase φ
ARφthe duration of all-red interval for phase φ
Variable:
trajkl to be the trajectory of vehicle kon lane l,{dkl (t) : t∈Tkl} ∀ l∈ L,∀k∈ Kl
Tkl To be the time interval from vehicle detection to its departure at the
stop bar
dkl(t)to be the center-lane distance of vehicle kon lane lto the stop bar
Recursive State Equation for Automated vehicle Trajectory Optimization (ATO):
trajkl =
FTO(sig, sptkl, attk l, traj(k−1)l) for k∈Kl\{1}, typekl =AV
FTE(sptkl, attkl, traj(k−1)l) for k∈Kl\{1}, typekl =CV
LT O(sig, sptkl, attkl, spdm) for k∈ {1}, m ∈M , typekl =AV
∀l∈ L
(1)
Sub-models to ATO model:
FTO(.)to be Follower vehicles Trajectory Optimizer for AVs
FTE(.)to be Follower vehicle Trajectory Estimator for CVs
LT O(.)to be Lead vehicle Trajectory Optimizer for AVs
Eq. 1 represents the trajectory of kth vehicle in lane lto be a function of signalization,
characteristics of the vehicle itself, speed limits, and recursively trajectory of its lead
vehicle. However, in absence of dependency to trajectory of vehicle in front, as it will be
discussed in section. 3.1.2, the model considers the vehicle as a lead vehicle by itself. The
sub-models (i.e. LTO, FTO, and FTE) to ATO problem will be discussed next.
3.1.1. Lead vehicle Trajectory Optimization (LTO)
In this section, we formulate and solve the Lead vehicle Trajectory Optimization
(LTO) problem. The problem aims to minimize an automated lead vehicle's travel time
delay. An appropriate functional form for automated vehicle trajectory—also called the
space-time function—should meet several qualifications: (1) to offer sufficient flexibility
to capture and improve the movement of AVs; (2) to produce an accurate trajectory that
the vehicle can implement; (3) to belong to a family of functions uncomplicated to be
parametrized.
Here we formulate the LTO problem assuming the vehicle travels the detection range in
three ordered stages. The first and third stages adjust the speed by a constant acceleration
or deceleration rate, while the vehicle maintains a constant speed during the second
stage. The three-stage trajectories closely models the behavior of the lead AV, however,
a follower AV may peruse a more general strategy. Depending on the arrival parameters,
the LTO solution may omit any of three stages by assigning it zero time duration. Eqs. 2
to 4 provide the formulas to compute the travel time of each stage using fundamental
motion equations.
6
∆tkl,1=v2−v1
a1
∀l∈ L,∀k∈ Kl(2)
∆tkl,2= (d0−v2
2−v2
0
2a1
−v2
3−v2
2
2a3
)/v2∀l∈ L,∀k∈ Kl(3)
∆tkl,3=v3−v2
a3
∀l∈ L,∀k∈ Kl(4)
Tkl =
3
X
n=1
∆tkl,n ∀l∈ L,∀k∈ Kl(5)
Where, to avoid lengthy mathematical expressions, we excluded vehicle and lane in-
dices and used a more compact notation as:
d0center-lane distance from the stop bar at detention moment, dkl(t0)
v0initial speed of vehicle at the detection, Vkl(t0)
v2constant speed at second stage, Vkl(t0+dt)∀dt ∈[∆t1,∆t1+ ∆t2]
v3discharge speed of vehicle at the stop bar, Vkl(t0+Tkl )
a1acceleration/deceleration rate at first stage
a3acceleration/deceleration rate at third stage
Assuming the ideal travel time associated with the kth vehicle in lane lto be the time
required to travel the detection range at its desired speed, we compute the total travel
time delay as given in Eq. 6:
Dkl(Tkl) = Tkl −d0
Vdes
kl
∀l∈ L,∀k∈ Kl(6)
Where Dkl denotes the total travel time delay of vehicle kon lane l
Next, we present the LTO mathematical program by minimizing vehicle's travel time
delay subject to restrictions from signalization, vehicle attributes, and regulation, as
follows:
(LT O) min
v2,v3,a1,a3
Dkl(Tkl) (7)
subject to
tsφ≤δφlTkl ≤tsφ+Gφ+Yφ(8)
v2≤Vmax
m(9)
v3≤Vcross
m(10)
amax−≤a1≤amax+(11)
amax−≤a3≤amax+(12)
Where:
Dkl(Tkl)Travel Time Delay of vehicle kon lane las a function of its travel time Tkl
tsφtime when phase φstarts
δφl equal to one if lane lbelongs to phase φ, 0 otherwise
Gφgreen duration for phase φ
7
Yφyellow duration for phase φ
v2constant speed at second stage
v3discharge speed of vehicle at the stop bar
a1acceleration/deceleration rate at first stage
a3acceleration/deceleration rate at third stage
amax−maximum deceleration rate
amax+maximum acceleration rate
Vmax
mmaximum allowable speed within the detection range
Vcross
mmaximum allowable speed at the stop bar
The first set of bound–constraints keeps only solutions that the travel time belongs to
the green or yellow interval. The next constraint guarantees the speed profile of vehicle
does not exceed the maximum allowable speed starting from the second stage. The third
constraint controls the discharge speed depending on the type of movements i.e. left
turn, straight through, or right turn. The last set of constraints limit any acceleration or
deceleration rate to the range that vehicle can execute.
The non-positive-definite Hessian matrix of the travel time delay, as appears in both
LTO objective function and set of constraints, causes non-convexity. Even at four decision
variables, standard non-linear methods are unable to distinguish the global optimal from
non-optimal or infeasible solutions. By taking advantage of the size and structure of LTO
problem, we develop an exact algorithm to find the global minimum.
The gradient of the objective function reveals that the travel time delay monotonically
varies with respect to acceleration or deceleration rate in the first and the last stages. The
necessary condition—setting gradient to zero—also indicates absence of any stationary
point. Thus, considering the non-convex feasible region, the optimal solution must belong
to the boundaries of the feasible region. Therefore, we solve LTO, model. 7, by devising
an algorithm to minimize the travel time delay on the boundaries and not inside of feasible
region, as shown by Algorithm. 1.
3.1.2. Follower Vehicle Trajectory Optimization
Similar to the car following model for conventional vehicles, the Follower vehicle Tra-
jectory Optimization (FTO) model intends to compute the trajectory of an automated
follower. If the vehicle in front is going to depart at time tdep
(k−1)l, assuming that the sat-
uration headway at the stop bar is sh, an automated follower can depart no sooner than
tdep
(k−1)l+sh. Therefore a hypothetical trajectory for vehicle kcan be computed by lagging
trajectory of vehicle k−1 to the saturation headway sh. The hypothetical trajectory
may not be compatible to the arrival of the kth vehicle.
Equivalently, the automated follower may fail to depart at the saturation headway if
it is not close enough, or moves much slower, relative to its lead vehicle. Thus, even at
the maximum acceleration rate, the automated vehicle may not be able to reduce its time
headway down to the saturation time headway. Under this case, the proposed algorithm
no longer considers that automated vehicle as a follower, and optimizes the trajectory as
a lead vehicle by solving the LTO problem instead.
The procedure within Algorithm. 2 outputs the trajectory with minimum travel time
that keeps headway higher than, or equal to, the saturation headway. The principal reason
comes from the fact that the trajectory is constructed either by joining the transition
component with the hypothetical trajectory, or by solving LTO problem. Under the
former case, the trajectory has a headway greater than or equal to the saturation headway;
8
Algorithm 1 AV Lead vehicle Trajectory Optimizer
Require: signal control events, vehicle arrival information, vehicle attributes, and speed
limits
Ensure: valid trajectory with minimal delay for the AV
1: procedure LTO Exact Solver(sig, sptkl , attkl, spdk l)
2: D∗
kl ←M M to be a relatively large value
3: flag ←0
4: for counter = 1:4 do LTO has four variables: v2, v3, a1, a3
5: Select a new variable
6: Set non-selected variables to limit(s) based on bound-constraints
7: Obtain the bounds on the selected variable
8: Solve the remaining single-variable constrained problem by minimizing travel
time delay over corrected bound
9: Dkl ←travel time delay corresponding to selected and computed variables
10: if Dkl < D∗
kl then current solution can be improved
11: D∗
kl ←Dkl
12: flag ←1
13: end if
14: end for
15: if flag = 1 then
return D∗
kl optimal solution
16: else
return LTO problem is infeasible
17: end if
18: end procedure
the higher headway corresponds to the transition part while the equality associates with
the hypothetical part. The latter case, when the LTO problem is solved, no trajectory
point can have a headway lower than the saturation headway. Having a lower headway
would be in contradiction to not finding any transition to the hypothetical trajectory
at lines 6-11. Finally, the trajectory takes the minimum travel time resulting in the
minimum achievable headway at the stop bar.
3.1.3. Trajectory Estimation for Conventional Vehicles
For undersaturated condition, we assume that a lead conventional vehicle would desire
to maintain its speed as recorded when entering the detection range. The rest of this
section explains the model to estimate a follower conventional vehicle's trajectory.
Sensors on the roadside, i.e. radar or camera, obtain the lane, location and speed
of conventional vehicles once they enter the detection range. Although they are non-
communicative vehicles, conventional vehicles affect both signalization and trajectory
computation for automated vehicles. Therefore, the Automated vehicle Trajectory Op-
timization (ATO) model predicts their movements through a Car-Following model. For
the purpose of this study, we implement the Gipps (1981) car-following model—as the
FTE sub-model in Eq. 1 —to estimate the trajectory of a conventional follower. Below
is the equation that yields the speed profile of conventional follower vehicle:
9
Algorithm 2 AV Follower vehicle Trajectory Optimizer
Require: trajectory of the lead vehicle, follower attributes, follower vehicle arrival in-
formation, and signal control events
Ensure: valid trajectory with minimal departure headway for automated follower
1: procedure FTO Solver(sig, sptkl, attkl , traj(k−1)l)
2: tdep,hypo
kl ←max{tsφ, tdep
(k−1)l+sh}set the hypothetical earliest departure time to
either initiation of green or departure at saturation headway
3: dt ←tdep,hypo
kl −tdep
(k−1)l
4: Construct the hypothetical trajectory, trajhy po
kl by lagging all timestamps of
traj(k−1)lup to dt
5: flag ←0
6: for index ∈trajectory point indices on trajhy po
kl do Searching for a feasible
transition from arrival point to the hypothetical trajectory
7: if feasible deceleration/acceleration from detection speed to speed at index
exist then Earliest hypothetical trajectory is feasible
8: construct the earliest trajectory, trajkl , by the feasible transition appended
by all trajectory points of tdep,hypo
kl with the timestamps greater than index
9: flag ←1
10: end if
11: end for
12: if flag = 1 then
return computed trajkl
13: else
return trajkl =LT O E xact Solver(sig, sptkl , attkl , spdkl)use algorithm. 1 as
vehicle kl could not be a follower
14: end if
15: end procedure
vkl(t+ ∆t) = min{vkl(t)+2.5amax+
kl ∆t(1 −vkl (t)
vdes
kl
)s0.025 + vkl (t)
vdes
kl
,
(13)
amax−
kl ∆t+samax−
kl (2(d(k−1)l(t) + Lkl −dkl (t)) + ∆t(amax−
kl ∆t+vkl (t)) + v(k−1)l(t)2
amax−
kl
}
where:
∆ttime steps to compute trajectory points
vkl(t)speed of follower vehicle ∆tunit of time after t
v(k−1)l(t)speed of lead vehicle ∆tunit of time after t
In the context of the model, Eq. 1, Algorithm. 2 implements the Gipps Car-Following
model to compute a conventional vehicle's trajectory.
3.2. Adaptive Signal Control with Trajectory Optimization
We devise an enhanced adaptive signal control logic based on trajectory information
to make decisions on whether to extend or switch a phase. The proposed algorithm, as
10
Algorithm 3 Conventional Follower vehicle Trajectory Estimator
Require: trajectory of lead vehicle, lead and follower's attributes, follower vehicle arrival
information
Ensure: trajectory of conventional follower
1: procedure FTE Solver(sptkl, attkl , att(k−1)l, traj(k−1)l)
2: t←detection time
3: d←follower initial distance to stop bar
4: while d > 0do
5: t←t+ ∆t
6: Compute vkl(t) using Eq. 13
7: akl(τ)← {vkl(t+∆t)−vk l(t)
∆t|τ∈[t, t + ∆t]}
8: d←1
2akl(τ)∆t2+vkl(t)∆t
9: end while
return computed pairs of (t, d)
10: end procedure
shown in Fig. 3, re-evaluates the signal control status every time a new vehicle arrives.
If the current signal phase can serve the earliest newly detected vehicle, it asks the
signal controller for a green extension. Otherwise, it terminates the ongoing green and
switches the right-of-way to the phase that leads to least travel time delay for incoming
vehicles. The information from optimized trajectories allow for exact scheduling of phases.
Although the algorithm has no control over conventional vehicles, they can have greater
time headway as AVs travel the detection range in least time.
The timing for each phase should meet several practical criteria. Any green interval
lower than a minimum green or higher than a maximum green causes too frequent or late
phase switches which forces excessive delay to vehicles.
While the enhanced adaptive control logic mimics the traditional adaptive signal
control strategy, the proposed algorithm makes decisions using the trajectories of AVs
instead of calls coming from loop detectors or cameras. Fig. 4 illustrates the association
of each arrival interval and the corresponding signal decision for a few consecutive phases.
The minimum time to travel the detection range necessitates a lag time, tLag , between
the end of the green and the end of the associated arrival interval. In other words, the
lag time represents the time between when the algorithm makes signal decision and when
the corresponding traffic will depart at the stop bar.
4. Algorithm Implementation and Numerical Results
We program the proposed IICS process in MATLAB (2016b) customized for a four-leg
intersection with six incoming lanes as shown in Fig. 5.
According to Fig. 4, the intersection includes: six approaching lanes, four departing
lanes, and two approaches with exclusive left turn lanes.
We implement the IICS based on the following assumptions:
•Sum of critical flows results in undersaturated conditions.
•Gipps (1981) car-following model predicts the conventional followers'movement, as
described in section. 3.1.3.
•For simulation purposes, no data loss due to communication malfunction occurs.
11
Initialization&
Traf�ic
Generation
EnhancedAdaptiveSignal Controller
Start
InitializeIntersection
Parameters(Movements,Lanes,
Phases,Speedlimits,Detection
ranges)
GenerateRandomArrivals
atDetectionRanges
UpdateVehicle
LocationUsing
ReceivedMessage
Timestamp
Ongoinggreenphase
servesallvehicles?
CalculateTrajectoriesfor
NewVehicles(solveATO
givenupdatedsignal
decision)
No
Doallnewvehicles
belongtolanesingreen
phase?
Yes Extendthegreento
servenewvehicles
No
Provideenoughgreen(and
atleastminimumgreen)to
theearliestarrivingvehicle.
Yes
Yes
Allnewvehicles
processed?
No
Updatethesignaldecision
withthenewphaseand
timing
Figure 3: Enhanced Adaptive Signal Control to use Trajectory Data.
•Intersection's geometry:
–The four-leg test intersection is on level terrain with six incoming lanes and
all turning movements available, see Fig. 4.
•Operating conditions:
–Maximum allowable speed is 40 mph.
–Turning movements cross the stop bar at speeds no more than 30 mph.
–Minimum green time for all phases is 4.5 seconds.
–Yellow and all-red time are 1.5 seconds per phase.
–No lane changing occurs once a vehicle arrival is detected.
–No pedestrians are present in the vicinity of the intersection; therefore, no
pedestrian phases are required.
•Traffic generation:
–Vehicles arrive at the communication distance and are simulated in a 15-minute
period.
–The initial speeds of vehicles follow the triangular distribution with minimum,
peak, and maximum values equal to 34 mph, 40 mph, and 44 mph (as 0.85, 1,
and 1.1 factors of the maximum allowable speed), respectively.
–Vehicles, regardless of being automated or conventional, are capable of decel-
eration/acceleration of -15 ft/s2to 10 ft/s2.
12
Phase2
Phase3
Phase1
Phase4
tLag2
tLag3
tLag1
ΔtArr 2
ΔtArr 3
ΔtArr 1
ΔtArr 4
tLag4
G1G3G2G4G2G3G1G4
ar ar ar ar ar ar ar
Signalization y1y5y2y4y2y3y1y4
Time
tLag2
tLag3
tLag1
tLag4
(NBL,TH,R)
(WBL/TH,R)
(SBL,TH,R)
(EBL/TH,R)
Figure 4: Schematic Signal Control Plan(Giand yiare the green and yellow duration for phase i; ∆Arr(i)
indicates the arrival interval in phase i;tLag(i)denotes the time before the end of yellow interval in phase
i).
–Conventional vehicles'desired speed is 40 mph.
–The IICS algorithm uses a safe speed recommendation inside the communica-
tion area, however, in some cases the initial speed of individual vehicles might
be slightly higher—as reflected by the triangular distribution with maximum
of 44 mph.
4.1. Simulation Experiments
This section reports the results of 3000 simulation experiments. Using the algorithm
described in section. 3, the following four variables are used to formulate the test scenarios:
•The detection range for all lanes varies from 500 to 3000 feet (ten equidistant values).
•The AV ratio for all lanes varies from 0.3 to 1 (ten equidistant values); 1 being the
traffic with all automated vehicles and no conventional vehicles.
•Vehicle inter-arrival times follow the exponential distribution with rate parameter
equal to the inverse of the average time headway. The average time headway for all
lanes varies from 8 to 60 seconds (ten equidistant values).
•The saturation headway at stop bars to be 1, 1.5, or 2 seconds. Lioris et al. (2017)
showed that connectivity of vehicles can reduce the saturation headway by forming
platoons.
Fig. 6 illustrates how the algorithm served arriving vehicles in a lane. The horizontal
time gap between arrival and departure curve represents the time that each vehicle spent
traveling through the detection prior to the stop bar.
In order to quantify the performance, a module monitors three outcome variables
including: average travel time (measured from detection to departure at the stop bar),
average delay (determined as the extra travel time relative to the free flow travel time),
and average effective green (sum of actual green and yellow times). Under the set of
assumptions stated in section. 4, we observed the following patterns (Fig. 7):
•The average travel time and average delay surge as flow increases. For saturation
headway equal to 2 second, once the sum of critical flows approaches the flow
threshold, the operation becomes unstable—indicating queues are inevitable.
13
ONLY
ONLY
①
②
③
④
⑤
⑥
Phase Movement
1SBL,TH,R
2NBL,TH,R
3WBL/TH,R
4EBL/TH,R
N
Figure 5: A four-leg test intersection with six incoming lanes and four phases.
•As expected, capacity increases as the saturation headway decreases (see the first
row of panels in Fig. 7).
•The average delay slightly decreases as the detection range increases. The higher
the available distance, the more flexibility in the trajectory optimization, which
reduces the total delay.
•The higher the ratio of AVs, the lower the average delay.
•In higher flows, the IICS model assigns less amount of effective green to each phase
(see the last row of panels in Fig. 7). This reflects the increase in the likelihood that
multiple phases would claim the right-of-way simultaneously as flow intensifies.
•The IICS algorithm also allocates more green for higher communication distances
to guarantee serving incoming vehicles. This trend is less noticeable for higher flow
as the conflicting movements are more likely to prevent green extensions.
4.2. Comparison to VISSIM
In order to compare the proposed IICS framework with state-of-the-art intersection
control, we model the same intersection under fully-actuated signal control in VISSIM.
To keep the same basis for comparison, the 15-minute simulations in VISSIM: (1) have
the same incoming flows and arrival distributions; (2) collect travel time information at
distances equal to the detection range in IICS; (3) use the same saturation headways at
the stop bar. The VISSIM implementation differs from the IICS model in terms of: (1)
a fully actuated logic—using loop detectors for all incoming lanes; (2) traffic consists of
only conventional vehicles.
For the calibration process, only a few parameters were adjusted. The default num-
ber of observed vehicles and the look ahead distance from the car-following model were
increased. Those variations allow for a smoother simulation and a model closer to an au-
tomated environment where vehicles will gather more information from the surroundings
14
0 100 200 300 400 500 600 700 800 900
time(s)
0
10
20
30
40
50
60
70
80
90
throughput(veh)
ArrivalandDepartureCurvesforLane3
Departures
Arrivals
Figure 6: Cumulative arrival and departure curves after 15 minutes of simulation (Notice departures
occur at the stop bar while arrivals occur at the detection distance, in this case 1000 feet far from the
stop bar.)
than actual drivers, even though the actual model only simulates conventional vehicles.
Fig. 8 shows a snapshot of the fully actuated intersection control implemented in VISSIM.
Fig. 9a compares the average travel time per mile under IICS and fully actuated
control strategy. The following can be observed: (1) The proposed IICS strategy leads
to lower average travel times per mile compared to fully actuated control with all con-
ventional vehicles (2) The rate of improvement increases as the saturation headway de-
creases, AV penetration rate increases, or average flow increases, Fig. 10. Our enhanced
adaptive strategy made more frequent switches of right-of-way—using trajectories infor-
mation—under higher flows, as shown in Fig. 9b.
4.3. Practical Considerations for Implementation
The term detection range refers to the farthest center-lane distance from each lane's
stop bar that roadside units sense a vehicle's arrival. While present-day technology limits
the maximum detection range, safety measures necessitate a minimum for the control
algorithm to function in a timely manner. This section estimates the minimum detection
range based on vehicle arrival information, deceleration capability, maximum crossing
speed, and algorithm's computation time.
We indicate serving time ∆tserve as the time gap between detecting an automated
vehicle and the time the vehicle is ready to follow a trajectory. Assuming the AV main-
tains constant speed and receives no trajectory, ∆tserve, it travels a portion of detection
range based on the speed and serving time. After subtracting the uncontrolled traveled
distance (Fig. 11a), the remaining distance should be enough for the vehicle to safely
decelerate. Eq. 14 yields the minimum detection range to address the safe deceleration
problem:
ddet ≥v0∆tserve +v2
c−v2
0
2amax−(14)
Where:
15
500 3000
DetectionRange(f..
AVRatio
0.3000
0.4000
0.6000
0.8000
1.0000
100 200 300 400
averagelow(veh/hr/ln)
0
100
200
averagetraveltime(sec)
SaturationHeadway=1.0sec
100 200 300 400
averagelow(veh/hr/ln)
0
100
200
averagetraveltime(sec)
SaturationHeadway=1.5sec
100 200 300 400
averagelow(veh/hr/ln)
0
100
200
averagetraveltime(sec)
SaturationHeadway=2.0sec
100 200 300 400
averagelow(veh/hr/ln)
0
50
100
150
averagetraveltimedelay(sec)
100 200 300 400
averagelow(veh/hr/ln)
0
50
100
150
averagetraveltimedelay(sec)
100 200 300 400
averagelow(veh/hr/ln)
0
50
100
150
averagetraveltimedelay(sec)
100 200 300 400
averagelow(veh/hr/ln)
5
10
15
averageeffectivegreen(sec)
100 200 300 400
averagelow(veh/hr/ln)
5
10
15
averageeffectivegreen(sec)
100 200 300 400
averagelow(veh/hr/ln)
5
10
15
averageeffectivegreen(sec)
Figure 7: Sensitivity analysis of results for 3000 scenarios (panels in same column associate with same
saturation headway; panels in same row associate with same measure of effectiveness on the vertical axis;
AV ratio: Automated/Connected Vehicle ratio in the traffic stream, the rest to be conventional vehicles.)
ddet the feasible detection range (in ft)
v0the automated vehicle's speed at the detection range (in ft/s)
vcthe maximum crossing speed at the stop bar (in ft/s)
amax−the maximum deceleration rate (in ft/s2)
∆tserve the time delay to compute, and transmit AV's trajectory.
Eq. 14 shows that the required detection range increases with initial speed and the
time latency, see Fig. 11. For the current implementation of the proposed algorithm, the
time latency is lower than a tenth of a second which makes it functional for very short
detection ranges as low as 200 feet.
5. Conclusions and Recommendations
We developed a modeling framework (IICS) to integrate AVs with signalized intersec-
tion operations. The IICS model adjusts the signalization and trajectory of automated
16
Figure 8: Near undersaturated flow threshold, the implemented fully-actuated signal control VISSIM
fails serving all conventional vehicles without queue formation.
vehicles on a real-time basis to minimize total travel time delay. The method incorporates
the following factors into the decision-making process:
•Vehicle arrival information
–Traffic stream composition (e.g. automated versus conventional ratio)
–Individual vehicle
∗Spatial information (e.g. speed and location of an entering vehicle)
∗Attributes (e.g. acceleration/deceleration capabilities)
–Flow fluctuation (e.g. randomness of incoming vehicles in each lane)
•Phase plan (e.g. Serving maximum movements without merge or crossing conflicts)
•Speed limits (e.g. the maximum allowable speed near an intersection, and the
maximum crossing speed at the stop bars)
The proposed algorithm prevented queue formation for undersaturated conditions,
jointly optimized signalization and trajectories of automated vehicles, and utilized both
connectivity and programmability of AVs. The implementation also made decisions in a
fraction of a second suitable for real-time application.
Several assumptions limit the scope of this study and left unanswered questions for
future research. The process turns unstable for oversaturated conditions as queue forma-
tion becomes inevitable. The situation requires a more rigorous signal control logic that
considers residual vehicles at the end of red intervals.
Acknowledgment
This material is based upon work supported by the National Science Foundation (un-
der Grant No. 1446813, titled: Traffic Signal Control with Connected and Autonomous
Vehicles in the Traffic Stream).
References
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17
0 500 1000 1500 2000
averagetravel timepermilebyVISSIM(sec/mile)
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500
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2000
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0 10 20 30 40
ATTpermilebyVISSIM(min/mile)
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2.042
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2.059
1.776
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s=2.0sec,lowin[50,150]veh/hr/ln
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ATTpermilebyVISSIM(min/mile)
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ATTpermilebyIICS(min/mile)
2.514
1.996
2.514
s=1.0sec,lowin(150,250]veh/hr/ln
0 10 20 30 40
ATTpermilebyVISSIM(min/mile)
0
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30
40
ATTpermilebyIICS(min/mile)
2.527
2.028
2.527
s=1.5sec,lowin(150,250]veh/hr/ln
0 10 20 30 40
ATTpermilebyVISSIM(min/mile)
0
10
20
30
40
ATTpermilebyIICS(min/mile)
2.528
2.125
2.528
s=2.0sec,lowin(150,250]veh/hr/ln
0 10 20 30 40
ATTpermilebyVISSIM(min/mile)
0
10
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30
40
ATTpermilebyIICS(min/mile)
2.898
2.126
2.898
s=1.0sec,lowin(250,350]veh/hr/ln
0 10 20 30 40
ATTpermilebyVISSIM(min/mile)
0
10
20
30
40
ATTpermilebyIICS(min/mile)
2.929
2.192
2.929
s=1.5sec,lowin(250,350]veh/hr/ln
0 10 20 30 40
ATTpermilebyVISSIM(min/mile)
0
10
20
30
40
ATTpermilebyIICS(min/mile)
3.035
2.431
3.035
s=2.0sec,lowin(250,350]veh/hr/ln
0 10 20 30 40
ATTpermilebyVISSIM(min/mile)
0
10
20
30
40
ATTpermilebyIICS(min/mile)
22.32
2.426
22.32
s=1.0sec,lowin(350,450]veh/hr/ln
0 10 20 30 40
ATTpermilebyVISSIM(min/mile)
0
10
20
30
40
ATTpermilebyIICS(min/mile)
21.27
3.426
21.27
s=1.5sec,lowin(350,450]veh/hr/ln
0 10 20 30 40
ATTpermilebyVISSIM(min/mile)
0
10
20
30
40
ATTpermilebyIICS(min/mile)
21.28
7.98
21.28
s=2.0sec,lowin(350,450]veh/hr/ln
AVRatio
0.30-0.50
0.50-0.75
0.75-1.00
Figure 10: Average Travel Time per mile compared between IICS and fully-actuated signal control for
conventional vehicles in VISSIM (panels in same column associate with same saturation headway; Dashed
lines show average values; Panels in same row associate with same flow spectrum; sto be the saturation
headway at the stop bar.)
19
ddet
Time
Distance
Δtserve
(a) The remaining distance to control the trajectory
of an automated vehicle depends on initial speed, ser-
vice time ∆tserve , detection distance ddet, deceleration
rate, and maximum crossing speed at the stop bar.
35 40 45 50 55 60
0
5
10
15
20
25
30
V0(
mph
)
Δtserve (sec)
ddet (ft)
500
1000
1500
2000
2500
(b) Feasible detection range increases
with service delay ∆tserve, and arrival
speed V0(other parameters: decelera-
tion rate is -15 ft/s2, crossing speed is
40 mph).
Figure 11
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