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Stability Analysis of Connected and Automated Vehicles
to Reduce Fuel Consumption and Emissions
Yanyan Qin1; Hao Wang2; and Bin Ran3
Abstract: Obtaining an optimal stability condition is very important to benefit traffic flow operations for a mix of connected and automated
vehicles (CAVs) and regular vehicles. In view of multiple spatial anticipations of CAV car-following models, this paper presents a stability
analysis method for mixed CAV flow from the perspective of the uniform local platoon. Transfer function theory was used to derive the
stability criterion of the uniform local platoon, based on which a stability chart of equilibrium speeds and CAV feedback coefficients was
calculated. Numerical simulations were also performed on a segment of highway with an on-ramp using car-following models to evaluate the
impacts of the stability analysis on fuel consumption and emissions [carbon monoxide (CO), hydrocarbons (HC), and nitrogen oxides
(NOX)]. The stability chart indicates that by controlling CAV feedback coefficients, the optimal stability condition can be obtained, in which
the uniform local platoon remains stable for all driving speeds. Moreover, the stability analysis method can reduce fuel consumption and
traffic emissions. DOI: 10.1061/JTEPBS.0000196.© 2018 American Society of Civil Engineers.
Author keywords: Connected and automated vehicle; Stability analysis; Fuel consumption; Traffic emissions; Transfer function theory;
Car-following model.
Introduction
In recent years, traffic emissions have become a key concern in
transportation (Tan et al. 2017). In China, about 28.8% of total
nitrogen oxide (NOX) emissions were caused by the transportation
sector, of which 91.6% were vehicle emissions (Ministry of
Environmental Protection of the People’s Republic of China
2014). Similarly, transportation produced about 32.7% of the total
greenhouse gas in the United States (DOE 2012). Reducing fuel
consumption saves energy and decreases traffic emissions. Fortu-
nately, the development of intelligent vehicular systems provides
new potential for reducing fuel consumption and traffic emissions.
The adaptive cruise control (ACC) vehicle was first developed
based on vehicular detection equipment, following which the co-
operative adaptive cruise control (CACC) vehicle further reduced
desired intervehicle distance using vehicle-to-vehicle (V2V) com-
munication (Shladover et al. 2015). From the perspective of a con-
nected environment, the connected and automated vehicle (CAV) is
attracting increasing attention of researchers (Mahmassani 2016).
Among studies on CAV impacts (Talebpour and Mahmassani 2016;
van den Berg and Verhoef 2016;Rios-Torres and Malikopoulos
2017;Shladover 2018), fuel consumption and traffic emissions
were have been relatively rarely investigated. Lee and Park
(2012) proposed a cooperative vehicle intersection control (CVIC)
algorithm. Based on simulations, it indicates that the CVIC could
reduce carbon dioxide (CO2) by 44% and also save fuel consump-
tion by 44%. Lin et al. (2017) presented a novel coordination
method for connected vehicle traffic management. The method
saved 22.1%–52% of fuel consumption. Fuel optimization systems
were studied for reducing fuel consumption (van der Voort et al.
2001;Brundell-Freij and Ericsson 2005;Wu et al. 2011). Also,
some green driving strategies were proposed to save fuel consump-
tion and reduce emissions (Shladover et al. 2009;Yang and Jin
2014;Grumert et al. 2015;HomChaudhuri et al. 2016;Wan
et al. 2016). An eco-driving system for CAV was also developed
by Jiang et al. (2017), in which fuel consumption benefits ranged
from 2.02% to 58.01% and CO2emissions benefits ranged from
1.97% to 33.26%.
However, little research has been conducted from the view of
analyzing traffic flow stability. Stability is a core factor affecting
traffic flow operations, such as fuel consumption and emissions,
and has been studied since the 1950s (Chandler et al. 1958;Herman
et al. 1959). Generally speaking, there are two types of stability:
local and string (Treiber and Kesting 2013). string stability is
the focus of this paper. While much literature has analytically in-
vestigated car-following model stability (Wilson and Ward 2011;
Treiber and Kesting 2013;Sau et al. 2014), there have been few
studies on stability analysis of mixed traffic flow (Holland 1998;
Ward 2009;Mahmassani 2016;Talebpour and Mahmassani
2016). Additionally, stability methods for mixed flow used in these
studies cannot be directly applied to the case in which CAV and
regular vehicles are mixed. The main reason is that the CAV
can monitor multiple vehicles ahead and pairs of successive
vehicles cannot describe the stability condition of mixed vehicu-
lar flow. Hence, the idea of a local platoon should be considered
to deal with this problem (Ge and Orosz 2014;Qin and Wang
2018).
In view of the shortcomings of previous studies, this paper
presents a stability analysis of vehicular flow mixed with CAV,
thereby reducing fuel consumption and emissions. This paper is
organized as follows: the uniform local platoon for stability analy-
sis of CAV mixed flow is introduced. Then a stability analysis
is conducted using transfer function theory. Next, numerical
1Ph.D. Candidate, School of Transportation, Jiangsu Key Laboratory of
Urban ITS, Southeast Univ., Nanjing 210096, China. Email: qinyanyan@
seu.edu.cn
2Professor, School of Transportation, Jiangsu Key Laboratory of Urban
ITS, Southeast Univ., Nanjing 210096, China (corresponding author).
Email: haowang@seu.edu.cn
3Professor, Dept. of Civil and Environment Engineering, Univ.
of Wisconsin–Madison, Madison, WI 53706. Email: bran@wisc.edu
Note. This manuscript was submitted on November 14, 2017; approved
on June 13, 2018; published online on August 23, 2018. Discussion period
open until January 23, 2019; separate discussions must be submitted
for individual papers. This paper is part of the Journal of Transportation
Engineering, Part A: Systems, © ASCE, ISSN 2473-2907.
© ASCE 04018068-1 J. Transp. Eng., Part A: Syst.
J. Transp. Eng., Part A: Systems, 2018, 144(11): 04018068
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simulations are performed based on car-following models to evalu-
ate reductions in fuel consumption and emissions, such as carbon
monoxide (CO), hydrocarbons (HC), and NOX. Finally, some
conclusions are drawn.
Uniform Local Platoon
There are two types of vehicles in mixed traffic flow, the CAV and
the regular vehicle, in which longitudinal movement is the concern
in this paper. These two vehicle types are randomly distributed in a
single lane. Suppose that the regular vehicle can broadcast its travel
information, such as instantaneous speeds and accelerations. Then
one CAV can monitor multiple vehicles ahead. Because of the
CAV’s multiple feedbacks and its random spatial distribution, it
is difficult to analyze the stability of the entire mixed flow directly
(Ge and Orosz 2014;Qin and Wang 2018). Therefore, the uniform
local platoon is considered as the study objective, as shown in
Fig. 1. In the platoon, one tail CAV monitors mregular vehicles
ahead. Regular vehicles are usually unstable and amplify perturba-
tions spreading from downstream. Hence, the tail CAV receives
messages from multiple regular vehicles ahead and is designed
to smooth these perturbations.
The CAV in Fig. 1belongs to another local platoon upstream.
In view of vehicle spatial distribution randomness, the value of min
each local platoon may vary. In particular, the value of mcan be
considered 0, which means that two successive CAVs appear in
the mixed traffic flow. In this case, the tail CAV can monitor multi-
ple vehicles ahead. In view of control complexity and the uniform
requirement for the local platoon, the tail CAV may only monitor
the preceding CAV. In this case, this special local platoon consists
of the tail CAV and the preceding CAV. In addition, the number of
vehicles that the tail CAV can monitor is limited by the V2V com-
munication range. When mexceeds this maximum value, the tail
CAV cannot receive information from regular vehicles ahead that
are out of range. Although these regular vehicles may be unstable in
the mixed traffic flow, the perturbation has to be mitigated when it
spreads through the uniform local platoon upstream. Moreover, the
value of mis apt to satisfy the V2V communication range, with the
increase in CAV penetration rates. In any case, what is important is
that the mixed vehicular flow will have optimal stability when each
local platoon is maintained as stable.
Stability Analysis
Car-Following Models
Car-following models are essential for analyzing traffic flow stabil-
ity. In the case of regular vehicles, many such models have been
proposed (Newell 1961;Bando et al. 1995;Brackstone and
McDonald 1999;Treiber et al. 2000;Jiang et al. 2001;Newell
2002;Chen et al. 2012;Ardakani and Yang 2016;Wang et al.
2017). The optimal velocity model (OVM) (Bando et al. 1995)
is used in this paper as the surrogate model for regular vehicles
because of its extensive application (Ge and Orosz 2014;Wang
et al. 2017). However, it should be remembered that the method
proposed here can be also applied to other car-following models.
The OVM is written as
˙
vnðtÞ¼κ½VðhnðtÞÞ −vnðtÞ ð1Þ
where ˙
vnðtÞ= acceleration of vehicle nat time t;vnðtÞ= speed;
hnðtÞ= spacing between vehicle nand its preceding vehicle
n−1;κ= sensitivity parameter; and VðhnðtÞÞ = optimal speed
function with respect to spacing.
The exponential optimal speed function was first proposed by
Newell (1961) and is defined as
VðhnðtÞÞ¼v01−exp−α
v0
ðhnðtÞ−s0Þ ð2Þ
where v0= free-flow speed; s0= jam spacing; and α= parameter
positively related to the wave speed in a traffic jam (Del Castillo
and Benitez 1995).
Based on Wang et al. (2012), the calibration results of the OVM
are as follows: v0¼33.0m=s, κ¼0.700 s−1,α¼0.999 s−1,
and s0¼1.62 m.
The CAV car-following model is usually developed by taking
multiple feedbacks into consideration. These feedbacks can be po-
sition, speed, or acceleration. The electronic throttle angle (ETA)
feedback (Ioannou and Xu 1994;Li and Ioannou 2004) is em-
ployed for the CAV car-following model because it is an integration
of speed and acceleration and has the potential to be installed in real
vehicles in the future (Baskar et al. 2011). The ETA feedback is
written as follows:
˙
vnðtÞ¼−bðvnðtÞ−vÞþcðθnðtÞ−θÞð3Þ
where θnðtÞ= ETA of vehicle nat time t;vand θ= equilibrium
speed and equilibrium angle, respectively; and band c= sensitivity
parameters, whose values can be 0.8 and 0.27, respectively
(Li et al. 2016).
Feedback information is usually added to form the CAV car-
following model (Ge and Orosz 2014). Based on previous studies
(Li et al. 2016;Qin and Wang 2018) with ETA feedbacks for CAV,
the car-following control of CAV is modeled as follows:
˙
vnðtÞ¼κ½VðhnðtÞÞ −vnðtÞ þ X
m
i¼1
γiðθn−iðtÞ−θnðtÞÞ ð4Þ
where κhas the same meaning as in Eq. (3); m= maximum number
of vehicles that the CAV can monitor; and γi= feedback coefficient
related to the ith vehicle ahead.
The feedback coefficient γiin Eq. (4) is considered to be con-
trolled for stable vehicular flow depending on all possible vehicle
speeds. The parameter κshould be calibrated using actual obser-
vation data—that is, the microcosmic trajectories of vehicles.
However, CAVobservation data are not yet available. Here we con-
sider that κhas the same value that it has in Eq. (3): κ¼0.700 s−1.
In this way, determining the parameter values of CAV car-following
models is also the same as in previous studies (Ge and Orosz 2014;
Qin and Wang 2018), taking into account the missing CAV obser-
vation data.
Analysis Method
Previous methods (Holland 1998;Ward 2009;Mahmassani 2016;
Talebpour and Mahmassani 2016) cannot be directly used to ana-
lyze the stability of the uniform local platoon, where the tail CAV
Tail CAV
# n
Re gul ar vehicl e
# n-1
Regular vehicle
# n-m
Feedback
#1
Feedback
#m
CAV
# n-m-1
Fig. 1. Uniform local platoon.
© ASCE 04018068-2 J. Transp. Eng., Part A: Syst.
J. Transp. Eng., Part A: Systems, 2018, 144(11): 04018068
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monitors multiple regular vehicles ahead. In this paper, transfer
function theory is employed as the analysis method. Transfer func-
tion theory is a favorite in theoretical analysis for control systems.
Hence, the uniform local platoon is considered a control system, in
which the perturbation of the head regular vehicle is the input and
that of the tail CAV is the output. In addition, speed perturbation has
been proven to be better for stability analysis and has been widely
used in previous studies (Konishi et al. 2000;Naus et al. 2010;
Treiber and Kesting 2013;Ge and Orosz 2014;Milanés and
Shladover 2014;Milanés et al. 2014). Therefore, the speed pertur-
bation transfer function of the uniform local platoon should be
calculated. To deal with this, speed perturbation transfer functions
spreading from the immediately preceding vehicle to the regular
vehicle and the tail CAV are calculated first, respectively.
Before calculating the transfer function, the speed and spacing
perturbations are defined as follows:
~
vnðtÞ¼vnðtÞ−v
~
hnðtÞ¼hnðtÞ−hð5Þ
where ~
vnðtÞ= speed perturbation with respect to equilibrium speed
v; and ~
hnðtÞ= spacing perturbation with respect to equilibrium
spacing h.
The equilibrium spacing his considered the function of
equilibrium speed v, denoted by hðvÞ. Based on the optimal speed
function used in Eq. (2), hðvÞis calculated as
hðvÞ¼s0−v0
αln1−v
v0ð6Þ
Regular Vehicle Transfer Function
We linearize the car-following model of regular vehicles in Eq. (1)
using Taylor expansion in the equilibrium state. Thus, the optimal
speed function in Eq. (1) is linearized as follows:
VðhnðtÞÞ ¼ VðhÞþV0ðhÞðhnðtÞ−hÞð7Þ
Because VðhÞ¼vin the equilibrium state, Eq. (7)is
rewritten as
VðhnðtÞÞ¼V0ðhÞðhnðtÞ−hÞþvð8Þ
Eq. (8) is substituted into Eq. (1) to obtain the linearization
results
˙
vnðtÞ¼κV0ðhÞðhnðtÞ−hÞ−κðvnðtÞ−vÞð9Þ
where V0ðhÞ= derivative of the optimal speed function in Eq. (2)
with respect to spacing about the equilibrium state. It can be calcu-
lated as
V0ðhÞ¼αexp−α
v0
ðhðvÞ−s0Þð10Þ
Eq. (5) is substituted into Eq. (9) to obtain the linear differential
equation about the perturbations
˙
~
vnðtÞ¼κV0ðhÞ~
hnðtÞ−κ~
vnðtÞð11Þ
Taking the Laplace transform in Eq. (5) with zero initial con-
ditions, we obtain the following relationship of the two equations
in Eq. (5):
~
HnðsÞ¼
~
Vn−1ðsÞ−~
VnðsÞ
sð12Þ
where ~
HnðsÞ= Laplace transform of the spacing perturbation
of vehicle n~
hnðtÞ;~
VnðsÞ= Laplace transform of the speed
perturbation of vehicle n~
vnðtÞ; and ~
Vn−1ðsÞ= speed perturbation
of the preceding vehicle n−1; and sstands for Laplace domain.
In Eq. (11), the Laplace transform is taken with zero initial
conditions and Eq. (12) is substituted into the calculation. This
calculation finally yields the transfer function GR(s) of the speed
perturbation spreading from the immediately preceding vehicle to
the regular vehicle
GRðsÞ¼ κV0ðhÞ
s2þκsþκV0ðhÞð13Þ
CAV Transfer Function
The CAV car-following model in Eq. (4) can also be linearized at
the equilibrium state. Substituting Eq. (5) into the linearized result-
ing equation to obtain the differential equation about perturbations
˙
~
vnðtÞ¼κV0ðhÞ~
hnðtÞ−κ~
vnðtÞþ1
cX
m
i¼1
γið
˙
~
vn−iðtÞ−
˙
~
vnðtÞÞ
þbð~
vn−iðtÞ−~
vnðtÞÞÞ ð14Þ
Then the Laplace transform is also taken in Eq. (14) to calculate
the transfer function GC(s) of the speed perturbation spreading
from the immediately preceding vehicle to the tail CAV
GCðsÞ¼
κV0ðhÞþs2þbs
cPm
i¼1γihκV0ðhÞ
s2þκsþκV0ðhÞiði−1Þ
s2þκsþκV0ðhÞþs2þbs
cPm
i¼1γi
ð15Þ
As noted before, the speed perturbation of the head regular ve-
hicle in the uniform local platoon, shown in Fig. 1, is the input,
whereas the speed perturbation of the tail CAV is the output. There-
fore, the transfer function GðsÞof the speed perturbation passing
though the uniform local platoon can be obtained based on Eqs. (13)
and (15). It follows that
GðsÞ¼GCðsÞ½GRðsÞðm−1Þ
¼2
4
κV0ðhÞþs2þbs
cPm
i¼1γihκV0ðhÞ
s2þκsþκV0ðhÞiði−1Þ
s2þκsþκV0ðhÞþs2þbs
cPm
i¼1γi
3
5
×κV0ðhÞ
s2þκsþκV0ðhÞðm−1Þ
ð16Þ
Let s¼jΩ,Ω≥0to transfer the transfer function GðsÞin
Eq. (16) from the Laplace domain into the frequency domain.
Although the control logits of CAV and regular vehicles are differ-
ent, the property of vehicles is constant regardless of vehicle type.
This means that GCðsÞand GRðsÞhave the same range in the
frequency domain (Ge and Orosz 2014;Qin and Wang 2018).
Then the uniform local platoon is stable if the following condition
is satisfied:
jGðjΩÞj ¼
κV0ðhÞþ−Ω2þjΩb
cPm
i¼1γihκV0ðhÞ
κV0ðhÞ−Ω2þjΩκiði−1Þ
κV0ðhÞ−Ω2þjΩκþ−Ω2þjΩb
cPm
i¼1γi
×
κV0ðhÞ
κV0ðhÞ−Ω2þjΩκ
ðm−1Þ
<1ð17Þ
where j·j= transfer function amplitude in the frequency domain.
Based on Eqs. (6) and (10), the derivative V0ðhÞis related only
to equilibrium speed v. Thus, it can be found that the stability cri-
terion of the uniform local platoon presented in Eq. (17) is deter-
mined by the equilibrium speed vand the feedback coefficient γi.
© ASCE 04018068-3 J. Transp. Eng., Part A: Syst.
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Not only is this property be used to theoretically analyze the
stability situation with respect to equilibrium speeds and feedback
coefficients; it is also useful for stable vehicular flow by controlling
feedback coefficients to obtain the stable situation for any driv-
ing speed.
Analysis Results
By placing the parameters of car-following models into the stability
criterion of Eq. (17), the stability condition of the uniform local
platoon can be calculated. As noted before, the V2V communica-
tion has a limit, which determines the maximum number of vehicles
that the tail CAV can monitor—that is, the maximum value of feed-
back m. Based on previous studies (Ge and Orosz 2014;Milanés
and Shladover 2014), it is appropriate and reliable that mcan be 1,
2, and 3 for any driving speed with the control technology consid-
ered in this paper.
m1
When m¼1, the uniform local platoon contains two vehicles: the
tail CAV and the preceding regular vehicle. This means that there is
only one feedback coefficient γ1in the stability criterion of
Eq. (17). Then the stability situation of the uniform local platoon
with respect to equilibrium speed vand feedback coefficient γ1is
calculated following Eq. (17). The calculation result is given in
Fig. 2, which shows the stability chart of the uniform local platoon.
The stability chart is divided into two regions, in which the lower
left region represents the stable condition; the upper right region,
the unstable condition.
When the feedback coefficient γ1is 0, the CAV car-following
model degenerates to that of the regular vehicle. In that case,
the critical velocity that distinguishes stability or instability is
21.5m=s based on the calculation result in Fig. 2. This means that
the regular vehicle is stable at speeds of 21.5–33.0m=s and unsta-
ble at other speeds. Moreover, the uniform local platoon is stable
for any value of feedback coefficient γ1when the speed exceeds
21.5m=s. More concerning, however, is that the uniform local pla-
toon should have large speed ranges to maintain stability. Thus, the
feedback coefficient γ1should be controlled to satisfy this concern.
Fig. 2shows that the uniform local platoon can be stable for any
speed when γ1is more than 0.65. Therefore, stability can be
obtained if γ1is controlled to be in the range [0.65, 1].
As mentioned previously, the tail CAV monitors a preceding
CAV when m¼0, which means that two successive CAVs appear.
In this special case, the local platoon contains two successive
CAVs, of which the tail also has a feedback coefficient γ1. There-
fore, the difference in local platoons between m¼1and m¼0is
the preceding vehicle type. This means that the tail CAV monitors
another CAV ahead if m¼0, whereas it monitors a preceding regu-
lar vehicle when m¼1. Generally speaking, because the CAV has
better stability than the regular vehicle in the same condition, the
special local platoon with m¼0is also stable under the stability
analysis result for m¼1—that is, γ1∈½0.65;1. In addition, for
the transfer function of local platoons, this paper defines the per-
turbation of the head vehicle as the input and that of the tail CAVas
the output. The input of perturbation does not depend on the type of
head vehicle of the local platoons because it is usually considered
the input generated in control systems (Naus et al. 2010). Hence,
the transfer functions of the local platoons with m¼0and m¼1
are in fact the same because they do not depend on the type of head
vehicle in the local platoons (Qin and Wang 2018). Based on this,
the stability analysis result with m¼0is that shown in Fig. 2.
m2
For m¼2, the tail CAV monitors two regular vehicles ahead in the
uniform local platoon. Thus, there are two feedback coefficients, γ1
and γ2, which are to be controlled. The analysis result for γ1is
known for m¼1and substituted into the stability calculation of
the uniform local platoon with respect to feedback coefficient γ2
and equilibrium speed v. The results are shown in Fig. 3, where
γ1gives three values of 0.65, 0.825, and 1 based on its analysis
range [0.65, 1]. It can be found that the larger value of γ1promotes
better stability in the uniform local platoon with m¼2, which
means that γ2will have larger ranges for the stable local platoon
at any speed. For the sake of sufficiency, the range [0.325, 1] is
considered the analysis result for γ2. Thus, the uniform local
platoon with m¼2will always be stable for any speed given
any values in the analysis ranges of both γ1and γ2.
m3
For m¼3, the tail CAV monitors three regular vehicles ahead in
the uniform local platoon and there are three feedback coefficients:
γ1,γ2, and γ3. The analysis results for γ1and γ2are used to cal-
culate the stability chart of the uniform local platoon with respect to
feedback coefficient γ3and equilibrium speed v. The calculation
results are shown in Fig. 4, where the stability situation becomes
better with the increase in both γ1and γ2.Fig.4(b) shows that the
uniform local platoon is stable for any values of vand γ3when
γ1¼0.65 and γ2¼1. Also, for the sake of sufficiency, the analysis
result for γ3is considered to be in the range [0.22, 1], based on
which the uniform local platoon with m¼3will always be stable
for any speed given any values in the analysis ranges of γ1,γ2,
and γ3.
Reductions in Fuel Consumption and Emissions
In this section, impacts of the uniform local platoon stability analy-
sis on the studied fuel consumption and emissions (CO, HC, and
NOX) are evaluated. Although some experimental tests of con-
nected vehicle platoons, such as CACC platoons, have been suc-
cessfully performed, they have all been small-scale (Rajamani et al.
2000;Rajamani and Shladover 2001;Geiger et al. 2012;Milanés
and Shladover 2014;Milanés et al. 2014). At present, it is difficult
to conduct large-scale vehicular experiments for evaluating fuel
consumption and emissions under different CAV penetration rates
(Mahmassani 2016). Therefore, simulations are necessary and im-
portant (Wu et al. 2011;Lee and Park 2012;Yang and Jin 2014;
Tang et al. 2015).
Fig. 2. Stability chart of the uniform local platoon with m¼1.
© ASCE 04018068-4 J. Transp. Eng., Part A: Syst.
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Evaluating Indicator
There are many fuel consumption and emissions models (Ferreira
1985;Barth et al. 2000;Hausberger et al. 2003). The VT-Micro
model (Ahn et al. 2002), employed in this paper because of its rel-
atively simple structure (Li et al. 2014;Tang et al. 2015), evaluates
each vehicle’s fuel consumption and emissions during the entire
simulation in the car-following models. The model equation is
written as follows:
lnðMOEeÞ¼X
3
i¼0X
3
j¼0
ke
i;jvi
nð˙
vnÞjð18Þ
where MOEe¼nth vehicle’s fuel consumption and emissions rate;
i= speed power; j= acceleration power; vn= instantaneous speed
of nth vehicle; ˙
vn¼nth vehicle’s instantaneous acceleration; and
ke
i;j= regression coefficient at speed power iand acceleration
power j.
Eq. (16) calculates each vehicle’s fuel consumption and CO,
HC, and NOXemissions if different regression coefficients ke
i;j
are defined (Ahn et al. 2002). Ahn et al.’s(2002) calibration values
for the corresponding regression coefficients ke
i;jhave been widely
used (Wu et al. 2011;Li et al. 2014;Tang et al. 2015), and are
employed in this paper. The input to the VT-Micro model is the
microcosmic simulation trajectory data: vehicle accelerations/
speeds over simulation time. Then the model calculates emission
impacts based on each simulation result. The simulation results for
different CAV penetration rates can be obtained when the simula-
tions are performed for each CAV penetration rate. Therefore,
based on Eq. (18), total fuel consumption and emissions for all ve-
hicles throughout the simulation can be obtained given different
CAV penetration rates. Then the homogenous regular vehicles
and the mixed traffic flow of different CAV penetration rates
can be compared.
Simulation Results
A highway with an onramp was selected as the simulation segment:
a segment of a hypothetical one-lane highway with an on-ramp lo-
cated in the middle (Mahmassani 2016;Talebpour and Mahmassani
2016). The length of the simulation segment was 6.5 km, the main-
line flow was 1,800 vehicles per hour, and the on-ramp flow was
360 vehicles per hour. All parameters needed for simulation were
set according to recent studies (Mahmassani 2016;Talebpour and
Mahmassani 2016).
The numerical simulation was performed based on car-
following models of the CAV and the regular vehicle using different
CAV penetration rates. Additionally, the stability analysis results
for the uniform local platoon given previously were employed.
The stability analysis gave the control ranges for the corresponding
CAV feedback coefficients. However, the feedback coefficient val-
ues were fixed as parameters of the CAV car-following model in the
Fig. 3. Stability chart of the uniform local platoon with m¼2: (a) γ1¼0.65; (b) γ1¼0.825; and (c) γ1¼1.
© ASCE 04018068-5 J. Transp. Eng., Part A: Syst.
J. Transp. Eng., Part A: Systems, 2018, 144(11): 04018068
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simulations. Without loss of generality, the resulting middle values
for the optimal control ranges for the corresponding feedback
coefficients were γ1¼0.825,γ2¼0.662, and γ3¼0.61.
Simulation time was 1 hour and the first 5 minutes were for
warm-up. In addition, the simulation time step was 0.1 s. The
CAV randomly monitored one, two, or three vehicles ahead based
on the random spatial distribution of vehicles in the mixed traffic
flow. The tail CAV also monitored one preceding CAV in the case of
two successive CAVs. In order to remove random errors in the sim-
ulation, each simulation was repeated for three times. Then the
average value was used to evaluate reductions in fuel consumption
and emissions with increases in CAV penetration rate. The results
are shown in Table 1, in which the percentage reduction is calcu-
lated for the mixed traffic flow with different CAV penetration rates
compared with regular vehicular flow: 0% CAV penetration rate.
From Table 1, it is seen that the stability analysis led to reductions
in fuel consumption and emissions. Fuel consumption and CO, HC,
and NOXemissions decreased with increases in CAV penetration
rate. Moreover, the CAV flow reduced fuel consumption, CO, HC,
and NOXby 46.23%, 37.50%, 33.33%, and 44.49%, respectively,
compared with regular vehicle flow. The fuel consumption and
emissions reductions summarized in Table 1benefited the entire
system of CAVs and regular vehicles. They indicate that the stabil-
ity analysis of the uniform local platoon can decrease fuel con-
sumption and emissions for mixed vehicular flow on a highway
with an on-ramp.
For better visualization, Fig. 5shows average reductions with
CAV penetration growth based on the results in Table 1. It can
be seen that the decreases in fuel consumption and emissions
gradually slow with as the CAV penetration rate increases.
Although the VT-Micro model (Ahn et al. 2002) is very popular
and helpful (Wu et al. 2011;Li et al. 2014;Tang et al. 2015)
in calculating the influence on fuel consumption and emissions us-
ing microcosmic simulation trajectories—that is, instantaneous
accelerations/speeds of vehicles—different evaluating models may
Fig. 4. Stability chart of the uniform local platoon with m¼3: (a) γ1¼0.65,γ2¼0.325; (b) γ1¼0.65,γ2¼1; and (c) γ1¼1,γ2¼0.325.
Table 1. Percentage reductions in fuel consumption and emissions
CAV
penetration
rate (%)
Average reduction (%)
Fuel
consumption
CO
emission
HC
emission
NOX
emission
0— ———
10 19.43 15.91 15.83 22.16
20 26.23 21.02 20.02 26.95
30 29.81 23.86 22.42 30.54
40 33.30 27.27 24.94 33.53
50 38.02 30.68 27.34 36.53
60 40.09 32.39 29.02 38.92
70 42.64 34.66 30.70 40.84
80 44.25 35.80 31.77 42.40
90 45.47 36.93 32.49 43.29
100 46.23 37.50 33.33 44.49
© ASCE 04018068-6 J. Transp. Eng., Part A: Syst.
J. Transp. Eng., Part A: Systems, 2018, 144(11): 04018068
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result in various results. To further validate the simulation results
obtained in Table 1, we used another emission model to calculate
the percentage reduction obtained with increasing CAV penetration
rate. For the sake of simplicity, here we employed vehicle-specific
power (VSP) (Jimenez-Palacios 1998) as the second model because
it represents instantaneous tractive power per unit of vehicle mass
and so has a direct relationship with vehicle fuel consumption and
emissions (Song and Yu 2009). If road grade is assumed to be zero,
the VSP model can be written as (Jimenez-Palacios 1998;Song and
Yu 2009)
VSPnðtÞ¼vnðtÞ½1.1˙
vnðtÞþ0.132þ0.000302ðvnðtÞÞ3ð19Þ
where VSPn= value of VSP of vehicle nat time t;vnðtÞ= instanta-
neous speed of vehicle nat time t; and ˙
vnðtÞ= instantaneous accel-
eration of vehicle nat time t.
Therefore, based on the accelerations/speeds during the simula-
tion, we could calculate the average value of VSP of all vehicles
over that time via Eq. (19). The calculation results are shown in
Table 2, in which percentage reductions are calculated for different
CAV penetration rates versus 0% CAV penetration. Accordingly, it
is seen that the reduction trend is similar to that in Table 1as the
CAV penetration rate increases. We are aware that different models
may result in different influences in terms of quantitative percent-
age reductions under different CAV penetration rates. However, the
qualitative trend—that the stability analysis proposed in this paper
promotes reductions in fuel consumption and emissions—remains
constant. The simulation results should be validated using real
experimental data. Unfortunately, such data are presently missing,
and so validation must be left to future investigations.
Conclusions
The proposed stability analysis of CAV in mixed vehicular flow
was presented from the perspective of the uniform local platoon.
The analysis method can be applied to various car-following mod-
els, although the OVM was used here for regular vehicles and
multiple ETA feedbacks were considered to develop car-following
control of the CAV. The analytical stability criterion for the uniform
local platoon derived using transfer function theory was useful for
calculating a stability chart of equilibrium speeds and CAV feed-
back coefficients, thereby guiding the stability analysis by control-
ling those feedback coefficients. The stability analysis achieved the
stable condition for the uniform local platoon given any driving
speed. On this basis, the mixed vehicular flow reached the optimal
stability condition. Additionally, the impacts of the stability analy-
sis on fuel consumption and CO, HC, and NOXemissions were
evaluated using simulations, with the results indicating that the sta-
bility analysis method leads to reductions in fuel consumption and
emissions for mixed vehicular flow on a highway with an on-ramp.
The proposed stability analysis may not be applicable with low
CAV penetration rates because regular vehicles are assumed to
broadcast operating information within the limitation of the V2V
communication range. The maximum number of vehicles that the
tail CAV can monitor was set as three in this study. We might set
the minimum limit of CAV penetration rate at 25%, above which
the proposed theory might satisfy the applicable requirement.
Notably, the results here were obtained mainly based on theoretical
analysis in view of the fact that actual CAV observation data are as
yet unavailable. Therefore, the proposed method should be vali-
dated using real CAV data when available in the future.
Acknowledgments
This research was supported by the National Natural Science
Foundation of China (51478113), the National Key R&D Program
in China (2016YFB0100906), the Fundamental Research Funds for
the Central Universities and the Postgraduate Research & Practice
Innovation Program of Jiangsu Province (KYCX17_0146), and
the Scientific Research Foundation of the Graduate School of
Southeast University (YBJJ1792).
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