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From Search-for-Parking to Dispatch-for-Parking in an
Era of Connected and Automated Vehicles:
A Macroscopic Approach
Cong Zhao1; Jing Cao2; Xinyuan Zhang3; and Yuchuan Du4
Abstract: The advantage of self-relocation of connected and automated vehicles (CAVs) can eliminate heavy searching-for-parking traffic in
areas with limited parking availability. However, the floating trips will exacerbate local traffic congestion and parking competition if relocated
CAVs are not well distributed in the network. To address these issues, this paper proposes a centralized dispatching-for-parking system to
dynamically dispatch CAVs between different regions to optimize parking resource utilization and traffic distribution. A macroscopic mod-
eling approach is presented with the consideration of mixed traffic flows of human-driven vehicles (HDVs) and CAVs. The system dynamics
are modeled with the representation of the macroscopic fundamental diagram (MFD) in a multiregion road network. The objective of the
system is to minimize the total network delay, which is formulated by the framework of model predictive control (MPC). Results of
the numerical experiments in a two-region network show that the approach improves the performance of system operation and alleviates
traffic congestion and imbalance between parking supply and demand in downtown areas. The sensitivity analysis on the level of CAV
penetration reveals that the total network delay gradually decreases with the penetration increase, and HDVs benefit more from the MPC
controller. The study demonstrates the applicability and implication of the dispatching-for-parking system in an era of CAVs. DOI: 10.1061/
JTEPBS.0000640.© 2021 American Society of Civil Engineers.
Author keywords: Macroscopic fundamental diagram (MFD); Connected and automated vehicles (CAV); Searching-for-parking; Model
predictive control (MPC); Traffic congestion.
Introduction
Due to a local imbalance of parking supply and demand, drivers
have to search for available parking spots for long periods of time
or even fail, which is a perpetual problem for most large cities in the
world. Shoup (2006) found that the searching-for-parking traffic
account for 30%, and 8.1 min on average is spent for finding an
available parking spot in a city center during rush hours. Fulman
and Benenson (2021) conducted practical experiments in the Israeli
city of Bat Yam, which demonstrates that the average time of
onstreet searching-for-parking is longer than 5 or even 10 min.
The main reason for a parking search is the imbalance of parking
demand and supply in local areas, as well as the fact that drivers do
not want to park too far and then have to cruise for parking around a
circle near the destination (Arnott and Williams 2017). This excess
travel after vehicles arrive at their destinations has a significant in-
fluence on traffic congestion (Arnott and Inci 2006).
To alleviate urban parking and traffic congestion problems, vari-
ous management strategies and intelligent parking applications
have been introduced and developed in recent years. Wei and
Sun (2018) proposed a two-layer traffic assignment model for dy-
namic congestion pricing within the network, which consists of the
expressway and arterial networks. Gu et al. (2020) modeled urban
network dynamics with searching-for-parking to optimize real-time
onstreet and garage parking pricing. Cheng et al. (2018) designed a
time-limit plan for different groups of parking spots in a large park-
ing garage. The results of the case study showed that the proposed
parking management strategy decreases users’average walking
time by 25%. Meanwhile, a parking permit is also an effective and
practical parking demand management strategy for areas with
limited parking resources (Wang et al. 2020). Gurbuz et al. (2020)
calibrated and validated a beta regression total demand model to
determine the number of student parking permits and a tobit regres-
sion parking base price model for the permits of university cam-
puses based on actual operating data. Meanwhile, with the rapid
development of emerging sensors and Internet of Things (IoT)
technologies, parking guidance and information (PGI) systems
have been widely developed in large cities, and the parking variable
message sign location and display problems have been extensively
studied (Sun et al. 2016;Ni and Sun 2018). Smartphone-based
parking applications have been widely developed in recent years,
which makes it easier for drivers to find available parking spots
through parking reservations, online parking assignments, and
parking sharing (Levin 2019;Jiang et al. 2021;Liu et al. 2021;
Zhao et al. 2019). However, all these strategies and measures
1Associate Research Professor, Key Laboratory of Road and Traffic
Engineering of the Ministry of Education, Tongji Univ., Shanghai 201804,
China. ORCID: https://orcid.org/0000-0002-1017-9118. Email: zhc@tongji
.edu.cn
2Associate Research Professor, Key Laboratory of Road and Traffic
Engineering of the Ministry of Education, Tongji Univ., Shanghai 201804,
China (corresponding author). Email: jcao@tongji.edu.cn; caojingbetter@
foxmail.com
3Ph.D. Candidate, Key Laboratory of Road and Traffic Engineering of
the Ministry of Education, Tongji Univ., Shanghai 201804, China. Email:
irsths@tongji.edu.cn
4Professor, Key Laboratory of Road and Traffic Engineering of the
Ministry of Education, Tongji Univ., Shanghai 201804, China; Shanghai
Engineering Research Center of Urban Infrastructure Renewal, Shanghai
200032, China. Email: ycdu@tongji.edu.cn
Note. This manuscript was submitted on July 23, 2021; approved on
October 27, 2021; published online on December 6, 2021. Discussion per-
iod open until May 6, 2022; separate discussions must be submitted for
individual papers. This paper is part of the Journal of Transportation En-
gineering, Part A: Systems, © ASCE, ISSN 2473-2907.
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are focused on parking problems related to human-driven vehicles
(HDVs).
Connected and automated vehicles (CAVs) have the ability of
self-relocation after dropping off passengers, which may eliminate
the burden of searching-for-parking traffic near destinations with
limited parking resources. Zakharenko (2016) demonstrated how
a typical city changes with the widespread deployment of CAVs.
The study predicted that a parking belt will emerge located outside
of the commuter work zone and may accumulate as much as 97%
of all commuting CAVs to avoid occupying large amounts of the
downtown area. Harper et al. (2018) explored the travel implication
of changes for urban parking of CAVs using an agent-based sim-
ulation approach. They found that CAVs would travel an additional
5.6–6.4km=day on average with low CAV penetration and an
additional 9.0–13.5km=day on average with high CAV penetra-
tion. Millard-Ball (2019) analyzed the parking problems in an era
of CAVs. A traffic microsimulation model with a game-theoretic
framework was formulated, and the results of a case study demon-
strated that vehicle miles traveled (VMT) would increase and traffic
congestion would worsen because of the floating trips of relocated
CAVs. Furthermore, CAVs would actively generate traffic con-
gestion with each other to reduce operating costs. Above all, the
relocated behavior of CAVs blurs the boundary between static
parking and dynamic traffic, which leads to the ineffectiveness
of traditional parking management strategies.
As self-driving is an inevitable trend, new parking management
policies and approaches for CAVs urgently need to be studied and
developed. Relocated parking of CAVs can mitigate parking imbal-
ance in crowded local areas; however, the additional floating trips
have an adverse effect on network congestion when CAVs are not
well distributed. To ease the parking problems for CAVs, Millard-
Ball (2019) recommended implementing network congestion
pricing instead of parking pricing. Wang et al. (2021) developed
a control-theoretic approach to maintain the availabilities of park-
ing facilities at desired levels for CAVs. Bahrami et al. (2021)
modeled the private parking choice problem of CAVs in a nonco-
operative manner. The experimental results indicated that parking
pricing and information provision could not eliminate traffic con-
gestion without the aid of a congestion toll for CAVs. Zhao et al.
(2021) presented a macroscopic modeling approach to dynamically
dispatch CAVs and provide regional route guidance via model
predictive control (MPC). The results showed that the dispatching-
for-parking approach could optimize the distribution of searching-
for-parking CAVs and alleviate traffic congestion.
The centralized dispatching-for-parking is an essential and
efficient way to improve parking operations in the era of CAVs.
In addition, CAVs are foreseen to become a new tool to optimize
the spatial-temporal distribution of urban traffic to improve mobil-
ity efficiency, as they can be dynamically dispatched by the
management centers. Nevertheless, for the system modeling, the
preceding studies shed light on the transformation of CAVs’choice
behaviors considering parking monetary costs. To the authors’
knowledge, there is no study that provides a fundamental frame-
work to describe the dynamics of the parking-traffic system and
control of the dispatching-for-parking CAVs in real-time.
The dynamics of the onstreet parking-traffic system have been
studied in various analytical methods. Arnott and Inci (2006) mod-
eled it from an economic perspective and provided useful relation-
ships between parking and congestion in a downtown area. Boyles
et al. (2015) proposed a novel equilibrium framework of traffic
assignment incorporating drivers’cycling behavior of onstreet
searching-for-parking. However, these static models cannot fully
depict the dynamic interaction process of searching-for-parking
and traffic congestion. Zhao et al. (2018) proposed an advanced
management approach in parking spot level via agent-based sim-
ulation optimization; however, it focused on the large parking
garage, and dynamic traffic was not considered. Ni and Sun (2017)
developed a perfect agent-based simulation environment to analyze
the processes of drivers’parking decision-making considering
parking reservations, in which the components of vehicles, parking
lots, and road networks were fully considered. However, despite the
fact that agent-based simulation can finely describe drivers’travel
and parking behaviors, it also has the limitations of requiring large
amounts of detailed data to calibrate the model, which leads to low
transferability across different scenarios or cities.
The recent developments on the macroscopic traffic modeling
approach show prospective outcomes to depict the interactive dy-
namics of parking-traffic systems in the urban network, e.g., macro-
scopic fundamental diagrams (MFD) (Geroliminis and Daganzo
2008). Geroliminis (2015) modeled onstreet parking searches in
congested cities with the theory of MFD. The study demonstrated
that searching-for-parking vehicles affect all moving traffic in the
network, even those with destinations outside the area with limited
parking resources. Liu and Geroliminis (2016) modeled morning
commute traffic using the concept of MFD with the considera-
tion of searching-for-parking in the destinations. Then, Leclercq
et al. (2017) extended the MFD theory and formulated onstreet
searching-for-parking from an accumulation-based view to a trip-
based view, which could finely tune the related travel distances
according to the real-time parking occupancy. These studies dem-
onstrated that macroscopic models certainly perform effectively in
depicting the interactions between onstreet searching-for-parking
and traffic congestion in a dynamic manner.
In our study, we propose a generalized macroscopic control frame-
work to regulateCAVs from searching-for-parkingto dispatching-for-
parking in each region under different demand-supply patterns to
achieve system optimum. As it is envisioned that HDVs and CAVs
will coexist for a long time (Sharma et al. 2021;Zhao et al. 2019),
we develop a bimodal traffic model to assess the performance of
the integrated parking-traffic system at a large-scale urban road
network, following the efforts by Geroliminis (2015). Then, a
dispatching-for-parking controller of CAVs is formulated based on
MPC, which is widely investigated for perimeter control and regional
route guidance with the representation of MFD (Geroliminis et al.
2013;Zhao et al. 2021;Ramezani and Nourinejad 2018).
The remainder of this paper is organized as follows. “Model
Formulation”formulates the dynamics of the parking-traffic system
considering cruising-for-parking and dispatching-for-parking.
“Optimal Control of Dispatching-for-Parking for CAVs”presents
the methodology of a rolling horizon control of dispatching-for-
parking for CAVs. “Numerical Experiments”conducts numerical
experiments in a two-region urban road network and explores the
effectiveness of the proposed approach. “Conclusions and Future
Research”concludes the findings and discusses further research.
Model Formulation
First, a brief description of the concept of the MFD is made in a
multiregion urban road network. Then, the formulations with more
complicated structures are developed to depict the system dynamics
of the mixed traffic of HDVs and CAVs, which considers the extra
traffic of searching-for-parking and dispatching-for-parking.
Macroscopic Fundamental Diagram
We assume that a heterogeneous road network is divided into sev-
eral homogeneous regions denoted by R, and each has a well-
defined MFD. The niðtÞdenotes the vehicle accumulation in region
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iat time t;nijðtÞdenotes the accumulation of the part of vehicles in
iwith the travel destination in jat t;PiðniðtÞÞ denotes the network
production with vehicle accumulation niðtÞin region iat t;
ViðniðtÞÞ and MiðniðtÞÞ denote the space-mean velocity and the
trip completion rate with vehicle accumulation niðtÞin region i
at t; and lidenotes the average trip length for vehicles in region i
ViðniðtÞÞ ¼ PiðniðtÞÞ
niðtÞ∀i∈Rð1Þ
MiðniðtÞÞ ¼ PiðniðtÞÞ
li
∀i∈Rð2Þ
where Eq. (1) was defined by Edie (1963); and Eq. (2) was intro-
duced by Little (1961) for the queuing systems with steady-
state, called Little’s formula. The MiðniðtÞÞ denotes the total
completion rates in region iat time t,MiðniðtÞÞ ¼ Mii ðniðtÞÞ þ
Pj∈UiMijðniðtÞÞ, where Mii ðniðtÞÞ denotes the part of the com-
pleted trips from region iwith the destination in the same region;
MijðniðtÞÞ denotes the part of completed trips from region iwith
the destination in region j; and Uidenotes the set of regions that are
in the surrounding of i.
Macroscopic Modeling of the Parking-Traffic System
Due to the limited onstreet parking availability in the downtown
area, HDVs may have to search for available parking spots near
the destinations, and CAVs may relocate to search for parking
in other regions. To model the mixed traffic of HDVs and CAVs,
we denote kas the vehicle type, k∈fh;cg, where hrepresents
HDVs, and crepresents CAVs.
The vehicle accumulation in region iat time t,niðtÞ, consists of
four categories of vehicles:
•moving vehicles toward internal destinations before searching-
for-parking, nm
iðtÞ(Category m), nm
iðtÞ¼Pknm;k
iðtÞ, where
nm;k
iðtÞis the number of moving vehicles of type kwith desti-
nations in region iat t;
•searching-for-parking vehicles in region iat time t,ns
iðtÞ
(Category s), ns
iðtÞ¼Pkns;k
iðtÞ, where ns;k
iðtÞis the amount
of searching-for-parking vehicles of type k;
•moving vehicles with destinations that are not in region iat t,
no
iðtÞ(Category o), no
iðtÞ¼PkPj∈Uino;k
ij ðtÞ, where no;k
ij ðtÞis
the amount of moving vehicles of type kfrom region ito the
external region j(j∈Ui); and
•dispatching-for-parking CAVs from region ito other regions
at t,nd
iðtÞ(Category d), nd
iðtÞ¼Pj∈Uind
ijðtÞ, where nd
ijðtÞis
the amount of dispatching-for-parking CAVs from region ito
region j.
Taken together, Eq. (3) is obtained
niðtÞ¼ns
iðtÞþnm
iðtÞþno
iðtÞþnd
iðtÞ∀i∈Rð3Þ
Denote by np
iðtÞthe number of vehicles parked onstreet in re-
gion iat time t,np
iðtÞ¼Pknp;k
iðtÞ, and by OPithe total number of
onstreet parking spots. Let piðtÞ¼ðOPi−np
iðtÞÞ=OPibe the pro-
portion of available parking spots in iat t, and dp
ibe the mean
distance between two successive onstreet parking spots. We model
the process of searching-for-parking as a Bernoulli trial (Arnott and
Rowse 1999;Geroliminis 2015), and the success rate is piðtÞ.
Then, the total number of parking spots screened follows a geomet-
ric distribution, and the mean value is 1=piðtÞ. When the availabil-
ity rate of onstreet parking spots is piðtÞin iat t, the average travel
distance of searching-for-parking, ls
iðtÞ, is calculated
ls
iðtÞ¼ dp
i
piðtÞ∀i∈Rð4Þ
To model the effect of searching-for-parking, we divide every
region iinto three reservoirs:
•a moving reservoir Rmo
iðtÞwith nm
iðtÞþno
iðtÞvehicles;
•a searching reservoir Rsd
iðtÞwith ns
iðtÞþnd
iðtÞ, where vehicles
transfer from Rmo
iðtÞwhen they arrive at their destinations;
meanwhile, flows of searching-for-parking CAVs transfer from
Rsd
iðtÞto Rmo
iðtÞif CAVs are dispatched to other regions; and
•a parking reservoir Rp
iðtÞ, where vehicles transfer from Rsd
iðtÞ
when they find free parking spots.
Also, trips generated in Rp
iðtÞtransfer from Rp
iðtÞto Rmo
iðtÞand
lead to their destinations. Figs. 1(a and b) show these partitioning
and movements of HDVs and CAVs between different reservoirs,
respectively.
The transfer flows of categories m,s,o, and dof vehicle type k
in region iat time tare estimated using Little’s formula (Little
1961)
Mm;k
ii ðtÞ¼nm;k
iðtÞ
niðtÞ·PiðniðtÞÞ
lm
iðtÞ∀i∈R;k∈fh;cgð5Þ
Ms;k
ii ðtÞ¼ns;k
iðtÞ
niðtÞ·PiðniðtÞÞ
ls
iðtÞ¼ns;k
iðtÞ
niðtÞ·piðtÞ
dp
i
·PiðniðtÞÞ
∀i∈R;k∈fh;cgð6Þ
Mo;k
ij ðtÞ¼no;k
ij ðtÞ
niðtÞ·PiðniðtÞÞ
lo
iðtÞ∀i∈R;j∈Ui;k∈fh;cg
ð7Þ
Md
ijðtÞ¼nd
ijðtÞ
niðtÞ·PiðniðtÞÞ
ld
iðtÞ∀i∈R;j∈Uið8Þ
where Mm;k
ii ðtÞand Ms;k
ii ðtÞdenote the trip completion rates of mov-
ing vehicles with internal destinations of type kfrom Rmo
iðtÞto
Rsd
iðtÞat tand searching-for-parking vehicles of type kfrom
Rsd
iðtÞto Rp
iðtÞat t, respectively; Mo;k
ij ðtÞand Md
ijðtÞdenote the
trip completion rates of moving vehicles with external destinations
of type kfrom Rmo
iðtÞto Rmo
jðtÞat tand dispatching-for-parking
CAVs from Rsd
iðtÞto Rsd
jðtÞat t, respectively. The lm
iðtÞ,ls
iðtÞ,lo
iðtÞ,
and ld
iðtÞdenote the average travel distances of the corresponding
transfer processes in region iat time t, respectively.
As HDVs cannot be dispatched, then, the evolution of HDVs
over time is formulated
dnm;h
iðtÞ
dt ¼qh
iiðtÞþX
j∈Ui
Mo;h
ji ðtÞ−Mm;h
ii ðtÞ∀i∈R;j∈Ui
ð9Þ
dns;h
iðtÞ
dt ¼Mm;h
ii ðtÞ−Ms;h
ii ðtÞ∀i∈R;j∈Uið10Þ
dno;h
ij ðtÞ
dt ¼qh
ijðtÞ−Mo;h
ij ðtÞ∀i∈R;j∈Uið11Þ
dnp;h
iðtÞ
dt ¼Ms;h
ij ðtÞ−qh
iiðtÞ−qh
ijðtÞ∀i∈R;j∈Uið12Þ
where qh
iiðtÞand qh
ijðtÞ= new trips generated of HDVs starting from
region iwith internal (inside region i) and external destination
(i.e., region j) at time t, respectively.
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On the other hand, CAVs can be dispatched by the system, and
the evolution of CAVs over time is formulated
dnm;c
iðtÞ
dt ¼qc
iiðtÞþX
j∈Ui
Mo;c
ji ðtÞ−Mm;c
ii ðtÞ∀i∈R;j∈Ui
ð13Þ
dns;c
iðtÞ
dt ¼Mm;c
ii ðtÞþX
j∈Ui
Md
jiðtÞ−Ms;c
ii ðtÞ−X
j∈Ui
wijðtÞ
∀i∈R;j∈Uið14Þ
dno;c
ij ðtÞ
dt ¼qc
ijðtÞ−Mo;c
ij ðtÞ∀i∈R;j∈Uið15Þ
dnp;c
iðtÞ
dt ¼Ms;c
ij ðtÞ−qc
iiðtÞ−qc
ijðtÞ∀i∈R;j∈Uið16Þ
where wijðtÞ= dispatch rate of CAVs from region ito region j
(j∈Ui) at time t, which represents that a part of searching-for-
parking CAVs in iis being dispatched to jto search for available
parking spots. Thus, wijðtÞis the rate of change of the number
of CAVs from region ito region jat time t. The last negative
component in Eq. (14) and the first positive component in
Eq. (17) represent the CAVs transfer from searching-for-parking to
dispatching-for-parking.
Finally, the dynamics of dispatching-for-parking CAVs are
formulated
dnd
ijðtÞ
dt ¼wijðtÞ−Md
ijðtÞ∀i∈R;j∈Uið17Þ
Eq. (17) indicates that once wijðtÞof searching-for-parking
CAVs are being dispatched to region jat time t, they are
Fig. 1. A multireservoir system with well-defined MFD representations: (a) different movements of HDVs; and (b) different movements of CAVs.
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immediately changed as dispatching-for-parking CAVs from
Rmo
iðtÞto Rsd
iðtÞin region iuntil they arrive at region j.
Optimal Control of Dispatching-for-Parking for CAVs
The network parking-traffic system of the mixed HDVs and CAVs
is a nonlinear system with complex state dynamics. To achieve the
optimal control of dispatching-for-parking for CAVs, constraints
and measurement errors of system states and future predicted trip
demand should be considered. Therefore, we choose the MPC
framework to formulate the dispatching-for-parking controller,
which can handle multiple levels of measurement errors over time
with a feedback loop in realistic applications (Garcia et al. 1989).
Problem Formulation with MPC
The aim of the centralized dispatching-for-parking system is to
minimize the total network delay via dynamically controlled dis-
patch rates of CAVs [i.e., wijðtÞ], which is the time integral of ve-
hicle accumulation of HDVs and CAVs in moving subreservoir and
searching subreservoir in each region. The objective of minimizing
the total network delay Jis formulated
minimize
wijðtÞJ¼Ztf
t0α1X
i∈R
ðnm;h
iðtÞþno;h
iðtÞÞ
þα2X
i∈R
ðnm;c
iðtÞþno;c
iðtÞÞdt
þZtf
t0β1X
i∈R
ns;h
iðtÞþβ2X
i∈R
ns;c
iðtÞdt
þZtf
t0γX
i∈R
nd
iðtÞdt ð18Þ
where t0= initial time; tf= finishing time; and t∈½t0;tf= control
duration. As shown in Eq. (18), the first time integral represents the
weighted total travel time of moving HDVs and CAVs with internal
and external destinations in each region. The second time integral
represents the weighted total travel time of searching-for-parking
HDVs and CAVs in each region. The last time integral represents
the weighted total travel time of dispatching-for-parking CAVs in
each region. The weights, α1and α2, denote the relative values of
travel time of moving HDVs and CAVs, respectively; β1and β2
denote the relative values of travel time of searching-for-parking
Fig. 2. The MPC framework of dispatching-for-parking for CAVs.
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HDVs and CAVs, respectively; γdenotes the relative value of travel
time of dispatching-for-parking CAVs.
Specifically, the MPC controller of dispatching-for-parking
should satisfy the constraints
nm;k
iðtÞ;ns;k
iðtÞ;no;k
ij ðtÞ;nd
ijðtÞ≥0∀i∈R;j∈Ui;
k∈fh;cg;t∈½t0;tfð19Þ
niðtÞ≤njam
i∀i∈R;t∈½t0;tfð20Þ
wijðtÞ≥0∀i∈R;j∈Ui;t∈½t0;tfð21Þ
where constraints in Eq. (19) indicate that the accumulation of each
category and each vehicle type in each region of the network
remains nonnegative; constraints in Eq. (20) indicate that the total
vehicle accumulation is no larger than the capacity in each region,
njam
i; and constraints in Eq. (21) indicates that the dispatch rate of
CAVs remains nonnegative in each region.
The problem of Eqs. (18)–(21) is a nonconvex nonlinear
program (NLP) with a receding horizon feature. These types of
problems can be effectively solved by sequential quadratic pro-
gramming (SQP) or interior-point solvers (Sirmatel and Geroliminis
2018).
The framework of the MPC controller of dispatching-for-
parking for CAVs is shown in Fig. 2. There is a demand prediction
module to provide the future trip information based on the histori-
cal data mining, in which white noise is added to the actual travel
demand to simulate the prediction errors in real world scenarios.
The module of the dispatching-for-parking controller for CAVs
dynamically outputs the dispatch rate, wijðtÞ. Then, different cat-
egories of traffic will evolve in the plant based on the control com-
mand. In the next time step, real-time information of traffic state
estimations (e.g., the number of moving, searching-for-parking,
dispatching-for-parking, and parked vehicles) will feedback to the
prediction model in the controller. We add noises to the actual val-
ues to simulate the measurement errors in real applications. Based
on information feedback and demand prediction, the prediction
model computes the evolution of vehicle accumulations in each
region with the representation of MFD, i.e., Eqs. (3)–(17). Then,
the MPC controller computes with the sliding time window via the
optimization model, i.e., Eqs. (18)–(21), and provides control
commands back to the plant in the closed-loop.
MPC Controller Tuning and Computational Efficiency
Analysis
There are two key parameters in the MPC controller, Npand Nc.
The Npdenotes the number of time steps for the prediction horizon,
and the Ncdenotes the number of time steps for the control horizon.
Then, the parameter selection of Npand Ncwill highly affect
the running performance of the CAV dispatching-for-parking con-
troller. To accurately predict the evolution of the complex parking-
traffic system, the prediction horizon Npshould be set large
enough. Meanwhile, the larger Ncwill improve the optimization
effect of the model; however, the larger values for the parameters
require more computing resources, which leads to the quite
Fig. 3. MPC controller tuning and computational efficiency analysis: (a) the relative improvement of objective function against no dispatching-for-
parking for tuning the MPC parameters; and (b) average CPU times with the direct methods of DSS and DMS as a function of Np.
Table 1. Description of main parameters of the macrosimulation
Parameter Value Description
f11 0.1 fij = fraction of demand generated from i
with destination j
f12 0.2 i,j¼1(internal) or 2 (external)
f21 0.4
f22 0.3
lm11.743 Average trip length without searching-for-
parking in Region 1 (km)
lm21.743 Average trip length without searching-for-
parking in Region 2 (km)
Mp
16,000 Total number of onstreet parking spots in
Region 1
Mp
212,000 Total number of onstreet parking spots in
Region 2
n1p
01,500 Vehicles parked in Region 1 at t¼0
n2p
08,000 Vehicles parked in Region 2 at t¼0
L156.25 Total street length in Region 1 (km)
L2112.5 Total street length in Region 2 (km)
dp
12L1=Mp
1Average distance traveled between two
adjacent spots in Region 1
dp
22L2=Mp
2Average distance traveled between two
adjacent spots in Region 2
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laborious real-time application for the MPC controller. Further-
more, the choices of the direct method and the solver also affect
the computational efficiency, such as the popular methods of direct
single shooting (DSS) and direct multiple shooting (DMS) (Diehl
et al. 2009;Hicks and Ray 1971;Bock and Plitt 1984) and the
common solvers of SQP and IPOPT (Wächter and Biegler 2006).
Fig. 3(a) shows the tuning results of the parameters Npand
Ncin the MPC controller. The vertical axis depicts the improve-
ments of the objective function compared with the case without
dispatching-for-parking control. The results indicate that the perfor-
mance of the MPC controller is not highly affected by the control
horizon Ncwith the prediction horizon Np≥16. Note that the
Fig. 4. Results for the cases without and with the MPC controller of dispatching-for-parking: (a) vehicle accumulation; (b) mean speed; (c) number of
searching-for-parking vehicles; (d) onstreet parking occupancy; (e) dispatch rate of CAVs; and (f) number of dispatching-for-parking CAVs.
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MPC controller does not perform better than no dispatching-for-
parking scheme when Np≤6and Nc≤2. Accordingly, the choice
of MPC parameters is set as Np¼16 and Nc¼4. Based on this,
Fig. 3(b) shows the results of the computational efficiency for the
different direct methods. The results indicate that DSS performs
more efficiently than DMS when the prediction horizon Np≥10.
Then, we choose the direct method as DSS for the subsequent
numerical experiments.
Numerical Experiments
In this section, we present a macrosimulation with mixed traffic
flows of HDVs and CAVs in a two-region urban road network.
The simulation is conducted via the CasADi (Andersson et al.
2019) toolbox in MATLAB R2020a on a 64-bit Windows PC with
a 3.7-GHz Intel Core i7 processor and 32-GB RAM.
Simulation Setup
The simulation executes for a period of 4.5 h using a discrete
version, which is uniformly divided into 10,000 time units with
1.62 s in each. We assume that CAVs have the ability to search
for available parking spots across different regions in urban road
networks. However, HDVs search for available parking spots just
within the regions of their destinations. Table 1shows the descrip-
tion of main parameters in the macrosimulation in which Region 1
represents the downtown area of the city with limited onstreet
parking resources, while Region 2 represents the suburb area of
the city with enough parking resources. The total amounts of on-
street parking spots in the two regions are denoted by Mp
1and Mp
2,
respectively. The total trip demand follows a trapezoidal form
(Geroliminis 2015), which starts with 0veh=min at time unit 0,
increases gradually with the maximum value of 375 veh=min be-
tween time units 3,000 and 4,500, decreases linearly after 4,500
time units, and then reaches zero at time unit 8,500. This depicts
the scenario of commuting from Region 1 to Region 2. The fij
denotes the fraction of travel demand generated from Region iwith
the destination in Region j. All the trips are generated from the
parking reservoir Rp
iðtÞin each region i. According to Geroliminis
(2015), the well-defined MFD with a third-degree polynomial
shape for the two regions is defined
PðnÞ¼1.52 ×10−7n3−2.88 ×10−3n2þ14.11nð22Þ
where PðnÞ= production with vehicle-meters for each time unit;
and n= vehicle accumulation. Furthermore, as no passengers are
on the searching-for-parking and dispatching-for-parking CAVs,
we set the weights α1¼α2¼β1¼1and β2¼γ¼0.6in the
objective function to simplify the simulation experiments.
Relative Analysis of the Cases without and with
Dispatching-for-Parking
To analyze the effect and implication of the proposed dispatching-
for-parking system, we conduct multiple relative experiments under
the cases without and with the MPC controller. To simplify, we
assume that all vehicles are CAVs (the penetration rate of CAVs
is 100%) in the simulation, and all CAVs are able to be dynamically
dispatched by the centralized management center.
Fig. 4presents the simulation results for the cases without and
with the MPC controller of dispatching-for-parking. It shows that
there exists significant searching-for-parking traffic in Region 1 oc-
curring at time t¼2,200 and peaking at time t¼6,000 for the case
without dispatching-for-parking [Fig. 4(c)], and there is no search-
ing-for-parking effect in Region 1 for the case with dispatching-for-
parking. Figs. 4(a, b, and d) show the time series of accumulation,
mean speed, and parking occupancy in each region, respectively.
In Region 1, the traffic changes from severely congested to un-
congested with the MPC controller of dispatching-for-parking
[Fig. 5(a)]. For the case without dispatching-for-parking at the same
time, onstreet parking occupancy is larger than 95% in Region 1
and is very abundant (>85%) in Region 2, as shown in Fig. 4(d).
This indicates that searching-for-parking traffic can lead an uncon-
gested network to congested, despite that travel demand is not very
high. It is demonstrated that the proposed dispatching-for-parking
system is effective in the era of CAVs, especially for cities with
severe parking problems.
With the MPC controller of dispatching-for-parking, some
CAVs after dropping off passengers are dispatched to search for
available parking spots from Region 1 to Region 2 at time t¼
1,800, as shown in Fig. 4(e), to mitigate parking competition and
improve the utilization of parking resources in Region 1. Conse-
quently, the number of dispatching-for-parking CAVs from Region
1 to Region 2 increases at time t¼1,800 as well [Fig. 4(f)].
Fig. 5. MFDs (a) in the internal region; and (b) in the external region.
© ASCE 04021112-8 J. Transp. Eng., Part A: Systems
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The MFDs for the cases without and with dispatching-for-parking
in the two regions are illustrated in Fig. 5. Fig. 5(a) depicts that
Region 1 predominantly suffers traffic congestion problems with-
out the dispatching control because low parking availability will
cause large amounts of searching-for-parking traffic. On the other
hand, the traffic condition of Region 1 transfers to undersaturation
during the simulation with dispatching-for-parking control. Fig. 5(b)
shows that Region 2 is in the uncongested conditions under the cases
without and with the MPC controller of dispatching-for-parking,
respectively.
Fig. 6. Results for different penetrations of CAVs under the case with dispatching-for-parking in the internal region: (a) vehicle accumulation;
(b) mean speed; (c) number of searching-for-parking vehicles; (d) onstreet parking occupancy; (e) dispatch rate of CAVs; and (f) number of
dispatching-for-parking CAVs.
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Many studies argue that relocated parking of CAVs increases
large floating VMT, which may cause extra traffic congestion
(Millard-Ball 2019). An interesting observation in this study is that
the total travel time of searching-for-parking under the case without
dispatching-for-parking is 1.04 ×107[time unit], while the total
travel time of searching-for-parking and the extra trip time of re-
located CAVs under the case with dispatching-for-parking is 1.41 ×
106[time unit], which only takes a proportion of 13.6% compared
Fig. 7. Results with different penetrations of CAVs under the case with dispatching-for-parking in the external region: (a) vehicle accumulation;
(b) mean speed; (c) number of searching-for-parking vehicles; (d) onstreet parking occupancy; (e) dispatch rate of CAVs; and (f) number of
dispatching-for-parking CAVs.
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to the case without dispatching-for-parking. The effectiveness of
the MPC controller is also evident for moving vehicles, whose total
travel time has a reduction of 41.6%. This implies that searching-
for-parking traffic also has a big impact on all vehicles in the road
network. Meanwhile, the effect of extra floating trips of CAVs gen-
erated to park remotely under the case with dispatching-for-parking
is much less than the effect of searching-for-parking under the case
without dispatching-for-parking.
Different Penetration Rates of CAVs
To evaluate the implications of the penetration rate of CAVs, which
is denoted by γ, we conduct multiple simulation experiments in the
same two-region network with mixed CAVs and HDVs, where γ
varies from 0% to 100% with 10% as the common difference.
The simulation results are presented in Fig. 6(Region 1) and
Fig. 7(Region 2). Figs. 6(a and b) show the evolution of vehicle
accumulation and mean speed in Region 1, with the CAV penetra-
tion γvarying from 0% to 100%, respectively. Traffic congestion
will gradually disappear with the increase of γbecause of the re-
duction of the searching-for-parking traffic, as shown in Fig. 6(c).
However, when the penetration γis larger than 60%, the phenome-
non of searching-for-parking completely disappears in Region 1,
which suggests that more than 60% of vehicles have to park
remotely during rush hour to ease the inner-urban parking problems
under our simulation settings. Fig. 6(d) shows the time evolution of
onstreet parking occupancy in Region 1, and we find that the peak
value is less than 85% when the penetration γis larger than 50%.
This is consistent with the results of pricing-driven schemes in curb
parking management (Shoup 2006). Figs. 6(e and f) show the rate
and the total number of dispatching-for-parking CAVs from Region
1 to Region 2, respectively.
On the other hand, the traffic state of Region 2 is slightly af-
fected by the part of dispatching-for-parking CAVs from Region 1.
Figs. 7(c and d) show the evolution of vehicle accumulation of
searching-for-parking and onstreet parking occupancy in Region 2,
respectively. We find that searching-for-parking traffic slightly in-
creases with the increase of penetration γ. As shown in Fig. 7(c),
there are spikes of the curve (100% penetration) after 8,000 s.
Although this can be negligible compared to the amount of Region
1, it illustrates in another way that Region 2 will cause traffic
congestion and fierce competition if CAVs self-relocate without
dispatching-for-parking. Meanwhile, with the MPC controller of
dispatching-for-parking, parking resource utilization is more bal-
anced in the two regions during rush hour with increased γ, which
will be too busy in Region 1 and free in Region 2 under the case of
no CAVs. Figs. 7(e and f) show the rate and the accumulation of
dispatching-for-parking CAVs from Region 2 to Region 1, respec-
tively. However, with the onstreet parking occupancy of Region 2
increase [Fig. 7(d)], a small part of CAVs are dispatched back to
Region 1. There are spikes after 6,000 s in Figs. 7(e and f). This is
because of the setup of the different weights in the objective func-
tion, which leads to the backflow phenomenon of the dispatching-
for-parking CAVs. Therefore, the weights of different categories of
vehicles need further investigation.
Fig. 8shows the total travel time under cases of penetration γ
varying from 0% to 100% with dispatching-for-parking for CAVs.
The bar in Fig. 8represents the total travel time of the system with
the corresponding γ, i.e., TðγÞ, where the total travel time of HDVs
is represented, i.e., ThðγÞ, and the total travel time of CAVs is also
represented, i.e., TcðγÞ. In addition, TðγÞ¼ThðγÞþTcðγÞ. The
total travel time of the system gradually decreases with the increase
of the penetration γand almost remains constant after the penetra-
tion larger than 60%, which is about 50% of the amount that the
penetration γis 0%. This implies that the proposed dispatching-for-
parking strategy is more effective when the penetration γis less
than 60%. To compare the total travel time of HDVs and CAVs
under the mixed traffic conditions, we assume that TCAV ðγÞ¼
TcðγÞ=γ, where TCAV ðγÞis the total travel time of the system if
all vehicles are assumed to be CAVs based on the average travel
time of CAVs in the mixed traffic with the penetration γ. Similarly,
we assume THDVðγÞ¼ThðγÞ=ð1−γÞ, where THDV ðγÞis the total
travel time of the system if all vehicles are assumed to be HDVs.
The line with the cross in Fig. 8represents THDVðγÞ, and the line
with the circle represents TCAV ðγÞ. These two lines gradually move
downward with the increase of penetration γ, which suggests that
Fig. 8. Total travel time under cases with different penetrations of CAVs.
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the average travel time of HDVs and CAVs in the system decreases
when the penetration γincreases. Furthermore, the line with the
circle is positioned higher than the line with the cross, which im-
plies that the average travel time of CAVs is higher than HDVs in
the mixed traffic environment with the proposed MPC controller
for dispatching-for-parking.
Table 2shows the total travel time under cases of different pen-
etrations γ. For example, when the penetration γis 40%, the actual
total travel time of the system under mixed traffic conditions,
i.e., Tð40%Þ,is3.01 ×107[time unit]; the assumed total travel time
of CAVs, i.e., TCAV ð40%Þ,is4.06 ×107[time unit], which is
35.2% larger than the actual total travel time of the system;
and the assumed total travel time of HDVs, i.e., THDVð40%Þ,is
2.30 ×107[time unit], which is 23.5% less than the actual total
travel time of the system. In addition, the difference between the
assumed total travel time of CAVs and HDVs, i.e., CAV–HDV, is
58.7% of the actual total travel time of the system.
As shown in Fig. 8, we divide the graph into three areas, low,
medium, and high, which represent the market penetration levels of
CAVs. In the low area, the average travel time of HDVs decreases
rapidly; however, the average travel time of CAVs is no better than
the case without dispatching-for-parking. When the penetration γis
less than 20%, the assumed total travel time of CAVs, i.e., TCAV ðγÞ,
is larger than the actual total travel time of the system when the
penetration γis zero, i.e., Tð0%Þ(Table 2). This implies that the
average travel time of CAVs under the case with dispatching-for-
parking is larger than the case without dispatching-for-parking.
Large parts of searching-for-parking CAVs are dispatched to park
remotely to minimize the total network delay with the MPC con-
troller of dispatching-for-parking. In the medium area, the average
travel time of HDVs and CAVs all decrease rapidly with the MPC
controller; however, the difference between the assumed total travel
time of CAVs and HDVs gradually increase to the peak at 40% and
then have a large fall between 40% and 60% (Table 2). This may
lead to severe equity problems between HDVs and CAVs, which
should be improved for the proposed dispatching-for-parking strat-
egy in the future study. In the high area, the average travel time of
HDVs and CAVs tend to be the steady-state, which implies the
effectiveness of the proposed dispatching-for-parking system is
low when the penetration γis larger than 60%.
Conclusions and Future Research
In this paper, a centralized dispatching-for-parking system is pro-
posed to dispatch connected and automated vehicles to search for
available parking spots in suitable regions. The system facilitates
floating CAVs to find free parking spots as soon as possible and to
ease traffic congestion for road networks. The concept of a macro-
scopic fundamental diagram is applied to model the system dynam-
ics with the mixed traffic flow of human-driven vehicles and CAVs
in a multiregion road network. The objective of the proposed sys-
tem is to minimize the network delay by dynamically dispatching
searching-for-parking CAVs among different regions. The frame-
work of the model predictive control is suggested to formulate the
dispatch controller. Numerical experiments in a two-region city
demonstrate that the proposed approach significantly improves the
performance of the parking-traffic system. The congested network
of the area with highly limited onstreet parking spots transfers
to undersaturated conditions under the case of dispatching-for-
parking. Meanwhile, the effect of different penetrations rates of
CAVs on the system is also investigated. The results reveal that
the total travel time of the system gradually decreases with the in-
crease of the penetration rate of CAVs, and the average travel time
Table 2. Total travel time under cases with different penetrations of CAVs
×1070% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
TðγÞ4.67 3.81 3.44 3.17 3.01 2.82 2.39 2.28 2.29 2.27 2.26
TCAV ðγÞ—5.32 (þ39.8%) 4.74 (þ37.8%) 4.36 (þ37.5%) 4.06 (þ35.2%) 3.51 (þ24.5%) 2.65 (10.9%) 2.41 (þ5.6%) 2.36 (þ3.3%) 2.30 (þ1.4%) 2.26
THDVðγÞ4.67 3.64 (−4.4%) 3.11 (−9.5%) 2.66 (−16.1%) 2.30 (−23.5%) 2.13 (−24.5%) 2.00 (−16.3) 1.98 (−13.2%) 1.98 (−13.3%) 1.98 (−12.8%)—
CAV–HDV (%) —44.2% 47.3% 53.6% 58.7% 49% 27.2% 18.8% 16.6% 14.2% —
© ASCE 04021112-12 J. Transp. Eng., Part A: Systems
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of CAVs is larger than the average travel time of HDVs with the
MPC controller. The study demonstrates the applicability and im-
plication of the proposed system in the era of CAVs.
In future research, we will study the impact of price and
nonprice-based policies fluctuations on the parking-traffic system
of mixed traffic flow of HDVs and CAVs. The equity of CAVs and
HDVs with MPC controllers of dispatching-for-parking also needs
to be investigated, in which CAVs have to travel much longer
than HDVs.
Data Availability Statement
Some or all data, models, or code that support the findings of this
study are available from the corresponding author upon reasonable
request.
Acknowledgments
This work is jointly sponsored by the National Natural Science
Foundation of China (52102383), the China Postdoctoral Science
Foundation (2021M692428), and the Scientific Research Program
of Shanghai Municipal Science and Technology Commission
(19DZ1208700; 21DZ1205100). The work of Cong Zhao is sup-
ported by the Shanghai Sailing Program (21YF1449400). The
authors would like to thank the anonymous reviewers for their con-
structive comments.
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