METS-R SIM: A simulator for Multi-modal Energy-optimal Trip Scheduling in Real-time with shared autonomous electric vehicles

Abstract

We develop an agent-based simulator named METS-R SIM to support operational decisions for multi-modal shared autonomous vehicle (SAEV) services. Compared with existing traffic simulators, METS-R SIM offers several valuable features including: 1) A microscopic vehicle movement model for SAEV services, which allows us to explicitly model vehicular interactions and generate detailed speed and acceleration profiles for energy estimation. 2) An efficient implementation in which parallel computing is embedded in METS-R SIM which can update the state of different agents (e.g., vehicle locations in different links) simultaneously. 3) A modular and extensible framework as the simulator is built upon an agent-based modeling environment named Repast Simphony which is featured by its well-factored abstractions; in addition, a server-client structure is introduced to implement real-time operational algorithms such as energy-efficient routing and adaptive transit scheduling. 4) Open-source, reproducible with web-based visualization (METS-R SIM introduces these features to promote transparency). We validate METS-R SIM by matching the aggregated travel time and travel distance with the real observed ones obtained from New York City (NYC). We also compare the generated speed profiles qualitatively to the ones reported in published studies. We demonstrate the functionalities of our simulator by simulating SAEV services deployed to serve travel needs related to three main transportation hubs in NYC.

Full text

METS-R SIM: A Simulator for Multi-modal Energy-optimal Trip
Scheduling in Real-time with Shared Autonomous Electric Vehicles
Zengxiang Leia,Jiawei Xuea,Xiaowei Chena,Xinwu Qianc,Charitha Saumyab,Mingyi Hed,
Stanislav Sobolevskyd,Milind Kulkarniband Satish V. Ukkusuria,∗
aLyles School of Civil Engineering, Purdue University, West Lafayette, IN, USA
bElmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA
cDepartment of Civil, Construction and Environmental Engineering, University of Alabama, AL, USA
dCenter for Urban Science and Progress, New York University, NYC, NY, USA
ARTICLE INFO
Keywords:
Shared autonomous vehicles
Electric taxis
Electric buses
Agent-based modeling
Charging station
ABSTRACT
We develop an agent-based simulator named METS-R SIM to support operational decisions
for multi-modal shared autonomous vehicle (SAEV) services. Compared with existing traffic
simulators, METS-R SIM offers several valuable features including: 1) A microscopic vehicle
movement model for SAEV services, which allows us to explicitly model vehicular interactions
and generate detailed speed and acceleration profiles for energy estimation. 2) An efficient
implementation in which parallel computing is embedded in METS-R SIM which can update
the state of different agents (e.g., vehicle locations in different links) simultaneously. 3) A
modular and extensible framework as the simulator is built upon an agent-based modeling
environment named Repast Simphony which is featured by its well-factored abstractions; in
addition, a server-client structure is introduced to implement real-time operational algorithms
such as energy-efficient routing and adaptive transit scheduling. 4) Open-source, reproducible
with web-based visualization: METS-R SIM introduces these features to promote transparency.
We validate METS-R SIM by matching the aggregated travel time and travel distance with the
real observed ones obtained from New York City (NYC). We also compare the generated speed
profiles qualitatively to the ones reported in published studies. Wedemonstrate the functionalities
of our simulator by simulating SAEV services deployed to servetravel needs related to three main
transportation hubs in NYC.
1. Introduction
Over the course of six decades, transportation simulation tools have evolved to become increasingly sophisticated
and practical, finding a wide range of applications in transportation planning, design, and operational evaluation.
The trends of modern transportation are characterized by technologies that promote autonomy, real-time coordina-
tion, and clean energy, which together shape a promising future for urban mobility. Compared with gasoline vehicles,
electric vehicles are able to achieve better fuel economy1with 40% less maintenance costs [1]. Autonomous driving
arguably not only frees people from the act of driving but also opens the space for cooperative operations and better
safety [2]. These technologies, when merged with smart mobility operations, can bring about significant operational
and safety benefits. Among these benefits, for instance, a self-driving taxi service can proactively relocate to better
match vehicle supply and demand [3]. Transit powered by autonomous driving can avoid congestion, and adapt to the
dynamic travel demand with a more flexible yet predictable schedule [4]. Finally, autonomous driving can also help
with the charging issue for electric vehicles [5]. However, to derive the full benefit of these approaches these methods
should work at scale.
These trends place new challenges for traffic simulation. Firstly, the rapid evolution of electric vehicles and
autonomous driving technologies, as evidenced by recent studies [6,7,8], suggests that existing simulations may
no longer be sufficient. Secondly, the multi-modal transportation system powered by new technologies is more
sophisticated than ever before in terms of data usage and real-time operations, bringing additional complexities in
system dynamics and leading to greater demands on the need for high-fidelity simulation modeling. Last but not least,
Declarations of conflict interests: none
∗Corresponding author
ORCID (s): 0000-0002-7639-438X (Z. Lei); 0000-0001-8754-9925 (S.V. Ukkusuri)
1See https://fueleconomy.gov/feg/atv-ev.shtml
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the simulation of such complex systems is usually computationally expensive, which became a barrier to efficient
system assessment and developing advanced control/optimization algorithms (e.g., an environment for reinforcement
learning-based solutions [9]). This study is dedicated to creating a tool that can efficiently and accurately model high-
fidelity multi-modal SAEV services, which support downstream tasks to handle these challenges.
In this study, we develop an agent-based simulator named METS-R SIM, where METS-R stands for the Multi-
modal Energy-optimal Trip Scheduling in Real-time (METS-R) with SAEVs. The main objective of METS-R SIM
is to estimate realistic, comprehensive, and reproducible metrics (e.g., passenger waiting time, vehicle mileage, and
energy consumption) for public SAEV services under different facility designs and operation strategies. To achieve this
objective, a series of components are implemented. These components include a microscopic traffic simulation module
to model the car following and lane changing behaviors; an operation module that captures the service processes of
autonomous electric taxis and buses; an energy estimation module to calculate the energy consumption using the data
obtained from the traffic simulation; and a data communication module to implement real-time operational algorithms;
a web-based visualization module to replay the simulation process. It is worth noting that parallel computing is
embedded into each component, enabling its scalability to effectively handle simulation tasks at the city level.
Furthermore, METS-R SIM promotes transparency using a web-based visualization module, making it simple for
users to comprehend and share the simulation results. In summary, METS-R SIM contributes to a practical solution to
connect the design and the deployment of the SAEV services, and we anticipate our simulation tool to introduce the
following benefits to the research community and practitioners:
1. Verification and testing: Our simulation, with sufficient coverage of SAEV system details, can be applied to
verify existing operational algorithms and test various counterfactuals.
2. Planning and design insights: METS-R SIM can inform practitioners about the gain and loss of different
planning/designs for city-scale SAEV systems; when integrated with new operational algorithms, it can be
leveraged to show their potential influences.
3. Collaborative decision-making: The results and insights obtained by our simulation can be effectively shared and
verified through web-based visualization, which would enable a more collaborative and informative decision-
making process.
4. Educational platform: As an open-source platform, our simulation can be utilized for educational purposes,
allowing others to create their own simulations and expand them to incorporate the latest technological
breakthroughs.
The rest of the paper is organized as follows. In Section 2, we review the existing simulators for electric and
autonomous vehicles to identify the research gaps. Section 3 shows the framework and key features of different modules
in METS-R SIM. In Section 4, we report the computational efficiency of METS-R SIM under different parallel
computing and trip demand settings. Section 5 presents the validation results of METS-R SIM by comparing the
aggregated metrics (travel time, travel distance) and individual vehicle trajectories obtained from the simulation with
those from the real world. In Section 6, we use a case study to demonstrate the practical functionalities of METS-R SIM
by showing how it can be used to analyze a specific scenario in which SEAV taxis and buses are deployed to commute
passengers who departure from/arrive at the major transportation hubs in New York City (NYC). We summarize our
work and discuss future directions in Section 7.
2. Literature review
In the literature, two distinct branches of research have emerged in relation to simulating Shared Autonomous
Electric Vehicles (SAEV). The first branch aims to examine the potential impact and implications of SAEV services,
while the second branch seeks to optimize the efficient operation of SAEV services. Additionally, several generally-
purposed traffic simulation options, including VISSIM [10], TransModeler2, and SUMO [11] have implemented
features for simulating autonomous and electric vehicles.
2https://www.caliper.com/transmodeler/
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2.1. Simulation for investigating the impacts of SAEV
Early studies can be traced back to 2014. Fagnant and Kockelman [12] developed an agent-based simulator on a
quarter-mile by the quarter-mile grid-based city to explore the travel and environmental implications of introducing
shared autonomous vehicles in Austin, Texas. Fagnant et al. [3] replaced the grid-cell setting using travel time profiles
generated by MATSim. Chen et al. [13] incorporated the grid-based simulator with the dynamics of electric vehicle
charging. The results suggest the proper fleet size is highly dependent on the EV specifications, i.e., vehicle range and
charging speed. Loeb et al. [14] extended the setting in [13] by implementing more scenarios with network-level traffic
modeling based on MATSim and richer charging strategies.
For the development of the MATSim modules for simulating SAEVs, Maciejewski et al. [15] developed a Dynamic
Vehicle Routing Problem (DVRP) package for the MATSim simulator, which consists of basic ride-hailing vehicles
and an optimizer to update vehicles’ schedules. In [16], MATSim was reported to be able to produce consistent
demand reactions against the introduction of autonomous taxi services. Ruch et al. [17] developed AMoDeus, an open-
source simulation for autonomous mobility-on-demand services, based on MATSim and the previous DVRP package.
AMoDeus incorporates four operational strategies including heuristic demand-supply rebalancing [18], global bipartite
matching [19], feedforward fluidic rebalancing and an adaptive real-time rebalancing [20]. AMoDeus had been applied
to understand the implication of introducing autonomous taxi services in Paris [21] and Zurich [19]. Using MATSim
and part of the AMoDeus, Ruch et al. [22] quantified the impacts of taxi fleets coordinations for the cities of San
Francisco, Chicago, and Zurich. The results suggested that fleet coordination can substantially reduce vehicle distance
and necessary fleet size. Zwick et al. [23] extended the MATSim model by implementing driver shifts and comparing
the impacts of different shift strategies (i.e., no shift, human-like shift, and a pseudo shift). MATSim was found to be
used in more studies [24,25,26,22] to investigate the potential of shared autonomous vehicle services in different cities.
We note that MATSim only considers a simplified queuing-based traffic model, which cannot capture the interactions
of multi-modal traffic and detailed controls like eco-driving [27].
Besides MATSim, SimMobility [28] is also a frequently used platform for autonomous mobility-on-demand
(AMoD) simulation. SimMobility synthesizes trip demand based on activity-based travel demand models and generates
vehicle trajectories using a microscopic traffic simulator named MITSIM [29]. This branch of studies quantified the
potential benefits of applying AMoD in Singapore. Marczuk et al. [30] extended SimMobiliy by adding an AMoD
controller module between the demand generation and high-resolution traffic simulation processes. This module is
responsible for assigning the closest available vehicle to each customer and managing the vehicle’s return to its original
station or parking at the drop-off location. Azevedo et al. [31] introduced to the AMoD controller module a minimum
weight bipartite matching in the vehicle-passenger assignment and an optimization-based vehicle rebalancing. Basu
et al. [32] added the mechanism of performing insertion-based ridesharing. Oh et al. [33] investigated the energy
consumption and emission impacts of AMoD, where the energy consumption and emission are computed based on
the total vehicle-km traveled (VKT). Biran et al. [34] incorporated the high-level impact of AMoD on trip-making
decisions using the activity-based model and explored the scenarios involving random cruising, where empty vehicles
are dispatched to random destinations. We notice that SimMobility integrates the AMoD operation at the mesoscopic
level through the creation of trip schedules for dispatching and rebalancing but certain operations (e.g., charging,
eco-driving) may necessitate more delicate information and low-level controls.
There are many other simulations for SAEV services. Comprehensive literature reviews are available in [35,23].
Here we emphasize the simulation functions. Ota et al. [36] developed STaRS to simulate a ride-hailing service
that greedily assigns orders to the closest available vehicles and uses the shortest path for traveling around. They
applied STaRs to quantify the benefits of promoting ridesharing in New York City. Alonso-Mora et al. [37] developed
a simulation for high-capacity AMoD services with vehicle routes generated by the open-source routing machine
(OSRM) engine, where the travel time is static during the simulation. Jäger et al. [38] created a JAVA JADE-based
simulator that encompasses ride-hailing dispatching, vehicle charging, and routing functions with travel time estimated
from discounted free-flow speeds. Bauer et al. [39] developed an agent-based simulation platform based on R to analyze
the routing and charging behaviors of SAEV fleets. Dandl et al. [40] implemented a real-time gaming framework to
simulate the competition among multiple AMoD operators. Kucharski and Cats [41] developed MaaSSim to reproduce
the interactions among ride-hailing riders, drivers, and the platform with a clear structure. We note that most of these
simulators are either closed-source or restricted to the case with dozens of vehicles.
It is worth noting that all of the studies under this branch deal with hypothetical scenarios with little concern about
model validation, making it a common challenge to compare and evaluate their results.
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2.2. Simulation for verifying the operational algorithms
Numerical simulation is also widely used for verifying the effectiveness of operational algorithms such as order
dispatching and vehicle repositioning for SAEV services. For completeness, here we consider a slightly larger scope
that involves general ride-hailing services.
Most studies [42,2,43,44,45,46,47,48,49,50,51,52,53,54,55] used trace-driven simulations which directly
use the demand, travel time, and vehicle location information from real-world data with the matching/dispatching
commands generated by algorithms being tested. For example, Miao et al. [42] verified their taxi dispatching algorithm
under the demand and vehicle location distributions estimated from real-world data. Lin et al. [43] verified their
reinforcement learning (RL)-based fleet management algorithm via a simulation with the available vehicle counted
from a pre-dispatch procedure based on real data. Lei et al. [56] tested the deep learning-based vehicle relocation
algorithm under the request sequences extracted from the real trip records. Haliem et al. [57] implemented a simulation
that can update vehicle location using the OSRM engine, but the congestion effect is not captured. Feng et al. [55]
tested the RL-based vehicle dispatching algorithm for coordinating ride-sourcing and subway by rewinding the taxi
trips under the assumptions of constant vehicle speed and subway waiting time. It should be noted that the congestion
effects caused by different operational algorithms are not captured in these simulators, which may lead to an overlook
of unexpected negative outcomes and cause an overestimation of algorithm benefits.
There are a few studies using simulations with richer details. Chen used the simulator created by Didi Chuxing
to validate their matching and pricing algorithms [58]. This simulation was also used to validate an RL-based vehicle
dispatching algorithm [59]. Chen and Cassandras [60] used SUMO to validate their online matching algorithm on Ann
Arbor Map for serving 30 requests by comparing it with a greedy algorithm. Some studies also tested their methods
in a hypothetical grid network [61,62,63]. We note that these simulators are usually not openly available or hard to
scale to reflect real-world SAEV systems.
2.3. Autonomous, connected, and electric vehicles in simulation software
Simulators for traffic management have detailed vehicle movement models that capture vehicles’ car-following
and lane-changing behaviors. Qurashi et al. [64] implemented autonomous dynamic vanpooling services based on the
traffic simulator SUMO, through the TraCI API. Dandl et al. [65] implemented an autonomous taxi service based
on a commercial microscopic traffic model named AIMSUN to explore its implication in Munich, Germany. Wu et
al. [66] generated the driving cycle of electric vehicles. Bracco et al. [67] presented a simulation method for estimating
the energy consumption of electric buses under different traffic conditions based on AIMSUN and Matlab/Simulink
energy model. Islam et al. [68] combined the POLARIS with an energy model named Autonomo to simulate the
regional energy impact of adopting connected autonomous electric vehicles in Chicago. More studies using simulation
software for modeling SAEV are listed in Table 1. We note that these extensions are dedicated to specific parts of SAEV
operation but not the full system. Even though the simulator was built for general traffic simulation, the implementation
of SAEV service behaviors will require substantial additional efforts.
2.4. Gaps in the literature
Based on the literature, we identify three gaps in SAEV simulation studies as follows.
Gap 1: Coverage of SAEV system details. Most existing SAEV simulators focus on isolated aspects such
as vehicle dispatching [2], charging facility analysis [14], and energy management strategy development [75].
Nonetheless, these simulators face challenges when it comes to providing a comprehensive simulation of SAEV
operations within urban environments. This limitation becomes problematic for researchers who aim to test and validate
new methodologies and policies, especially considering the availability of detailed Electric Vehicle (EV) simulators
like EVLibSim [89].
Gap 2: SAEV energy consumption calculation. Current simulation tools can not fully capture the complexity of
vehicles’ energy consumption, which can be influenced by various factors, involving internal engine features associated
with the vehicle itself and external features [90,91]. Bracco et al. [67] proposed an energy consumption model for
electric buses based on AIMSUN. They considered motor losses and the characteristic curves of torque and power in
the energy consumption estimation process, where the power of the heater and the air conditioner was also ignored.
Sagaama et al. [81] calculated the energy consumption from three parts: the mechanical subsystem, the electrical
subsystem, and the energy regeneration. Their simulation results showed that the proposed method was closer to reality
than the energy model in SUMO.
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Table 1. Summary of simulators for electric vehicles and shared autonomous vehicles
Simulator Studies Charging
behaviors
Vehicle
routing Ride-hailing Transit Energy
calculation
Open
source
Paramics
[69]
[66]✓ ✓
[70]✓
[71]✓
VISSIM
[72]✓
[73]✓
[74]✓
[75]✓
[76]✓
TransModeler [77]✓ ✓
MATSim
[78]
[14]✓ ✓
[79]✓ ✓
SimMobility
[28]
[31]✓ ✓ ✓
[32]✓ ✓ ✓ ✓
[33]✓ ✓ ✓ ✓
SUMO
[11]
[80]✓
[81]✓
[82]✓
[64]✓ ✓
AIMSUN
[83]
[65]✓
[67]✓
[84]✓ ✓ ✓
POLARIS
[85]
[68]✓ ✓
[86]✓ ✓ ✓
Others
[37]✓
[38]✓ ✓ ✓
Matlab Simulink [87]✓
Simfleet [88]✓ ✓
METS-R SIM (this study)✓ ✓ ✓ ✓ ✓ ✓
Note: SimMobility, SUMO, MATSim are open-source simulators, the checkmarks in this table are specific to their
respective extensions.
Gap 3: Reproducibility and extensibility. Most simulation studies for SAEV services are not open source.
As a consequence, their results are barely reproducible for readers, and new extensions for accommodating new
scenarios/operational algorithms are likely to be prohibitive.
These research gaps warrant the need for an openly available simulation platform that captures the complexity of
energy consumption and offers the feasibility to tackle multiple SAEV-related issues comprehensively. As such, we
propose METS-R SIM, which incorporates various emerging public EV services under different facility designs and
operational strategies.
3. Model
3.1. Overview
Fig. 1presents the framework of METS-R SIM, which consists of multiple simulation instances and one control
center named the high-performance computing (HPC) module. Each simulation instance has a full life cycle (the
initialization, processing, and termination) of the SAEV services. The inputs of each simulation instance are facility
shapefiles, test scenarios, and hyperparameters for human behaviors (i.e., the elasticity of selecting traffic modes for
passengers and choosing charging stations for drivers). The outputs of the simulation are aggregated service metrics
and detailed vehicle trajectories.
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Multiple simulator instances are connected with an HPC module. The HPC module receives various operational
data (such as link energy updates and vehicle speed) from the simulator instances, then generates vehicle plans using
operational algorithms and returns them to the corresponding simulation instances. The benefits of having such a
module are two-fold: 1) for testing some operational algorithms (e.g., reinforcement learning algorithms) that require a
large amount of simulation data, multiple simulation instances can generate more data for the learning algorithms; 2) for
some operational algorithms that require solving optimization problems (e.g., integer programming), other simulation
instances can reuse the cached results in the future avoiding the overhead of expensive recomputations.
The scientific contributions of METS-R SIM are listed below:
1. METS-R SIM is the first-of-its-kind simulation platform that integrates state-of-the-art planning, scheduling,
and operation algorithms to allow a comprehensive assessment of full-scale electrified public transportation
systems at the city level.
2. Compared to existing works, METS-R SIM represents a perfect blending of meso-micro dynamics of a
transportation system at the urban level, which offers a more comprehensive coverage of SAEV system details.
The simulation is able to generate data from all components in a typical SAEV system (involving car-following,
routing, EV charging, and service operations) and feed them into real-time operations. This enables high-fidelity
modeling of data-driven operational algorithms (e.g., online routing, ride-sharing, and transit scheduling) and
their combinations.
3. METS-R SIM is HPC-enabled to tackle the challenge of large-scale electrified transportation system
planning and operation with high-fidelity vehicle dynamics and system operational details.
4. METS-R SIM can produce an accurate estimation of energy consumption and electricity demand with
vehicle specification power simulation and parameters calibrated from real-world data.
5. METS-R SIM is open source3, which allows for a wide penetration that can be adopted by academic institutions,
transit agencies, MPOs, and other federal and state-level agencies that have an interest in the transportation
electrification process.
In the following subsections, we present more details about the key components in METS-R SIM.
3.2. Traffic simulator
3.2.1. Input & output data
The traffic simulator requires static and dynamic inputs. The static inputs contain road information such as road
and lane shapefiles, locations of charging stations, and the number of AEV taxis and buses. To ensure the road and link
connectivity for the correct simulation of vehicle movements, we implement a road network preprocessing algorithm to
automatically transform the GIS shapefiles into the data files required by the simulation. In our case study, the charging
station design and static AEV bus routes are generated by our previous work [92,93]. The dynamic inputs include the
(link-level hourly) target speed and hourly travel demand. The output data are stored in two formats (CSV and JSON).
The CSV files record tabular aggregated performance metrics such as the number of served passengers by AEV taxis
and buses, the vehicle trip numbers, the passenger waiting time, and the energy consumption. Meanwhile, the JSON
files record the detailed SAEV trajectories and road network information, which serve as the input for the visualization
module.
3.2.2. Microscopic traffic simulation
The microscopic traffic model is inherited from the A-RESCUE simulator [94]. It adopts a three-regime car
following model (CFM) from [95]. The lane-changing model comes from [96].
Parallel computing is integrated into the implementation of the microscopic traffic model. The network is
partitioned into multiple connected components using the KMetis algorithm [97] to ensure each component contains
a similar number of on-road and upcoming vehicles, then the vehicles in different components are updated simulta-
neously. We further extend this parallel computing approach to incorporate SAEV operational modules and charging
station modules in METS-R SIM.
3https://github.com/umnilab/METS-R_SIM.git
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Main loop
Partitioned network
Traffic simulator
Traffic simulator
…
Traffic simulator Two-way connection layer
START
END
Calculate
metrics
Tick=
maxtick
?
Road
network
Charging
stations
Parking
resources
Waiting
elasticity
Fleet size
& types
No,
tick +=1
Yes
Price
elasticity
Energy
profile
Service
income
Update
vehicle
states …
Update
vehicle
states
Update
vehicle
states
Operational algorithms
1. Eco-routing
2. Dynamic transit scheduling
3. Online ridesharing
4. Vehicle charging
5. …
Inputs
Outputs
Initialization
Road
network
Electric
fleets
Charging
stations
Parking
zones
Background
traffic
Travel
demand Update traffic condition; Generate
passengers; Assign vehicle actions
Facility
Scenario Behavior
Historical
data
Real-time
data stream
Operational
actions
Vehicle/Service/Traffic
condition visualization
1. Basemap layer
2. Vehicle layer
3. Speed/Energy
consumption layer
4. Service metrics layer
Traffic simulator (JAVA) HPC module (Python)
Visualization interface (JavaScript)
Fig. 1. Framework of METS-R SIM
3.2.3. SAEV module
We simulate microscopic movements and electricity states of shared autonomous electric taxis (AEV taxis) and
shared autonomous electric buses (AEV buses), which are two core modules in our simulation. AEV taxis follow the
shortest path or K-shortest path [98] based on the travel time estimated from realized trajectories or the free flow speed
plus the delay at the intersection (when no observation is available). One can also explicitly control the vehicle routes
using the control center, which allows the test of online data-driven routing algorithms. In our numerical experiment,
we use an online eco-routing algorithm [99] to demonstrate its effectiveness. Between two consecutive bus stops, the
AEV buses can be set to follow a fixed shortest path or a dynamic one adapted to the travel time estimation.
In terms of service operation, a zonal-level service is considered. For every minute, the requests are assigned to
the vehicles within the same zone on a first-come, first-served (FCFS) basis. A simplified ridesharing algorithm is
implemented. The algorithm forms clusters of up to four passengers who are willing to share and have both the same
origin and destination zones, assigning them to the same vehicle. The vehicle then picks up these passengers and visits
their destinations in a FCFS manner. Between different zones, we provide a default rebalancing algorithm that sends
idle vehicles from oversupplied zones to undersupplied ones.
Aside from AEV taxis, AEV buses (Fig. 2) run along a certain number of optimized routes with fixed schedules.
Specifically, we employ a two-stage framework to devise the AEV bus routing and scheduling solutions from our past
study [93]. The first stage takes into account multiple factors including travel time and travel demand, and generates
a collection of potential bus routes. Subsequently, the second stage utilizes optimization techniques to determine the
number of buses to each potential bus route. This optimization aims to minimize the sum of bus purchase cost, operation
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cost, and expenses associated with unmet demand. We use this two-stage framework in our simulator, because of its
demonstrated efficacy in catering to travel demand through comprehensive experiments as referenced in Section 5 of
the study [93]. Lastly, we implement a bus transit integration mechanism that allows transfers between AEV taxis and
AEV buses. When activated, passengers will be presented with the alternative of using a combined bus-taxi or taxi-bus
mode in addition to the options of exclusively using AEV buses or AEV taxis.
For vehicle charging, AEV taxis and buses will be routed to the closest available charging stations when their State
of Charge (SoC) is below a predetermined threshold upon the finish of the current tasks. In our numerical experiment,
we set the threshold to be 20%.
Enter the
station
Bus
Charging
2 3 4
5
67
8
State of Charge
(SoC) > 20%
1
1A bus station
Bus stops
82
from to
Charging
Station
Yes
No
origin,
destination,
maximal waiting time,
current waiting time,
check(): waiting time
Passenger Class Charging Station Class, bus part
Bus routing loop
Leave the
station
Fig. 2. AEV bus module
3.2.4. Passenger module
The passenger module describes the passenger decision-making process while traveling across different zones. As
shown in Fig. 3, the passenger module consists of five components: trip generation, time/cost-based mode split model,
queuing structure, passenger departure as well as bus/taxi departure. For each tick, passengers are generated based on
the generation rate in each service zone and initialized with the origin, destination, preferred mode of transportation,
maximum waiting time, and an indicator that specifies whether they are willing to share. Each passenger is then added
to the corresponding matching queue and assigned to the vehicles when they become available. When passengers
have been served or have reached their maximum waiting time, they will be removed from the queue. The maximum
passenger waiting time and the percentage of shareable passengers are estimated using real-world observations obtained
from 2019 NYC taxi and ride-hailing trip records4. In our numerical experiments, we calculate the maximum passenger
waiting time from the 90th percentile of the real observed values and calibrate the percentage of shareable passengers
using the percentage of actual shared rides. For AEV buses, we assume the maximum waiting time for AEV buses is
unlimited in our numerical experiments, but it can be adjusted to realistic values if relevant data is available.
3.2.5. Charging stations
We implement both the Level 2 (L2) and DC fast (L3) chargers5with nonlinear charging speeds that mimic the
dynamics of the popular Constant Current Constant Voltage (CC-CV) charging methods. In general, L3 charging is
faster than L2 charging, and they are both adopted in current electric vehicle operation. As shown in Fig. 4, vehicles first
select chargers according to their utility, then each charging station receives the SAEVs and assigns these vehicles to the
4https://www.nyc.gov/site/tlc/about/tlc-trip- record-data.page
5https://afdc.energy.gov/fuels/electricity_charging_public.html
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Passenger
generation
Passenger
destination
zone
Maximum
waiting
time
Query from the
corresponding zone
Model split by travel
time and prices
Taxi queue
Bus line 1 queue
Bus line n queue
Estimated waiting time
Tax i
Bus line 1
Bus line n
Travel time/ Prices
Passenger-vehicle matching queues
Tax i/bus
arrive
Tax i/bus
departure
Fig. 3. Passenger module
corresponding charging queues. The charging station distribution within the simulator can be determined through two
methods. The first method involves utilizing publicly available charging station datasets, which are typically provided
by government or private companies (Method 1). The second method entails employing cost-based optimization
techniques to determine the optimal charging station placements (Method 2).
Vehicle arrival
Enter a charging
station at a zone
Utility:
total time
price
Charging time, charging price
Waiting time
A queue to AC L2 charge
A queue to AC L3 charge
AC L2 charger
AC L2 charger
AC L3 charger
AC L3 charger
Vehicle queues in charging stations
Fig. 4. Charging station model
3.2.6. Energy calculation
For gasoline vehicles, there are several well-developed and documented methods such as MOVES proposed by the
Energy and Environmental Protection Agency [100]. This method describes vehicle gas consumption and emissions
based on VSP (vehicle-specific power), velocity, and acceleration. For SAEVs, however, there is no unified process
that describes the energy consumption as a function of their VSP and velocity. This is because SAEV is an emerging
technology, and most of these procedures are still under active research. Therefore, we choose an established model in
literature [101]. Our energy calculation method considers acceleration, which is crucial for properly estimating energy
consumption in urban areas since frequent accelerating/braking can significantly impact energy consumption. It is also
worth noting that multi-processing is employed in calculating the energy consumption for vehicles in different network
partitions, which reduces the runtime.
3.3. High-performance computing (HPC) module
A control center named the high-performance (HPC) module is implemented using a server-client framework
illustrated in Fig. 5. Under the server-client framework, multiple simulation instances can run in parallel and send
simulation data over web sockets to a Remote Data Client (RDC). These data can be analyzed to make various decisions.
The data communication is managed by the Remote Data Client Manager (RDCM). RDCM’s job is to manage the
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METS-R SIM
data senders (i.e. multiple simulation instances) and their corresponding RDCs. In this paper, we showcase the utility
of this framework by implementing the online eco-routing algorithm [99] and demand-adaptive transit scheduling
algorithm [93].
routeUCB:
potential OD +
candidate routes
Other simulation
procedure
linkUCB: energy
consumption
observations
Tick ≥ max Tick
Simulation
start
End
DataManager
RemoteData
Client
WebSocket
routeResult
RemoteData
ClientManager
Global: candidate routes
and the corresponding links
Local: link visited times,
recorded link energy
consumption
initialize routeResult
Multi-arm combinatorial
bandit algorithm: update the
UCB (upper confidence
bound) of the path energy
consumption
Select the best route for OD
based on the UCB, store the
best route in routeResult
routeResult
Simulation side Control center side
routeUCB/
linkUCB
RemoteData
Client
Fig. 5. Server-client framework. Here we use eco-routing as an example
3.4. Visualization module
We developed a web-based visualization module to display simulation information. It is a JavaScript program
written based on React framework with layers powered by Deck.gl. An online demo is available6, note that this demo
also showcases how our simulation results can be easily shared.
Fig. 6. Examples of visualization results
The visualization module consists of five components:
•1. Road map: The road map shows the vehicle locations, facilities, and link status. The vehicle locations can
be displayed as icons or as heat maps. For the link status, the user can choose among speed (mph), total energy
consumed by crossing EVs (kwh), and energy efficiency (kwh/mile). In addition, by hovering the individual
vehicle icon, the user can check detailed information such as the battery level and the number of served
6https://engineering.purdue.edu/HSEES/METSRVis/
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passengers; The user can also hover over different links to see information about the traffic flow and link energy
consumption.
•2. Control panel: In the control panel, the user can choose the layer to display in the energy map. The control
panel also allows the user to control the play speed of vehicle movement and to adjust the visualization to any
simulation time.
•3. Performance charts: The performance charts show the dynamics of the relevant metrics.
•4. Connection: The connection panel allows the user to input the URL of the data source for the visualization.
•5. Legend: The legend panel shows the example of different elements in the energy map.
4. Experiment 1: Computational efficiency
METS-R SIM adopts parallel computing in two levels, as shown in Fig. 7a. First, METS-R SIM distributes the
update tasks (the "step()" function) among multiple threads based on their estimated computational load for each
simulation instance. For example, links in METS-R SIM will be regularly clustered by their corresponding numbers
of vehicles so that each thread would be responsible for updating a similar amount of vehicles. Second, multiple
simulation instances share one control center for communicating simulation states and operational commands on top
of each simulation instance. In this section, we evaluate the efficiency of the simulation instance.
We use the road network and 2019 taxi and ride-hailing trip information from New York City (NYC) for simulation
inputs. The road network is based on NYC Street Centerline shapefile available at NYC Open Data7, which contains
120,977 roads associated with information about their road type, road width, level of height. We note that, in this
shapefile, the same road is interrupted if another road overlaps with it at a different height so that this shapefile can
be simplified. We further divide the two-way roads into two separate links. After processing, we obtain 131,490 one-
way links. In our experiment, we adopt the charging station distribution placement strategy denoted as Method 2 in
Section 3.2.5. This approach involves minimizing the total cost of charging station facilities and the expenses on trips
originating from or ending at these charging stations in our past study [102]. Readers can also refer to Method 1
described in Section 3.2.5 based on real-world charging station data released by the U.S. Department of Energy8. The
demand, represented as hourly OD matrices between taxi zones9, is calculated from the 2019 trip request records for
taxis and ride-hailing published by NYC Taxi & Limousine Commission. Each test runs a simulation that uses demand
for 30 hours with a buffer of 3 hours before and after the target day. For this experiment, we use the data from 3/29/2019
during which 1.34M of trip requests are recorded.
Fig. 7b shows the computational time for finishing the simulation under different combinations of thread numbers
and demand percentages. We observe that overall parallel computing indeed improves computational efficiency: as the
number of threads increases, the computational time drops significantly. In comparison to using 2 threads, the scenario
using 4 threads shows a 25% reduction in time consumption. Furthermore, when utilizing 8 threads, an additional 10%
decrease in time consumption is observed. However, the improvement becomes marginal as the number of threads
exceeds 8.
Fig. 7b also reveals the relationship between the number of trip requests and computational cost. As the number of
trip requests increases, the computational time rises almost linearly. However, the computational time grows at a slower
rate compared to the increase in trip requests. For instance, as the demand increases by 50 times from 1% to 50%, the
computational time only increases by 80%. This can be attributed to the mechanism that routing updates are already
performed for each potential origin-destination pair, thereby reducing the computational overhead. This suggests that
our simulator exhibits strong scalability as the demand increases.
5. Experiment 2: Simulation validation
In this section, we validate the simulation from its capability of replicating real system performances and its
consistency in vehicle speed/battery profiles. To account for typical demand scenarios, we use clustering to categorize
different days into four scenarios and then sample representative days for each scenario.
7https://data.cityofnewyork.us/City-Government/NYC- Street-Centerline- CSCL-/exjm-f27b
8https://www.nyserda.ny.gov/All-Programs/Drive- Clean-Rebate- For-Electric-Cars- Program/Charging-Options/
Electric-Vehicle- Station-Locator#/find/nearest
9https://www.nyc.gov/site/tlc/about/tlc-trip- record-data.page
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(a) Parallel computing framework in METS-R
0 10 20 30 40 50
Percentage of trip requests (%)
3000
4000
5000
6000
7000
8000
9000
Computational time (s)
2 threads
4 threads
8 threads
16 threads
(b) Comparison of simulation efficiency
Fig. 7. Computational efficiency framework and results
Fig. 8. Demand scenarios. Scenario 1 is mainly relevant to Saturday demand patterns, Scenario 2 is mainly to Sunday
demand patterns, Scenario 3 is for weekdays, and Scenario 4 is for abnormal cases.
5.1. Experiment settings
We use the same network as the previous section to conduct our experiment. To obtain representative demand
scenarios, We perform a two-step clustering: first, the Gaussian mixture model described in [103] is applied to
distinguish abnormal days; then, K-means clustering is performed to further categorize the normal days’ demand into
a number of clusters where the cluster number is selected based on the maximum value of the silhouette coefficient.
Thereby, we obtain three normal demand scenarios and one abnormal scenario. The dominant day of the week of each
scenario is shown in Fig. 8.
Since we only simulate the SAEV fleets, the congestion effects caused by other traffic are not observed. To
compensate for this, we use hourly speed data from Uber Movement10 and match it to our NYC network. The missing
values are filled by interpolation based on upstream/downstream links and neighboring time slots. The processed speed
data are then used as the target speed of each road. The same setting was applied in [104]. Here we simulate 5% of the
total trips with 4,000 vehicles which account for nearly 5% of the taxi and ride-hailing fleet in NYC.
For each demand scenario, we randomly select 5 target days as 5 cases to run the test. These dates are:
1. Scenario 1: 4/7/2019 (Case 1), 8/4/2019 (Case 2), 9/15/2019 (Case 3), 11/29/2019 (Case 4), 12/23/2019 (Case
5);
10https://movement.uber.com/cities/new_york/downloads/speeds?tp[y]=2019&tp[q]=1
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Table 2. Deviation of simulated travel distances/time from the real observed ones
Metric Scenario 1 Scenario 2 Scenario 3 Scenario 4
Trip distance (mile) RMSE 0.97 ± 0.05 1.25 ± 0.03 1.69 ± 0.98 3.73 ± 0.20
MAE 0.65 ± 0.03 0.84 ± 0.02 1.09 ± 0.56 2.31 ± 0.10
Trip time (min) RMSE 5.71 ± 0.70 5.42 ± 1.13 6.58 ± 3.08 12.62 ± 0.43
MAE 4.40 ± 0.46 3.77 ± 0.57 4.63 ± 2.00 8.67 ± 0.23
2. Scenario 2: 4/1/2019, 4/22/2019, 9/23/2019, 12/1/2019, 12/16/2019;
3. Scenario 3: 3/29/2019, 4/25/2019, 7/17/2019,8/27/2019, 12/17/2019;
4. Scenario 4: 3/15/2019, 3/25/2019, 4/23/2019, 4/30/2019, 6/1/2019.
For each test, we run a simulation that uses input data for 30 hours with a buffer of 3 hours before and after the
target day, and calculate hourly aggregated simulated travel time/distance based on the trips starting between the 3rd
and the 27th hours.
5.2. Simulation results versus real observations
We compare the aggregated simulated travel distance/time and the real observed ones provided by trip records.
Table 2shows the root mean squared error (RMSE) and mean absolute error (MAE) of the simulated hourly travel
time/distance between each origin and destination zone with at least 20 trips per hour (since we sampled 5% of the
demand). We observe that for normal scenarios, METS-R SIM shows high fidelity in reproducing the vehicle travel
time/distance with the travel time deviating by 3-5 minutes, and the travel distance deviating by around 1-2 miles.
However, in the abnormal scenario, we observe high deviations in the simulated trip distance/time from the real
observed ones. Note the aggregated travel time/distance mostly depends on two modules: one is the microscopic traffic
model and the SAEV module, where the microscopic traffic simulation model dictates the simulated trip distance/time
and the SAEV module influences the served requests. A good consistency between the simulated travel time/distance
suggests a high fidelity in the microscopic traffic model and SAEV module.
The fidelity of METS-R SIM can be further confirmed by visualizing the one-to-one relationship between the
hourly real and simulated travel time/distance between each origin, destination, and hour triplet, as shown in Fig. 9.
We report that in normal scenarios, METS-R SIM can retrieve the real travel time/distance nicely. Also, we visualize
the total travel time/distance and find that the total simulated trip time/distance is consistent with the real ones, as shown
in Fig. 10. In the abnormal case, we notice that METS-R SIM keeps overestimating the overall travel time/distance.
The reason could be that the trip demand is more intense in the abnormal case, which can cause significantly more
congestion even when simulating 5% of the real fleet size.
5.3. Simulated trajectory and energy consumption
In the previous section, we have verified METS-SIM in terms of reproducing the total trip time/distance under
different demand scenarios. In this section, we zoom in on the vehicle acceleration/energy profiles. We note that the
car-following model of autonomous vehicles and the energy model for electric vehicles are not yet mature. Therefore,
we evaluate METS-R SIM based on three basic criteria: 1. whether the speed is continuous; 2. whether the regenerative
braking can be captured; 3. whether the speed profiles are similar to established studies.
Fig. 11 shows the sampled vehicle speed/energy profiles. It can be observed that the speed of the vehicle is
continuous. In addition, the regenerative brake is captured as shown in the rightmost two columns. Our simulated speed
profiles and the state of charge (SoC) curves are consistent with the ones reported in the established studies [81,75].
6. Experiment 3: Simulation applications
To showcase the applications of METS-R SIM, a realistic scenario is investigated and the simulation is applied to
answer key design/operational questions for SAEV services, including the supply and operational issues of the SAEV
services.
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METS-R SIM
Fig. 9. Real trip distance/time between each OD pair in every hour versus simulated ones. The shaded area covers the
records with the deviation of trip time less than 10 minutes and 3 miles.
0 5 10 15 20
Hour
0.00
0.25
0.50
0.75
1.00
1.25
Normalized total trip time
Scenario 1 Case 2
Real
Simulation
× 20
0 5 10 15 20
Hour
0.00
0.25
0.50
0.75
1.00
1.25
Normalized total trip time
Scenario 2 Case 2
Real
Simulation
× 20
0 5 10 15 20
Hour
0.00
0.25
0.50
0.75
1.00
1.25
Normalized total trip time
Scenario 3 Case 2
Real
Simulation
× 20
0 5 10 15 20
Hour
0.00
0.25
0.50
0.75
1.00
1.25
Normalized total trip time
Scenario 4 Case 2
Real
Simulation
× 20
0 5 10 15 20
Hour
0.00
0.25
0.50
0.75
1.00
1.25
Normalized total trip distance
Scenario 1 Case 2
Real
Simulation
× 20
0 5 10 15 20
Hour
0.00
0.25
0.50
0.75
1.00
1.25
Normalized total trip distance
Scenario 2 Case 2
Real
Simulation
× 20
0 5 10 15 20
Hour
0.00
0.25
0.50
0.75
1.00
1.25
Normalized total trip distance
Scenario 3 Case 2
Real
Simulation
× 20
0 5 10 15 20
Hour
0.00
0.25
0.50
0.75
1.00
1.25
Normalized total trip distance
Scenario 4 Case 2
Real
Simulation
× 20
Fig. 10. Real total occupied trip distance/time versus the simulated ones
6.1. Experiment settings
We consider the case of replacing the existing taxi and for-hire vehicle (FHV) services with SAEV services at
three major transportation hubs, i.e., Penn Station (PENN), LaGuardia Airport (LGA), John F. Kennedy International
Airport (JFK). We target the transportation hubs because they bring together a large number of commuters in short
periods which may largely benefit from multi-modal SAEV services.
The coefficients of the discrete choice model come from a passengers’ behavior study at the airport [105]. For
vehicle-related parameters in the energy model, we use technical specifications of real vehicles in production. For
AEV buses, we take the Volvo 7900 as a reference given that its technical specifications are openly available and have
been used in various implementations around the world11. The capacity (i.e., the number of passenger seats) for the
AEV bus is set as 40, which aligns with the specifications of buses manufactured by EV bus companies and can be
adjusted as needed. For AEV taxis, we use the Nissan Leaf as it has been widely used in the literature [101].
The road network is a subsample of the one used in Section 5.1 where we restrict the links that AEV taxis/buses
can visit. Specifically, we remove the links that have a speed limit less than 25 mph. During this process, we manually
keep those links belonging to highway ramps to ensure the completeness of the highway overpass. After this, we obtain
a network with 25,896 links. Other settings are the same in Section 5.1.
11https://www.volvobuses.com/en/city-and-intercity/buses/volvo-7900-electric/specifications.html
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0 500 1000 1500
Time (
s
)
0
10
20
30
40
50
Speed (
mph
)
Scenario 1 Case 2
0 500 1000 1500
Time (
s
)
0.0
2.5
5.0
7.5
10.0
12.5
15.0
Travel distance (
miles
)
Scenario 1 Case 2
0 500 1000 1500
Time (
s
)
58
59
60
61
62
63
State of charge(%)
Scenario 1 Case 2
0 500 1000 1500
Time (
s
)
0
10
20
30
40
50
Speed (
mph
)
Scenario 2 Case 2
0 500 1000 1500
Time (
s
)
0
2
4
6
8
10
Travel distance (
miles
)
Scenario 2 Case 2
0 500 1000 1500
Time (
s
)
22
23
24
25
26
State of charge(%)
Scenario 2 Case 2
0 500 1000 1500
Time (
s
)
0
10
20
30
40
50
Speed (
mph
)
Scenario 3 Case 2
0 500 1000 1500
Time (
s
)
0.0
2.5
5.0
7.5
10.0
12.5
Travel distance (
miles
)
Scenario 3 Case 2
0 500 1000 1500
Time (
s
)
49
50
51
52
53
54
State of charge(%)
Scenario 3 Case 2
0 500 1000 1500
Time (
s
)
0
10
20
30
40
50
Speed (
mph
)
Scenario 4 Case 2
0 500 1000 1500
Time (
s
)
0
2
4
6
8
10
Travel distance (
miles
)
Scenario 4 Case 2
0 500 1000 1500
Time (
s
)
59
60
61
62
63
State of charge(%)
Scenario 4 Case 2
Fig. 11. Simulated vehicle speed/energy profiles. For different scenarios, we visualize the dynamics of one randomly
chosen vehicle’s speed, cumulative distance, and battery level (SoC).
The experiment is divided into two parts, named Experiment 3.1 and Experiment 3.2. Experiment 3.1 is aiming to
answer the questions on the supply of SAEV services:
1. What are the required numbers of AEV taxis and AEV buses to satisfy a certain level of demand?
2. For different fleet sizes, what are their impacts on the existing transportation system?
For Experiment 3.1, we generate five levels of fleet size for taxis ranging from 2,000 to 4,000 with a step size of 500.
We generate six levels of fleet size (0 to 100 with a step size as 20 ) for SAEV buses. We then test all 30 combinations
of different levels of taxis and buses.
Experiment 3.2 targets devising the operational strategies of the SAEV services, which involve three key operational
algorithms: the eco-routing algorithm for AEV taxis to select energy optimal paths; the demand-adaptive bus
scheduling algorithm that updates the bus schedule for a certain period of time to enhance system efficiency; and
the AEV bus-taxi integration algorithm that enables the transfer between AEV taxis and buses. Within this context,
we test the following:
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METS-R SIM
1. What is the best combination of the operational strategies in the multi-modal SAEV system?
2. Are there any patterns that can be leveraged to enhance the system efficiency?
For Experiment 3.2, we set the fleet size for SAEV taxis to be 3,000, and the SAEV bus number to be 40 based on
the results of the first experiment. Testing three operational results in 2 × 2 × 2 = 8 strategy combinations.
Lastly, it is worth noting that for each fleet size or strategy combination, we simulate four scenarios with five
selected days. Hence, each combination corresponds to 20 simulation rounds.
6.2. Experiment 3.1: Supply design
6.2.1. Fleet size versus service quality
The 30 strategies generated by combining different fleet sizes are first compared for their aggregated performances.
As shown in Fig. 12a, one needs at least 2,500 taxis to satisfy at least 80% of demand. We also note, from Fig. 12d,
that the share of taxi trips increases as the taxi fleet size increases and the bus fleet size decreases, which aligns with
the intuition.
Fig. 12b shows the average passenger waiting time for taxis, a consistent decrease trend in the waiting time can
be observed as the taxi fleet size increases. However, we find that the passenger waiting time for AEV buses is not
necessarily negatively correlated to bus fleet size. This is because the waiting time for AEV buses also depends on
their schedules. In Fig. 12c, we observe that the waiting time for AEV buses exhibits wave-like patterns: initially, a
conservative plan is adopted to cover the busiest route, and increasing the fleet size would only reduce the headway
of that route; as the number of AEV buses increases, more zones are covered so the passenger waiting time for AEV
buses increases then again decreases.
Fig. 12e and Fig. 12f show the externality of the service, including the energy consumption per served passenger
and the AEV taxis’ ratio of deadhead mileage. The energy efficiency, captured by energy consumption per served
passenger (the lower the better), keeps increasing as the number of AEV taxis increases. This reflects the influence
of vehicle re-positioning: as more passengers are served, more repositioning trips need to be made to pick up those
passengers. In terms of AEV bus fleet size, the energy consumption per passenger exhibits a different pattern. As we
increase the AEV bus number, the energy consumption per passenger first decreases, then increases. This is expected
as an increase in the number of AEV buses would result in less efficient routes being covered, thereby reducing the
energy efficiency of the overall system. It is worth mentioning that energy efficiency is significantly more responsive
to variations in the size of the AEV bus fleet as compared to the AEV taxi fleet. For instance, a change of 20 in the
AEV bus fleet size would result in a comparable level of influence as changing the AEV taxi fleet size by 500. One of
the straightforward reasons is that AEV buses consume more energy for traveling the same distance when compared
with AEV taxis. Additionally, we observe, from Fig. 12f, that increasing the AEV bus fleet size would incur a higher
ratio of deadhead mileage in AEV taxi trips, which can also contribute to this phenomenon.
In summary, we show that, through METS-R SIM, one can obtain comprehensive metrics in terms of service quality
and energy efficiency. Also, it can be observed that the trends of performance can be well and consistently captured.
6.2.2. Spatial and temporal traffic impact
From the previous section, we have seen that increasing the fleet size results in better service quality but also incurs
more energy consumption and AEV taxi deadhead mileage. In this section, we investigate the detailed spatial and
temporal patterns of different fleet size designs.
The first row of Fig. 13 shows a visualization of temporal service patterns with three selected fleet size
combinations. The hourly occupied trips during the daytime are relatively stable across the day, but there is a peak
of the lost requests in the early morning, which is due to the increment of the repositioning needs during that period.
This is interesting because it reflects the morning demand patterns: for trips toward the transportation hubs, their origins
are usually far away from the hubs so they need to depart early. Apart from this, one can also observe the charging
demand patterns, which suggest that the charging trips are evenly distributed across the day. This is mainly due to the
simple threshold-based charging strategy adopted in the simulation.
The second row of Fig. 13 shows the hourly traffic impact. It can be observed that for most links except the ones
between different transportation hubs, the rise in traffic is insignificant, with less than 100 vehicles/hour. For the links
that connect different transportation hubs, i.e., JFK, LGA, and the PENN station, the incurred traffic can reach around
800 vehicles per hour. This information can guide the adjustment of the road infrastructure.
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AEV bus fleet size
020 40 60 80 100
AEV taxi fleet size
2000
2500
3000
3500
4000
Total served passengers(%)
60
70
80
90
100
(a) Served passengers (%)
AEV bus fleet size
0
20
40
60
80
100
AEV taxi fleet size
2000
2500
3000
3500
4000
Average passenger waiting
time (min) for AEV taxis
0.8
0.85
0.9
0.95
1.0
1.05
1.1
1.15
1.2
(b) Average passenger waiting time for
AEV taxis
AEV bus fleet size
0
20
40
60
80
100
AEV taxi fleet size
2000
2500
3000
3500
4000
Average passenger waiting
time (min) for AEV buses
0
10
20
30
40
50
60
70
80
(c) Average passenger waiting time for
AEV buses
AEV bus fleet size
020 40 60 80 100
AEV taxi fleet size
2000
2500
3000
3500
4000
Taxi served demand(%)
75
80
85
90
95
100
(d) Share of taxi served demand (%)
AEV bus fleet size
020 40 60 80 100
AEV taxi fleet size
2000
2500
3000
3500
4000
Energy consumption (Wh)
per served passenger
190
195
200
205
210
215
220
(e) Energy consumption per passenger
AEV bus fleet size
020 40 60 80 100
AEV taxi fleet size
2000
2500
3000
3500
4000
Raio of deadhead mileage
for AEV taxis(%)
28.0
29.0
30.0
31.0
(f) Ratio of deadhead mileage for AEV
taxis
Fig. 12. The aggregated performance of different scenarios. The values above the corresponding mean are colored in
red. The red/blue arrow indicates the maximum/minimum value.
From the analysis of Fig. 13, it can be concluded that increasing the number of AEV taxis from 2,000 to 3,000,
and the number of AEV buses from 0 to 40, results in a notable increase in occupied trips and, therefore, an increase
in the number of passengers served. However, increasing the fleet size further would yield only a marginal difference.
Additionally, the implementation of this service, using any of the three selected combinations, would have a negligible
impact on most links, except for those that connect different transportation hubs.
6.3. Experiment 3.2: Operation design
In Experiment 3.1, we have used METS-R SIM to evaluate and compare the performance metrics of different supply
designs. The results indicate that the implementation of 3,000 AEV taxis and 40 AEV buses is a practical option. In this
section, we utilize this supply design to demonstrate the effectiveness of METS-R SIM in devising operational strategies
by adjusting different operational algorithms. To accomplish this, we test three distinct operational algorithms:
1. Eco-routing (ECO) uses the historical energy profiles to predict energy-efficient routes, the client (simulation
instances) uploads the link level energy consumption data, and the server distributes the route choices regularly.
The detailed implementation can be found in [99];
2. Demand adaptive bus scheduling (BUS) generates new bus schedules on the server side based on the future
demand of the simulation every two hours and sends it back to the client (simulation instance). The detailed
information can be found in [93]. Note that in the current simulator, we maintain a fixed set of potential bus routes,
which are derived from the first stage discussed in [93]. This decision is made to address the computational time
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0 2 4 6 8 10 12 14 16 18 20 22 24
Hour of day
0
500
1000
1500
2000
2500
3000
3500
4000
4500
Number of fulfilled trips
Occupied
Repositioning
Charging
Left passengers
0
500
1000
1500
2000
2500
3000
3500
Number of left passengers
(a) Temporal service patterns I
0 2 4 6 8 10 12 14 16 18 20 22 24
Hour of day
0
500
1000
1500
2000
2500
3000
3500
4000
4500
Number of fulfilled trips
Occupied
Repositioning
Charging
Left passengers
0
500
1000
1500
2000
2500
3000
3500
Number of left passengers
(b) Temporal service patterns II
0 2 4 6 8 10 12 14 16 18 20 22 24
Hour of day
0
500
1000
1500
2000
2500
3000
3500
4000
4500
Number of fulfilled trips
Occupied
Repositioning
Charging
Left passengers
0
500
1000
1500
2000
2500
3000
3500
Number of left passengers
(c) Temporal service patterns III
2000 AEV taxis, 0 AEV buses
Additional traffic
flow (veh per hour)
0.00, 10.00
10.00, 50.00
50.00, 100.00
100.00, 200.00
200.00, 500.00
500.00, 697.00
(d) Spatial traffic impact I
3000 AEV taxis, 40 AEV buses
Additional traffic
flow (veh per hour)
0.00, 10.00
10.00, 50.00
50.00, 100.00
100.00, 200.00
200.00, 500.00
500.00, 793.00
(e) Spatial traffic impact II
4000 AEV taxis, 100 AEV buses
Additional traffic
flow (veh per hour)
0.00, 10.00
10.00, 50.00
50.00, 100.00
100.00, 200.00
200.00, 500.00
500.00, 774.00
(f) Spatial traffic impact III
Fig. 13. The spatial and temporal impacts of the ASEV services with different numbers of AEV taxis and buses
constraints in our current computational resources. However, the flexibility of altering the bus route generation
is an option, if additional computational resources become accessible;
3. Bus-Taxi integration (BT) enables the transfer between AEV bus and AEV taxi, this is achieved by providing
information on the bus-taxi integrated trips to passengers. The idea comes from [106] and we implement a
simplified version that greedily recommends integrated trips whenever they are possible.
Here we highlight the difference between these operational algorithms. The eco-routing algorithm is asynchronized
since the vehicle movement does not need to wait for the return of the eco-routing solutions. The demand adaptive
transit scheduling is a synchronized algorithm as the simulation needs to stop and wait for the latest bus schedules.
The bus-taxi integration is a type of control that depends on other operational strategies: whenever the bus schedule is
updated, the corresponding transfer trip recommendation would also need to be updated.
6.3.1. Interaction between operational algorithms
We test the cases by turning the three operational algorithms on and off separately. The results are shown in Fig. 14.
We first examine the impact of the individual algorithms, as shown in Fig. 14a, eco-routing (ECO) can slightly reduce
energy consumption (by 1-2%) with the cost of serving fewer passengers. This energy saving percentage is smaller than
the value reported in [99] as here we also count the energy consumption for deadhead trips. In terms of the demand-
adaptive bus scheduling algorithm (BUS), we find turning it on would reduce the percentage of served passengers
by 3% and increase the passenger waiting time for buses by almost 30%. These are due to the multi-objective setting
of the bus scheduling algorithm to balance the objectives of minimizing the fixed bus purchase cost, the flexible bus
operation cost, and the penalty of unsatisfied demand. Here we put a large weight on saving operational costs so the
output schedule, when adapting to demand dynamically, should dispatch fewer buses on the road. As one can see in
Fig. 14b, turning the BUS on leads to roughly 18% of less energy consumption in the AEV bus sector, and 14% of
less bus charging duration. For the bus-taxi integration (BT), we note that it can increase the percentage of served
passengers by 10% and save the total energy consumption by 10-20%. Specifically, it incurs more energy consumption
(around 10%) for AEV buses but greatly cuts the energy consumption (by 12-27%) in the AEV taxi sector. However,
we also note that introducing transfer recommendations between AEV taxis and AEV buses would lead to higher
passenger waiting time for both AEV taxis and buses.
Lei et al.: Preprint submitted to Elsevier Page 18 of 27

METS-R SIM
We then analyze the combinatorial effect of two algorithms. Combining eco-routing (ECO) and bus scheduling
(BUS) has a similar effect of applying only bus scheduling algorithms, the influence of the eco-routing algorithm is
subtle. Similar observations hold for combining eco-routing (ECO) and bus-taxi integration (BT). However, when
combining bus scheduling (BUS) and bus-taxi integration (BT), we note that applying dynamic bus scheduling
dampens the benefit of introducing bus-taxi transferring. As a result, the performance metrics are closer to those of
only enabling BUS. A similar argument holds for the case with all operational algorithms enabled.
In summary, we observe that introducing operational algorithms can improve service quality and reduce energy
consumption. However, it is important to note that the performance of the tested algorithms does not follow a simple
additive relationship. Instead, it seems that different algorithms compete with each other in complex ways. This
phenomenon has not been thoroughly studied in the current literature, and we envision that simulation platforms like
METS-R SIM offer a promising starting point for investigating those phenomena.
Deadhead mileage
ratio (%)
Total served passengers (%)
Taxi share (%)
Average waiting time
for taxi (min)
Average waiting time
for bus (min)
29 31 33 35 37
80
84
88
92
96
74
79
84
89
94
0.9
1.15
1.4
1.65
1.9
44
67
90
113
136
ECO:off BUS:off BT:off
ECO:off BUS:off BT:on
ECO:off BUS:on BT:off
ECO:off BUS:on BT:on
ECO:on BUS:off BT:off
ECO:on BUS:off BT:on
ECO:on BUS:on BT:off
ECO:on BUS:on BT:on
(a) Service quality
Bus charging duration
(min per veh)
Total energy consumption (MWh)
Taxi energy
consumption
(MWh)
Bus energy
consumption (MWh)
Taxi charging duration
(min per veh)
61 68 75 82 89
181
194
207
220
233
147
162
177
192
207
25
28
31
34
37
42
47
52
57
62
ECO:off BUS:off BT:off
ECO:off BUS:off BT:on
ECO:off BUS:on BT:off
ECO:off BUS:on BT:on
ECO:on BUS:off BT:off
ECO:on BUS:off BT:on
ECO:on BUS:on BT:off
ECO:on BUS:on BT:on
(b) Charging loads
Fig. 14. Radar plots of performance metrics under different operational algorithms. The dashed line corresponds to the
case with demand-adaptive transit scheduling turned on, and the square mark corresponds to the case with bus-taxi
integration.
6.3.2. Emerging patterns
In this section, we employ METS-R SIM to investigate the link-level energy consumption patterns in the system.
The outcomes are displayed in Fig. 15. It is noteworthy that merely 1% of links account for 20% of the total energy
consumption, and 10% of links contribute to 70% of the energy consumption. This pattern is consistent across all
operational algorithm combinations. The identification of these critical links that account for a significant portion of
energy consumption could facilitate the design of electrified roads [107] to efficiently charge vehicles.
7. Conclusion
This paper introduces METS-R SIM, an agent-based simulator for supporting the planning and design of public
SAEV services. The simulator utilizes a microscopic simulation module that incorporates AEV taxis and buses,
generating detailed service profiles that offer valuable insights into the deployment of public SEAV services. Compared
to existing studies, our simulator provides a more comprehensive understanding of SAEV operations and their
interactions with multiple factors. We also utilize a physical-based energy calculation model to determine SAEV energy
consumption from speed/acceleration profiles and employ parallel computing to enhance computation efficiency.
Additionally, we open source our code12 for greater transparency and reproducibility.
We benchmark the computational efficiency and simulation fidelity. It is found that our simulator can fulfill a
30-hour real-sized simulation task in just two hours. Additionally, our simulator generates trip distance/time and their
dynamics closely resemble real observations.
We demonstrate the capabilities of METS-R SIM in designing the SAEV fleet size and operational strategies for
surrogating existing taxi and FHV services at three transportation hubs (PENN, LGA, and JFK). Our results suggest
12https://github.com/umnilab/METS- R_SIM.git
Lei et al.: Preprint submitted to Elsevier Page 19 of 27

METS-R SIM
10 1100101102
Number of links (%)
0
20
40
60
80
100
Cumulative energy
consumption (%)
(a) ECO: off; BUS: off; BT: off
10 1100101102
Number of links (%)
0
20
40
60
80
100
Cumulative energy
consumption (%)
(b) ECO: off; BUS: off; BT: on
10 1100101102
Number of links (%)
0
20
40
60
80
100
Cumulative energy
consumption (%)
(c) ECO: off; BUS: on; BT: off
10 1100101102
Number of links (%)
0
20
40
60
80
100
Cumulative energy
consumption (%)
(d) ECO: off; BUS: on; BT: on
10 1100101102
Number of links (%)
0
20
40
60
80
100
Cumulative energy
consumption (%)
(e) ECO: on; BUS: off; BT: off
10 1100101102
Number of links (%)
0
20
40
60
80
100
Cumulative energy
consumption (%)
(f) ECO: on; BUS: off; BT: on
10 1100101102
Number of links (%)
0
20
40
60
80
100
Cumulative energy
consumption (%)
(g) ECO: on; BUS: on; BT: off
10 1100101102
Number of links (%)
0
20
40
60
80
100
Cumulative energy
consumption (%)
(h) ECO: on; BUS: on; BT: on
Fig. 15. Cumulative distribution function of link-level energy consumption. One curve represents one round of
simulation.
that a fleet of 3,000 AEV taxis and 40 AEV buses can sufficiently serve 80% of the demand. We also visualize the
spatial and temporal impacts of the service, which can help inform the feasibility of the service design.
After determining the fleet size, we test various combinations of operational algorithms to understand their
interactions. Our results show that these algorithms can improve service performance from specific perspectives.
Moreover, our test quantifies the combinatorial impacts of different operational algorithms, which are currently
understudied in the existing literature. Finally, we explore emerging patterns with our simulation outputs and observe
that link-level energy consumption follows a long-tail distribution, which could be useful for designing electrified
roads.
Our work still has several limitations. First, vehicle specifications and choice models are not tuned using real
observations due to limited resources. Second, we simplify the vehicle movement in the intersection as the traffic
light scheme is unavailable in the supply design phase. Third, more operational algorithms, such as dynamic pricing
and charging scheduling, can be embedded. Addressing these limitations is our ongoing task to further improve the
simulation platform.
Acknowledgement
We would like to thank the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy for
funding this study under Award Number DE-EE0008524.
A. Full validation results
Here we report the full version of Fig. 9and Fig. 10.
CRediT authorship contribution statement
Zengxiang Lei: Methodology, Data processing, Numerical experiments, Writing - Original draft preparation.
Jiawei Xue: Methodology, Data processing, Numerical experiments, Writing - Original draft preparation. Xiaowei
Chen: Methodology, Data processing, Numerical experiments, Writing - Original draft preparation. Xinwu Qian:
Conceptualization of this study, Methodology, Writing. Charitha Saumya: Methodology, Data processing. Mingyi
He: Methodology, Data processing. Stanislav Sobolevsky: Conceptualization of this study, Methodology, Writing.
Milind Kulkarni: Conceptualization of this study, Methodology, Writing. Satish V. Ukkusuri: Conceptualization of
this study, Methodology, Writing.
Lei et al.: Preprint submitted to Elsevier Page 20 of 27

METS-R SIM
Fig. A.1. Real trip distance each OD pair in every hour versus simulated ones. The shaded area covers the records with
the deviation of trip time less than 3 miles.
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Fig. A.3. Real total occupied trip distance versus the simulated ones
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Fig. A.4. Real total occupied trip time versus the simulated ones
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