Modeling and Managing Operations of Mixed Human-driven andAutonomous Ride-sourcing Fleets
L. Chena , M. Ramezania,∗
a The University of Sydney, School of Civil Engineering, Sydney, Australia

linji.chen@sydney.edu.au, mohsen.ramezani@sydney.edu.au∗ Corresponding author
Extended abstract submitted for presentation at the 11th Triennial Symposium on
Transportation Analysis conference (TRISTAN XI)
June 19-25, 2022, Mauritius Island

January 12, 2022
Keywords: Dynamic modeling, MPC optimization, Simulation, Pricing

1INTRODUCTION

As the autonomous vehicle (AV) technology attracts more interests in both industry and academia,
it brings a vast set of new solutions and questions alike. One of the issues is the management ofsuch an automated fleet, especially in the presence of traditional human-driven vehicles (HVs).
The AV management problem includes many areas worth exploring, ranging from motion control to network design, detection technology to economic evaluation. In this paper, we study themodeling and control of AVs in ride-sourcing systems.
The modeling and control problem is complicated, involving stochastic behaviors of existing
market users. The labor supply may exhibit different behaviors based on wage changes, adhering
the income-targeting theory (Camerer et al., 1997) or the neoclassical theory (Farber, 2015).
Besides the labor supply, passengers also demonstrate varying behaviors. Wang et al. (2020)studies the order cancellation and its impact on a ride-sourcing system. Hörl et al. (2019) has
designed operational plans for AV fleets based on such behavioral assumptions. These works
mostly focus on pre-defined vehicle routing and order dispatching policies, rather than dynamic
controls in real time. It is shown that a non-equilibrium dynamic pricing control scheme canbring significant benefits to the ride-sourcing operator (Nourinejad & Ramezani, 2020).
This work focuses on the fleet size and price structure for ride-sourcing services by a mixedfleet composition. A network simulation is developed to replicate individual behaviors and interactions in a ride-sourcing market, considering various personal traits and preferences. A dynamiccontrol method utilizing a model predictive control (MPC) scheme is proposed to optimize thedynamic trip fares, driver wages, and AV fleet activation/deactivation in real time.

2METHODOLOGY2.1

Detailed Simulation Plant

A simulation environment is constructed to implement and test the proposed control method.
The simulation provides flexibility in regard to behaviors of individual agents, i.e. passengers,
drivers, and AVs. A static network map is also configured to replicate their path-finding andmatching processes in an urban ride-sourcing environment.
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L. Chen, M. Ramezani

2.1.1

2

Agent Behavior

The model involves two groups of agents, passengers and vehicles. Each individual passengergenerates a trip request from some origin location to some destination at some time. Thesetrip demands are obtained from NYC yellow taxi records in June 2016. Besides trip generation,
personal attributes such as their value of time (VoT) and maximum waiting time (patience)
would affect their mode choice and order cancellation behaviors.
It is assumed that a passenger chooses a vehicle type (HV or AV) before the trip request.
Such process is modeled as a Logit choice such that the utility depends on (1) the current trip
fare, (2) individual VoT, and (3) the estimated waiting time to be matched with a vacant vehicle.
In the case of undesirable utilities, passengers also have the option to select other modes, whichhave a fixed utility. Even if a passenger has requested for an AV or HV, the actual matchingprocess might take too long so that they decide to cancel the request. A passenger is assumed
to have some patience time (e.g., 1 minute, bounded by 0.5 and 2 minutes).
Both AVs and HVs provide the same trip services. They remain stationary until the platform(central system) assigns them with some passengers. They would pick up the passenger at theorigin location by the shortest travel time path and deliver them to the destination in the samemanner. The main difference is how the AV fleet can be directly managed by real-time activation/deactivation while human drivers are only partially influenced by monetary incentives.
Since drivers have different inherent preferences about working hours and incomes, their participation and exit from the labor market are more complicated. It is challenging to predict theirindividual impacts on the aggregated market condition. Both income-targeting and neoclassicaldriver behaviors are considered in this paper. HVs drivers make relevant decisions based oneither cumulative gain or the short-term income prospect.
2.1.2

Network and Matching

The road network of Manhattan is obtained from OpenStreetMap to build a directed graph withroads as edges and intersections as nodes. The resultant graph contains 9537 edges and 4360
nodes. Each edge is associated with a static travel time (i.e. constant speed), which is calibrated
from historical taxi trip records. The static map is used to facilitate path-finding and tripassignment. A batch matching algorithm is used to pair waiting passengers and vacant vehicles.
It operates at short intervals (e.g., 10 seconds) to pair the passenger requests queued during thisinterval with available vehicles such that the total pick-up travel time is minimized. Matching isconducted separately for AVs and HVs, as passengers cannot request both simultaneously.

2.2

Model Predictive Control

A model predictive control (MPC) scheme is applied in a closed-loop framework to maximize
the platform’s profit. The MPC relies on a prediction model to estimate future system states
within a finite prediction horizon so that the control variables can be optimized with respect tofuture states. The optimization process is repeated with a shifted (receding) horizon to update
the control inputs to be implemented in the simulation plant. In addition, the system model
considers periodic state feedback from the plant to improve the state prediction. The overallsystem framework is illustrated in Figure 1. The set of 4 control inputs at a certain step k within
the horizon, ū(k), are (1) trip fare per unit in-vehicle travel time for AVs, f AV (k); (2) trip fareper unit in-vehicle travel time for HVs, f HV (k); (3) wage per unit in-vehicle travel time for HVs,g HV (k); and (4) AV fleet activation/deactivation, ∆N AV (k).
By manipulating these control inputs, the platform aims to maximize its total profit for eachreceding horizon from k0 to k0 + h. The profit depends on (a) total revenues collected fromAV and HV fares for each successful ride; (b) wage payments to HVs (i.e. HV cost); (c) fixed
operational expenses of vacant and occupied AVs (i.e. AV cost); and (d) penalties from passenger
order cancellations which affect long-term reputation of the platform.
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L. Chen, M. Ramezani

3Figure 1 – method framework. Historical supply and demand data are used as exogenous demandand supply estimations in the prediction model. The closed-loop framework involves state feedback
from the plant, prediction of future states, optimization and implementation of control inputs.
Equations 1–4 outline market state dynamics for the two vehicle types m ∈ {AV, HV}. Them
first two define the number of waiting passengers pmw , and vacant vehicles nv of vehicle type mfrom time step k to k + 1. The estimation requires exogenous demand ∆Npm (including modechoice) and supply ∆N m inputs, as well as endogenous algorithmic estimations for the number ofm
order cancellations ñmcancel , number of expected drop-offs (trip completion) ñdrop , and the number
mof new trip matching which is equal to the minimum of the two agent sets (pmw and nv ) in acomplete bipartite graph. Likewise, the number of assigned vehicles nm
a would decrease by thenumber of pick-ups ñm,
once
they
reachthepassenger
locationandbecomeoccupied.
pickmmmmmpm
w (k + 1) = pw (k) + ∆Np (k) − ñcancel (k) − min{pw (k), nv (k)}

(1)

mm
m
m
m
nmv (k + 1) = nv (k) + ∆N (k) + ñdrop (k) − min{pw (k), nv (k)}
mm
m
m
nm
a (k + 1) = na (k) − ñpick (k) + min{pw (k), nv (k)}mmm
nmo (k + 1) = no (k) + ñpick (k) − ñdrop (k)

(2)
(3)
(4)

The controllers manage the system via the exogenous demand and supply. Trip fares woulddetermine the passenger demand and the mode split ratio; AV fleet size is a direct control
variable; and dynamic driver wages are indirect incentives to manage the HV supply.

3RESULTS

The preliminary results suggest that MPC has the potential to significantly improve the profit.
The test case simulates the morning passenger demand based on historical taxi trip records
from 04:00 to 10:00 with 1000 AVs and HVs respectively. The benchmark control variables are
assumed to be time-invariant. Figure 2 shows an example of state prediction for the benchmark
case. Plant feedback adjusts the initial guesses for each prediction. Table 1 summarizes results
for a scenario where only passenger fares are controlled. Thus, the solution for a supply surplus
is to increase both fares to gain more profits, which also drive out passengers, those above theplatform’s capacity, to lower the expected order cancellation. The AV fare is raised to an averageof $1.52/min (from $0.8/min) and HV fare is raised to $1.67/min (from $0.7/min).
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L. Chen, M. Ramezani

4

Figure 2 – example state predictions. An overestimation of assigned vehicles would correspondwith an underestimation of occupied vehicles due to longer/shorter pick-up time expectations.
Table 1 – Summary of Preliminary Results

Total demand (AV/HV/others)
Cancellation (AV/HV)
Total fare revenue
Total wage payment
Total AV cost
Total profit4Benchmark (fixed controls)
24456 / 21029 / 18736
6653 / 3299
$336,764$153,357$131,805$51,603

MPC (Fare control)
17167 / 19178 / 27876
1880 / 1229
$525,581$110,210$119,619$295,752

DISCUSSION

This paper proposes a model with dynamic optimization controls. Multiple levels of individual
decision-making processes make the models more realistic. The advantage of an MPC is that it
does not rely on accurate long-term predictions as much because it receives periodic feedback
corrections from the system. This allows the platform to optimize its goals at a macroscopic
level, and manage a mixed fleet by considering different options while predicting/monitoring
their impacts on the market states of interest.

References
Camerer, Colin, Babcock, Linda, Loewenstein, George, & Thaler, Richard. 1997. Labor Supply of New
York City Cabdrivers: One Day at a Time*. The Quarterly Journal of Economics, 112(2), 407–441.
Farber, Henry S. 2015. Why you Can’t Find a Taxi in the Rain and Other Labor Supply Lessons fromCab Drivers*. The Quarterly Journal of Economics, 130(4), 1975–2026.
Hörl, S., Ruch, C., Becker, F., Frazzoli, E., & Axhausen, K. W. 2019. Fleet operational policies forautomated mobility: A simulation assessment for Zurich. Transportation Research Part C: Emerging
Technologies, 102(May), 20–31.
Nourinejad, Mehdi, & Ramezani, Mohsen. 2020. Ride-Sourcing modeling and pricing in non-equilibrium
two-sided markets. Transportation Research Part B: Methodological, 132(Feb.), 340–357.
Wang, Xiaolei, Liu, Wei, Yang, Hai, Wang, Dan, & Ye, Jieping. 2020. Customer behavioural modellingof order cancellation in coupled ride-sourcing and taxi markets. Transportation Research Part B:Methodological, 132(Feb.), 358–378.

TRISTAN XI Symposium

Original abstract submittal