This paper studies optimal pricing and rebalancing policies for Autonomous Mobility-on-Demand (AMoD) systems. We take a macroscopic planning perspective to tackle a profit maximization problem while ensuring that the system is load-balanced. We begin by describing the system using a dynamic fluid model to show the existence and stability of an equilibrium (i.e., load balance) through pricing policies. We then develop an optimization framework that allows us to find optimal policies in terms of pricing and rebalancing. We first maximize profit by only using pricing policies, then incorporate rebalancing, and finally we consider whether the solution is found sequentially or jointly. We apply each approach on a data-driven case study using real taxi data from New York City. Depending on which benchmarking solution we use, the joint problem (i.e., pricing and rebalancing) increases profits by 7% to 40%
This paper treats an optimal scheduling problem of control nodes in networked systems. We newly introduce both the L0 and l0 constraints on control inputs to extract a time-varying small number of effective control nodes. As the cost function, we adopt the trace of the controllability Gramian to reduce the required control energy. Since the formulated optimization problem is combinatorial, we introduce a convex relaxation problem for its computational tractability. After a reformulation of the problem into an optimal control problem to which Pontryagin's maximum principle is applicable, we giv…
This paper studies congestion-aware route-planning policies for Autonomous Mobility-on-Demand (AMoD) systems, whereby a fleet of autonomous vehicles provides on-demand mobility under mixed traffic conditions. Specifically, we first devise a network flow model to optimize the AMoD routing and rebalancing strategies in a congestion-aware fashion by accounting for the endogenous impact of AMoD flows on travel time. Second, we capture reactive exogenous traffic consisting of private vehicles selfishly adapting to the AMoD flows in a user-centric fashion by leveraging an iterative approach. Finally…
In this paper, we investigate the problem of routing, rebalancing, and charging for electric autonomous mobility-on-demand systems concerning traffic congestion. We analyze the problem at the macroscopical level and use a volume-delay function to capture traffic congestion. To address this problem, we first formulate an optimization problem for routing and rebalancing. Then, we present heuristic algorithms to find the loop of the traffic flow and examine the energy constraints within the resulting loop. We impose charging constraints on the re-routing problem so that the new solution satisfies…
Mobility-on-Demand (MoD) services, such as taxi-like services, are promising applications. Rebalancing the vehicle locations against customer requests is a key challenge in the services because imbalance between the two worsens service quality (e.g., longer waiting times). Previous work would be hard to apply to large-scale MoD services because of the computational complexity. In this study, we develop a scalable approach to optimize rebalancing policy in stages from coarse regions to fine regions hierarchically. We prove that the complexity of our method decreases exponentially with increasin…
In this paper we study rebalancing strategies for a mobility-on-demand urban transportation system blending customer-driven vehicles with a taxi service. In our system, a customer arrives at one of many designated stations and is transported to any other designated station, either by driving themselves, or by being driven by an employed driver. The system allows for one-way trips, so that customers do not have to return to their origin. When some origins and destinations are more popular than others, vehicles will become unbalanced, accumulating at some stations and becoming depleted at others…
Mobility systems featuring shared vehicles are often unable to serve all potential customers, as the distribution of demand does not coincide with the positions of vehicles at any given time. System operators often choose to reposition these shared vehicles (such as bikes, cars, or scooters) actively during the course of the day to improve service rate. They face a complex dynamic optimization problem in which many integer-valued decisions must be made, using real-time state and forecast information, and within the tight computation time constraints inherent to real-time decision-making. We fi…
Spatiotemporal Pricing and Fleet Management of Autonomous Mobility-on-Demand Networks: A Decomposition and Dynamic Programming Approach with Bounded Optimality Gap
Single- vs. Dual-Policy Reinforcement Learning for Dynamic Bike Rebalancing
Department of Mathematical and Industrial Engineering, Polytechnique Montréal（蒙特利尔理工学院数学与工业工程系）；School of Management, Université du Québec à Montréal（魁北克大学蒙特利尔分校管理学院）；Cornell Tech and Technion - IIT（康奈尔科技与技术Ion研究所）
The performance of multimodal mobility systems relies on the seamless integration of conventional mass transit services and the advent of Mobility-on-Demand (MoD) services. Prior work is limited to individually improving various transport networks' operations or linking a new mode to an existing system. In this work, we attempt to solve transit network design and pricing problems of multimodal mobility systems en masse. An operator (public transit agency or private transit operator) determines the frequency settings of the mass transit system, flows of the MoD service, and prices for each trip…
This paper provides a framework to quantify the sensitivity associated with behavioral models based on Cumulative Prospect Theory (CPT). These are used to design dynamic pricing strategies aimed at maximizing performance metrics of the Shared Mobility On-Demand Service (SMoDS), as solutions to a constrained nonlinear optimization problem. We analyze the sensitivity of both the optimal tariff as well as the optimal objective function with respect to CPT model parameters. In addition to deriving analytical solutions under certain assumptions, more general numerical results are obtained via compu…
We consider a profit maximization problem in an urban mobility on-demand service, of which the operator owns a fleet, provides both exclusive and shared trip services, and dynamically determines prices of offers. With knowledge of the traveler preference and the distribution of future trip requests, the operator wants to find the pricing strategy that optimizes the total operating profit of multiple trips during a specific period, namely, a day in this paper. This problem is first formulated and analyzed within the dynamic programming framework, where a general approach combining parametric ro…
In a Shared Mobility on Demand Service (SMoDS), dynamic pricing plays an important role in the form of an incentive for the decision of the empowered passenger on the ride offer. Strategies for determining the dynamic tariff should be suitably designed so that the incurred demand and supply are balanced and therefore economic efficiency is achieved. In this manuscript, we formulate a discrete time Markov Decision Process (MDP) to determine the probability desired by the SMoDS platform corresponding to the acceptance rate of each empowered passenger at each state of the system. We use Estimated…
This paper investigates the impacts of competition in autonomous mobility-on-demand systems. By adopting a network-flow based formulation, we first determine the optimal strategies of profit-maximizing platform operators in monopoly and duopoly markets, including the optimal prices of rides. Furthermore, we characterize the platform operator's profits and the consumer surplus. We show that for the duopoly, the equilibrium prices for rides have to be symmetric between the firms. Then, in order to study the benefits of introducing competition in the market, we derive universal theoretical bounds…
Optimizing shared vehicle systems (bike/scooter/car/ride-sharing) is more challenging compared to traditional resource allocation settings due to the presence of \emph{complex network externalities} -- changes in the demand/supply at any location affect future supply throughout the system within short timescales. These externalities are well captured by steady-state Markovian models, which are therefore widely used to analyze such systems. However, using such models to design pricing and other control policies is computationally difficult since the resulting optimization problems are high-dime…
Learning-based Online Optimization for Autonomous Mobility-on-Demand Fleet Control
TUM School of Management（慕尼黑工业大学管理学院）；Technical University of Munich（慕尼黑工业大学）；CERMICS（法国桥路学校计算数学与科学工程中心）；École des Ponts（法国桥路学校）；Munich Data Science Institute（慕尼黑数据科学研究所）；CIRRELT（蒙特利尔物流、运输与计算机工程研究中心）；École Polytechnique de Montréal（蒙特利尔理工学院）；Pontifical Catholic University of Rio de Janeiro（里约热内卢天主教大学）
The presence of uncertainties in the ride-hailing market complicates the pricing strategies of on-demand platforms that compete each other to offer a mobility service while striving to maximize their profit. Looking at this problem as a stochastic generalized Nash equilibrium problem (SGNEP), we design a distributed, stochastic equilibrium seeking algorithm with Tikhonov regularization to find an optimal pricing strategy. Remarkably, the proposed iterative scheme does not require an increasing (possibly infinite) number of samples of the random variable to perform the stochastic approximation,…
Expected to operate in the imminent future, air taxi service (ATS) is an aerial on-demand transport for a single passenger or a small group of riders, which seeks to transform the method of everyday commute. This uncharted territory in the emerging transportation world is anticipated to enable consumers bypass traffic congestion in urban road networks. By adopting an electric vertical takeoff and landing concept (eVTOL), air taxis could be operational from skyports retrofitted on building rooftops, thus gaining advantage from an implementation standpoint. Motivated by the potential impact of A…
Technical University of Denmark（丹麦技术大学）；Technical University of Munich（慕尼黑工业大学）；University of Groningen（格罗宁根大学）；University of Twente（特文特大学）；Munich Data Science Institute（慕尼黑数据科学研究所）
Bike-sharing systems are a rapidly developing mode of transportation and provide an efficient alternative to passive, motorized personal mobility. The asymmetric nature of bike demand causes the need for rebalancing bike stations, which is typically done during night time. To determine the optimal starting inventory level of a station for a given day, a User Dissatisfaction Function (UDF) models user pickups and returns as non-homogeneous Poisson processes with piece-wise linear rates. In this paper, we devise a deep generative model directly applicable in the UDF by introducing a variational …
We propose a model of incentives for data pricing in large mobile networks, in which an operator wishes to balance the number of connections (active users) of different classes of users in the different cells and at different time instants, in order to ensure them a sufficient quality of service. We assume that each user has a given total demand per day for different types of applications, which he may assign to different time slots and locations, depending on his own mobility, on his preferences and on price discounts proposed by the operator. We show that this can be cast as a bilevel progra…
