[Paper Review] Joint Transportation and Charging Scheduling in Public Vehicle Systems - A Game Theoretic Approach

Ming Zhu, Xiao-Yang Liu+1 more|arXiv (Cornell University)|Dec 20, 2017

Electric Vehicles and Infrastructure32 references3 citations

TL;DR

This paper proposes a joint transportation and charging scheduling (JTCS) algorithm for public vehicle (PV) systems using a cake-cutting game to balance energy costs and service quality. By modeling PV groups as strategic players in a game, JTCS achieves a 10.86% lower average energy price than greedy charging, while maintaining near-identical transportation performance using real NYC taxi and grid data.

ABSTRACT

Public vehicle (PV) systems are promising transportation systems for future smart cities which provide dynamic ride-sharing services according to passengers' requests. PVs are driverless/self-driving electric vehicles which require frequent recharging from smart grids. For such systems, the challenge lies in both the efficient scheduling scheme to satisfy transportation demands with service guarantee and the cost-effective charging strategy under the real-time electricity pricing. In this paper, we study the joint transportation and charging scheduling for PV systems to balance the transportation and charging demands, ensuring the long-term operation. We adopt a cake cutting game model to capture the interactions among PV groups, the cloud and smart grids. The cloud announces strategies to coordinate the allocation of transportation and energy resources among PV groups. All the PV groups try to maximize their joint transportation and charging utilities. We propose an algorithm to obtain the unique normalized Nash equilibrium point for this problem. Simulations are performed to confirm the effects of our scheme under the real taxi and power grid data sets of New York City. Our results show that our scheme achieves almost the same transportation performance compared with a heuristic scheme, namely, transportation with greedy charging; however, the average energy price of the proposed scheme is 10.86% lower than the latter one.

Motivation & Objective

• To address the joint scheduling of transportation and charging in self-driving electric public vehicle systems under real-time electricity pricing.
• To balance competing demands between passenger service delivery and cost-effective battery charging in dynamic, high-occupancy PV operations.
• To ensure long-term system sustainability by preventing energy shortages during peak times while minimizing charging expenses.
• To develop a scalable, equilibrium-based coordination mechanism between PV groups, the cloud, and smart grids.

Proposed method

• Formalizing the joint transportation and charging scheduling problem as a cake-cutting game to model strategic allocation of energy and service resources among PV groups.
• Defining a composite utility function that captures transportation gains, battery satisfaction, and charging costs under real-time pricing.
• Proving the existence and uniqueness of a normalized Nash equilibrium in the proposed game-theoretic framework.
• Designing the JTCS algorithm to compute this equilibrium efficiently using constrained optimization.
• Integrating real-time electricity pricing and dynamic passenger demand data from NYC taxi and grid datasets into the simulation framework.
• Validating the scheme through simulations comparing JTCS against a baseline greedy charging (TGC) strategy.

Experimental results

Research questions

• RQ1 How can public vehicle systems optimally balance transportation demand and energy charging under real-time electricity pricing?
• RQ2 What game-theoretic model enables efficient coordination among PV groups to jointly maximize utility while minimizing energy costs?
• RQ3 Can a unique and stable equilibrium be achieved in the joint scheduling of transportation and charging operations in PV systems?
• RQ4 How does the proposed scheme compare to greedy charging in terms of energy cost and service performance?
• RQ5 To what extent can the system maintain service quality while reducing average energy prices through strategic scheduling?

Key findings

• The JTCS algorithm achieves a 10.86% reduction in average energy price compared to the greedy charging baseline (TGC), with no significant loss in transportation performance.
• Total energy payment under JTCS is 355 USD, a 29.8% reduction from 505 USD under TGC, demonstrating substantial cost savings.
• Charged energy under JTCS is 15,392 kWh, significantly less than TGC’s 19,315 kWh, indicating more efficient energy use.
• Despite lower charging volume, JTCS maintains sufficient battery levels during peak hours, with remaining energy dropping rapidly only when needed.
• The system remains stable over multiple days by ensuring final daily energy levels are not less than initial levels, enabling long-term scalability.
• The scheme effectively avoids overcharging during high-price periods while still meeting transportation demands, proving robustness under dynamic conditions.