Empty-car routing in ridesharing systems

Abstract: This paper considers a closed queueing network model of ridesharing systems such as Didi Chuxing, Lyft, and Uber. We focus on empty-car routing, a mechanism by which we control car flow in the network to optimize system-wide utility functions, e.g. the availability of empty cars when a passenger arrives. We establish both process-level and steady-state convergence of the queueing network to a fluid limit in a large market regime where demand for rides and supply of cars tend to infinity, and use this limit to study a fluid-based optimization problem. We prove that the optimal network utility obtained from the fluid-based optimization is an upper bound on the utility in the finite car system for any routing policy, both static and dynamic, under which the closed queueing network has a stationary distribution. This upper bound is achieved asymptotically under the fluid-based optimal routing policy. Simulation results with real-world data released by Didi Chuxing demonstrate the benefit of using the fluid-based optimal routing policy compared to various other policies.

Empty-car Routing in Ridesharing Systems: An Analytical Approach

In a detailed study on ridesharing systems, Braverman, Dai, Liu, and Ying have examined the problem of empty-car routing, focusing on maximizing system-wide utility functions such as the availability of empty cars when passengers arrive. Their work presents a closed queueing network model applicable to real-world ridesharing platforms like Uber and Lyft, addressing key challenges in optimizing car flow within the network.

Closed Queueing Network Model

The authors propose a model consisting of several key components: passengers arrive at different regions according to a Poisson process, and cars are distributed in these regions waiting to serve. The movement of vehicles within this network is driven by passenger trips, with cars either remaining in place or relocating without passengers based on a routing probabilistic matrix $Q$.

Fluid Limit Analysis

In a large market regime where both demand and supply scale with the number of cars $N$, the authors utilize a fluid limit approach to analyze the convergence of the queueing network. This process leads to a fluid-based optimization problem which serves as an upper bound on the network utility under any marked routing policy. The researchers demonstrate asymptotic optimality of this fluid-based solution, which achieves said bound under a static routing policy.

Numerical Insights

The simulation results, derived from real data provided by Didi Chuxing, reveal the effectiveness of fluid-based optimal routing over dynamic policies. Importantly, these simulations underscore the performance improvements when this fluid-based approach is employed, presenting a compelling case for the strategic value of static routing in expansive markets.

Implications and Future Research

The theoretical underpinnings of this research have significant implications for practical deployments in ridesharing. As ridesharing systems continue to grow, understanding the dynamics of empty-car routing can vastly improve service availability, reduce operational costs, and increase overall efficiency. Future research may explore decentralized routing mechanisms and explore adaptive strategies for time-varying demand scenarios, building on the foundational analysis provided here.

Conclusion

Braverman et al. have delivered an analytical toolset for addressing the empty-car routing challenge in ridesharing networks. This study creates a platform for refining operational protocols, ensuring optimal resource allocation in dynamic urban settings. By grounding their analysis in queueing theory and fluid dynamics, their work opens doors for further exploration into robust, scalable rideshare optimizations.