Dynamic Stochastic Matching Under Limited Time

Abstract

In “Dynamic Stochastic Matching Under Limited Time,” Aouad and Sarıtaç analyze the design of matching policies in dynamic markets such as carpooling platforms and kidney exchange schemes. A crucial distinction with previous literature is that the agents’ arrivals and departures are fully dynamic. The demand and supply side are constantly replenished; each market participant remains available for potential matches during a limited period of time. Specifically, the authors formulate a general dynamic matching model over edge-weighted graphs, where the agents' arrivals and abandonments are stochastic and heterogeneous. The platform controls how long each agent waits and whom s/he is matched with. These decisions are subject to a fundamental tradeoff between increasing market thickness and mitigating the risk of abandonments from certain participants. The authors’ main contribution is to devise simple matching algorithms with strong performance guarantees for a broad class of networks. In contrast, they show that widely used batching algorithms have an arbitrary bad performance on certain graph-theoretic structures. Their analysis involves novel techniques including linear programming benchmarks, value function approximations, and proxies for continuous-time Markov chains, which may be of broader interest. Extensive simulations on real-world taxi demand data demonstrate that the newly developed algorithms can significantly improve cost efficiency against batching algorithms.

Two-stage Matching and Pricing with Applications to Ride Hailing

“…In the small traffic regime, Aouad and Saritaç (2020) study a continuous time dynamic stochastic matching model where supply and demand have type dependant weights/costs and their arrivals and abandonments are stochastic and heterogeneous with given rates. While our work conceptually resembles some aspects in these work (e.g., the idea of batching improving the performance of matching policy is seen in Aveklouris et al 2021), it diverges from this line of work on several fronts.…”

Online Assortment Optimization for Two-Sided Matching Platforms

“…Dynamic matching. Motivated by the growth of online markets, several recent papers have studied dynamic variants of the online matching setting, where vertices arrive dynamically on the two sides of the graph; see, e.g., Gurvich and Ward (2015), Akbarpour et al (2020), Anderson et al (2017), Ashlagi et al (2019), Afeche et al (2019), and Aouad and Saritaç (2020) which propose various models in this spirit. This line of work focuses on capturing the market dynamics that describe the agents' arrivals and departures, while the matching decisions are controlled by a central platform.…”

Real-Time Driver-Request Assignment in Ridesourcing

“…In this paper, we limit our focus to the Poisson process with process rate λ d . This is a standard assumption for driver arrivals that has been considered in many works (Collina et al 2020;Aouad and Saritac ¸2020). After its arrival, the driver will stay in the system until it is matched.…”