Dynamic Matching for Real-Time Ridesharing
77 Pages Posted: 28 Sep 2016 Last revised: 21 Sep 2018
Date Written: June 15, 2017
In a ridesharing system such as Uber or Lyft, arriving customers must be matched with available drivers. These decisions affect the overall number of customers matched, because they impact whether or not future available drivers will be close to the locations of arriving customers. A common policy used in practice is the closest driver (CD) policy that offers an arriving customer the closest driver. This is an attractive policy because it is simple and easy to implement. However, we expect that parameter-based policies can achieve better performance.
We propose matching policies based on a continuous linear program (CLP) that accounts for (i) the differing arrival rates of customers and drivers in different areas of the city, (ii) how long customers are willing to wait for driver pick-up, and (iii) the time-varying nature of all the aforementioned parameters. We prove asymptotic optimality of a forward-looking CLP-based policy in a large market regime. We also prove the asymptotic optimality of a myopic LP- based matching policy when drivers are fully utilized. When pricing affects customer and driver arrival rates, we show that asymptotically optimal joint pricing and matching decisions lead to fully utilized drivers when parameters are time homogeneous under very mild conditions.
Keywords: Ridesharing Platforms, Dynamic Matching, Asymptotic Optimality
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