Dynamic Matching for Real-Time Ridesharing
76 Pages Posted: 28 Sep 2016 Last revised: 13 Feb 2019
Date Written: June 15, 2017
In a ridesharing system, 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 pro- gram (CLP) that accounts for (i) the differing arrival rates of cus- tomers and drivers in different areas of the city, (ii) how long cus- tomers are willing to wait for driver pick-up, (iii) how long drivers are willing to wait for a customer, and (vi) the time-varying nature of all the aforementioned parameters. We prove asymptotic optimal- ity of a forward-looking CLP-based policy in a large market regime and of a myopic LP-based matching policy when drivers are fully utilized. When pricing affects customer and driver arrival rates, and parameters are time homogeneous, we show that asymptotically opti- mal joint pricing and matching decisions lead to fully utilized drivers under mild conditions.
Keywords: Ridesharing Platforms, Dynamic Matching, Asymptotic Optimality
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