Abstract

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 no parameter information is required. However, we expect that a parameter-based policy can achieve better performance.We propose to base the matching decisions on the solution to a linear program (LP) that accounts for (i) the differing arrival rates of drivers and customers 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. Our main theorems establish the asymptotic optimality of an LP-based policy in a large market regime in which drivers are fully utilized. We show through extensive simulation experiments that an LP-based policy significantly outperforms the CD policy when there are large imbalances in customer and driver arrival rates across different areas in the city.

Highlights

  • We consider the control of a two-sided matching system with multiple item types on both sides arriving randomly to the system with potentially time-varying rates; see Figure 1

  • 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 pickup, (iii) how long drivers are willing to wait for a customer, and (iv) the time-varying nature of all the aforementioned parameters

  • The decisions on which driver to offer to each arriving customer in a ride-sharing system impact the overall number of customers matched

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Summary

Introduction

We consider the control of a two-sided matching system with multiple item types on both sides arriving randomly to the system with potentially time-varying rates; see Figure 1. Consistent with intuition, we see that demand spikes coupled with low nearby driver availability, such as, lead to the poor performance of the CD policy This is exactly when we recommend spending the extra effort of estimating parameters, such as customer and driver arrival rates, in order to be able to implement a CLP- or an LP-based matching policy. Banerjee et al (2018) consider dynamic matching control of a two-sided, continuous-time matching system where the objective is to maximize the number of matchings They propose a state-dependent matching policy that achieves the asymptotically optimal system performance with the fastest possible rate as the market size increases. Among all of the aforementioned ride-sharing studies, the only ones that allow time-varying parameters are that by Hu and Zhou (2015) and our study

Notation and Terminology
The Ride-Sharing Model
Admissible Policies
An Asymptotically Optimal CLP-Based Matching Policy
A Large Matching Market
An Asymptotic CLP Upper Bound
A CLP-Based Randomized Policy
An Asymptotically Optimal LP-Based Randomized Policy
An LP-Based Randomized Matching Policy
Jointly Optimizing Pricing and Matching When Parameters Are Time Homogeneous
Performance Evaluation
Simulation Experiments
Concluding Remarks
Preliminary Results
Proof of Theorem 2
Proof of Theorem 3
Proof of Theorem 4
Proofs of Lemmas 3 and 6
Findings
Proof of Lemma 5
Full Text
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