Non-asymptotic near optimal algorithms for two sided matchings

TL;DR

This paper develops near-optimal algorithms for two-sided matching systems with fixed server arrivals and price-controlled customer arrivals, addressing both loss and queueing models to maximize platform profit under quality constraints.

Contribution

It introduces a bang-bang optimal policy for the loss system and a simple bi-modal matching strategy for the queueing system, with approximation guarantees.

Findings

Bang-bang policy achieves optimality under certain conditions

Bi-modal matching strategy attains near optimal profit

Approximation guarantees for simple pricing policies

Abstract

A two-sided matching system is considered, where servers are assumed to arrive at a fixed rate, while the arrival rate of customers is modulated via a price-control mechanism. We analyse a loss model, wherein customers who are not served immediately upon arrival get blocked, as well as a queueing model, wherein customers wait in a queue until they receive service. The objective is to maximize the platform profit generated from matching servers and customers, subject to quality of service constraints, such as the expected wait time of servers in the loss system model, and the stability of the customer queue in the queuing model. For the loss system, subject to a certain relaxation, we show that the optimal policy has a bang-bang structure. We also derive approximation guarantees for simple pricing policies. For the queueing system, we propose a simple bi-modal matching strategy and show that it achieves near optimal profit.