Matching Queues with Reneging: a Product Form Solution

TL;DR

This paper derives explicit product form solutions for the steady state distribution of a parallel matching queue with reneging, modeling two-sided markets with compatibility constraints and abandonment.

Contribution

It provides the first explicit product form solution for a matching queue with reneging and a compatibility graph, advancing queueing theory in two-sided markets.

Findings

Explicit steady state distributions derived using partial balance conditions.

The model captures realistic features like abandonment and compatibility constraints.

Provides analytical tools for analyzing two-sided market dynamics.

Abstract

Motivated by growing applications in two-sided markets, we study a parallel matching queue with reneging. Demand and supply units arrive to the system and are matched in an FCFS manner according to a compatibility graph specified by an N-system. If they cannot be matched upon arrival, they queue and may abandon the system as time goes by. We derive explicit product forms of the steady state distributions of this system by identifying a partial balance condition.