Directed FCFS Infinite Bipartite Matching

TL;DR

This paper analyzes an infinite bipartite matching model with FCFS discipline, calculating matching rates and delays, with applications to various two-sided queueing systems and insights into related stochastic models.

Contribution

It introduces a bipartite FCFS matching model, deriving matching rates and delays, and explores its relation to other stochastic matching frameworks.

Findings

Derived explicit matching rates and delays for the model.

Established connections to other FCFS stochastic matching models.

Provided insights for designing related service systems.

Abstract

We consider an infinite sequence consisting of agents of several types and goods of several types, with a bipartite compatibility graph between agent and good types. Goods are matched with agents that appear earlier in the sequence using FCFS matching, if such are available, and are lost otherwise. This model may be used for two sided queueing applications such as ride sharing, web purchases, organ transplants, and for abandon at completion redundancy parallel service queues. For this model we calculate matching rates and delays. These can be used to obtain waiting times and help with design questions for related service systems. We explore some relations of this model to other FCFS stochastic matching models.