Flexibility can hurt dynamic matching system performance

TL;DR

This paper investigates how increasing matching options in a dynamic system can paradoxically increase the average population, revealing a Braess-like paradox in matching models.

Contribution

It demonstrates that adding edges in a matching graph can worsen system performance and provides conditions for when this paradox occurs.

Findings

Adding edges can increase average population due to a paradox.

Explicit example with a four-node graph shows non-intuitive behavior.

Conditions identified for the occurrence of the paradox in general graphs.

Abstract

We study the performance of general dynamic matching models. This model is defined by a connected graph, where nodes represent the class of items and the edges the compatibilities between items. Items of different classes arrive one by one to the system according to a given probability distribution. Upon arrival, an item is matched with a compatible item according to the First Come First Served discipline and leave the system immediately, whereas it is enqueued with other items of the same class, if any. We show that such a model may exhibit a non intuitive behavior: increasing the services ability by adding new edges in the matching graph may lead to a larger average population. This is similar to a Braess paradox. We first consider a quasicomplete graph with four nodes and we provide values of the probability distribution of the arrivals such that when we add an edge the mean number of items is larger. Then, we consider an arbitrary matching graph and we show sufficient conditions for the existence or non-existence of this paradox. We conclude that the analog to the Braess paradox in matching models is given when specific independent sets are in saturation, i.e., the system is close to the stability condition.