Flexibility can Hurt Dynamic Matching System Performance

Arnaud Cadas, Josu Doncel, Jean-Michel Fourneau, Ana Busic

Abstract: We study the performance of stochastic matching models with general compatibility graphs. Items of different classes arrive to the system according to independent Poisson processes. Upon arrival, an item is matched with a compatible item according to the First Come First Matched discipline and both items leave the system immediately. If there are no compatible items, the new arrival joins the queue of unmatched items of the same class. Compatibilities between item classes are defined by a connected graph, where nodes represent the classes of items and the edges the compatibilities between item classes. We show that such a model may exhibit a non intuitive behavior: increasing the matching flexibility by adding new edges in the matching graph may lead to a larger average population at the steady state. This performance paradox can be viewed as an analog of the Braess paradox. We show sufficient conditions for the existence or non-existence of this paradox. This performance paradox in matching models appears when specific independent sets are in saturation, i.e., the system is close to the stability condition.