New directions in pass-and-swap queues

Recently, driven by redundancy systems and matching systems, there has been renewed interest in models with product form stationary distributions. By a “product form,” we mean that the stationary distribution can be expressed as a product of terms, each of which corresponds to a job in the system. Given the recent discovery of many such systems, it is natural to ask: how broad is this class of systems? In this paper, we consider extensions and generalizations of the recently-proposed pass-and-swap queue, which has a product-form stationary distribution. We make three main contributions. First, we identify sufficient conditions under which pass-and-swap queues can be connected in a closed network, while still preserving the product form. Second, we identify dimensions along which the pass-and-swap system can be extended while preserving the product-form stationary distribution. At the same time, we also identify cases in which generalizing the pass-and-swap queue causes the product-form nature of the stationary distribution to break. Finally, we identify questions that remain open and present a road map for future study.