Queued cross-bar network models for replication and coded storage systems

Coding techniques may be useful for data center data survivability as well as for reducing traffic congestion. We present a queued cross-bar network (QCN) method that can be used for traffic analysis of both replication/uncoded and coded storage systems. We develop a framework for generating QCN rate regions (RRs) by analyzing their conflict graph stable set polytopes (SSPs). In doing so, we apply recent results from graph theory on the characterization of particular graph SSPs. We characterize the SSP of QCN conflict graphs under a variety of traffic patterns, allowing for their efficient RR computation. For uncoded systems, we show how to compute RRs and find rate optimal scheduling algorithms. For coded storage, we develop a RR upper bound, for which we provide an intuitive interpretation. We show that the coded storage RR upper bound is achievable in certain coded systems in which drives store sufficient coded information, as well in certain dynamic coding systems. Numerical illustrations show that coded storage can result in gains in RR volume of approximately 50%, averaged across traffic patterns.