Analysis of the shortest relay queue policy in a cooperative random access network with collisions

Abstract

The aim of this work concerns the performance analysis of systems with interacting queues under the join the shortest queue policy. The case of two interacting queues results in a two-dimensional random walk with bounded transitions to non-neighboring states, which in turn results in complicated boundary behavior. Although this system violates the conditions of the compensation approach due to the transitions to non-neighboring states, we show how to extend the framework of the approach and how to apply it to the system at hand. Moreover, as an additional level of theoretic validation, we have compared the results obtained with the compensation approach with those obtained using the power series algorithm and we have shown that the compensation approach outperforms the power series algorithm in terms of numerical efficiency. In addition to the fundamental contribution, the results obtained are also of practical value, since our analysis constitutes a first attempt toward gaining insight into the performance of such interacting queues under the join the shortest queue policy. To fully comprehend the benefits of such a protocol, we compare its performance to the Bernoulli routing scheme as well as to that of the single relay system. Extensive numerical results show interesting insights into the system’s performance.