A Control Theoretic Analysis of Arbitration and Matching Schemes for Packet Switches

Stability of a switch or router is one of the features of most interest. A stable input buffered switch means that occupancies in any of the input queues converges to a value different from infinity for admissible ingress traffic. Techniques to study stability in a switch are limited and sometimes unsuitable for elaborated schemes. Lyapunov functions have been used to analyze stability in maximum weight matching (MWM) schemes and may be hard to apply in other schemes. Here, we propose an alternative technique and it may be applied to a wide range of selection schemes, and furthermore, to different switch architectures. As an application of this technique, this paper discusses the impact of the granularity of the service time in the stability of an input-queued switch.