Decomposition results for general polling systems and their applications

In this paper we derive decomposition results for the number of customers in polling systems under arbitrary (dynamic) polling order and service policies. Furthermore, we obtain sharper decomposition results for both the number of customers in the system and the waiting times under static polling policies. Our analysis which is based on distributional laws, relaxes the Poisson assumption that characterizes the polling systems literature. In particular, we obtain exact decomposition results for systems with either Mixed Generalized Erlang arrival processes, or asymptotically exact decomposition results for systems with general renewal arrival processes under heavy traffic conditions. The derived decomposition results can be used to obtain the performance analysis of specific systems. As an example, we evaluate the performance of gated Markovian polling systems operating under heavy traffic conditions. We also provide numerical evidence that our heavy traffic analysis is very accurate even for moderate traffic.