Decomposition results for general polling systems and their applications

In this paper we derive decomposition results for the number of customers i n polling systems under arbitrary (dynamic) polling order and service polic ies. Furthermore, we obtain sharper decomposition results for both the numb er of customers in the system and the waiting times under static polling po licies. Our analysis, which is based on distributional laws, relaxes the Po isson assumption that characterizes the polling systems literature. In part icular, we obtain exact decomposition results for systems with either Mixed Generalized Erlang (MGE) arrival processes, or asymptotically exact decomp osition results for systems with general renewal arrival processes under he avy traffic conditions. The derived decomposition results can be used to ob tain the performance analysis of specific systems. As an example, we evalua te the performance of gated Markovian polling systems operating under heavy traffic conditions. We also provide numerical evidence that our heavy traf fic analysis is very accurate even for moderate traffic.