Second moments of the waiting time in symmetric polling systems

Multiple queue, cyclic service systems (called polling systems) have often been used as performance evaluation models in communication and production systems with cyclic resource allocation. However, most research has focused only on the mean waiting times due to prohibitively growing complexity in computing higher-order moments of the waiting time. This paper presents the explicit expressions for the second moments of the waiting time in symmetric exhaustive and gated service systems of two, three, and four queues with Poisson arrival processes. Numerical comparison reveals that they are ordered in the number of queues (increasingly/decreasingly for exhaustive/gated service systems, respectively) and bounded fairly tightly by those for single queue systems and by those for systems with infinitely many queues. Conjecture of their heavy traffic limits is also made.