PERFORMANCE ANALYSIS OF MARKOVIAN POLLING SYSTEMS WITH SINGLE BUFFERS

Abstract

In this paper, we analyze the Markovian polling system with single buffers, asymmetric arrival rates, service times, and switchover times. A virtual buffer model is introduced to derive the relationship of the joint generating function for the queue length of each station at a polling instant. The Laplace-Stieltjes transforms of the cycle time and the intervisit time are obtained from the marginal generating function. We analyze the cyclic, load-oriented-priority, and symmetric random polling schemes which are classified by adjusting the transition probabilities, and compare the merits and demerits of each scheme for the performance measures. In particular, we prove that the mean queue lengths at the polling instants are the same for all stations in case of the load-oriented-priority polling scheme for the buffer relaxation system in which a new message is stored as soon as the transmission of the message currently in the buffer is initiated.