Analysis of a polling system with correlated input

Abstract

In this paper, a polling system with correlated message arrivals is considered. The system consists of two stations each with infinite buffer. Messages arrive at each station according to an independent Poisson process. In addition to them, pairs of messages also arrive at the system according to a Poisson process and each of them is splitted into two messages, one to each station. Service discipline is either exhaustive or gated. The system is analysed to obtain the LSTs (Laplace-Stieltjes transform) of the waiting time of each message and the response time of a pair of messages which arrive simultaneously. Based on the analysis, it is shown that the difference in average waiting time between exhaustive and gated service disciplines is the same as that in the system without correlated input. It is also shown that the difference in average waiting time in the system with correlated input from that without correlated input is regardless of the two service disciplines.