Performance Analysis of a Polling System with Single Buffers and Its Application to Interconnected Networks

Abstract
We first consider the interdeparture process of a symmetric polling system with single buffer at each station, where distributions of transmission time and switchover time are assumed to be general. Under the assumption that consecutive interdeparture times are independent, the probability distribution is analyzed and the LaplaceStieltjes transform is given. Numerical examples show that the coefficient of variation of interdeparture time is not monotonic with respect to the arrival rate. Based upon the analysis, we can obtain the characteristics of outbound traffic if we are concerned with unidirectional traffic flow. In general, however, there is inbound traffic from external networks in the interconnected communication system and its effect on performance characteristics should be taken into account. We next propose the model of a polling system having the traffic from outside the system. The model consists of homogeneous stations with single buffers and a depot station with infinite buffer where inbound traffic is dealt with. We analyze the model and obtain throughput and mean waiting time for the case of constant transmission time and constant switchover times. Numerical examples show that the throughput of the system is not sensitive to inbound traffic if the total load of the system is moderate.