An exact analysis of an asymmetric polling system with mixed service discipline and general service order

This paper derives the exact mean waiting time for an asymmetric polling system with general service order and mixed service discipline. The mixed service discipline means that the service discipline of each stage (a turn in the service order sequence) for the same station can be gated or exhaustive. The gene-l-al service order denotes that each station can be polled more than once in a polling cycle. We use the mean age and the mean excess of a cumulative time to obtain the mean waiting times for stages and stations, where the cumulative time for a stage is defined as the total arrival time period of all customers that are served at one visit of the server to the stage. The accuracy of our analysis is verified by comparisons with previously published results and simulation results. We also use a genetic algorithm (GA) to search for an optimal pattern of service order and service discipline for the asymmetrical polling system. The results of the paper can be applied to the design of computer communication networks with polling schemes.