Approximate analysis of asymmetric single-service token-passing systems

Consideration is given to token-passing or polling systems in which the message arrival process, the message transmission time distribution, and the walk time vary from one station to another. An approximate analysis of these systems is obtained. The results obtained from the approximate analysis are compared against both simulation results and those obtained from two approximate methods that have been proposed earlier. For the special case of a symmetric system, it is shown that the approximate analysis is exact when the walk time is constant. Even when the walk time is exponentially distributed, it is shown that the approximate analysis gives an approximation error of less than 0.3% in the range of offered load that is generally of interest