Polling with a general service order table: gated service

Exact results are presented on the mean waiting time in a nonsymmetric polling system with general service order table and gated service. The results are obtained using a generalization of the work of Ferguson and Aminetzah (see IEEE Trans. on Commun., vol.COM-33, p.223-31 , 1985). Pseudocycle times are defined, the relationship between cycle times and pseudocycle times is expressed, and the generating functions for the waiting times and the number of messages at the stations and at the pseudostations are obtained as functions of pseudocycle times. Equations are derived for the case of zero first two moments of the switch-over time at every station. Using numerical examples, a previously published pseudoconservation law is verified. The numerical results quantify the significant reductions in the waiting time and the queue occupancy at a station (particularly at high server utilizations) by listing it more frequently in the polling table