Optimization of polling systems with Bernoulli schedules

Many computer-communication networks in which the transmission right is circulated among the nodes have been modeled as polling systems. This paper concerns optimization of cyclic polling systems with respect to the service disciplines at the nodes. The service disciplines are chosen to be Bernoulli schedules. Because the optimization problem is not analytically tractable, a numerical approach to determine the optimal schedule, based on the power-series algorithm, is discussed. Light- and heavy-traffic asymptotes of the optimal schedule are presented; they are based on light-traffic asymptotes of the mean waiting times and the stability condition, respectively. A partial solution of the optimization problem is given; this follows directly from the μc-rule for priority systems. The influence of system parameters on the optimal Bernoulli schedule is examined. Finally, a fast approach to approximate the optimal schedule is presented and tested.