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Optimization of polling systems with Bernoulli schedules

  • Communication
  • Computer Science


C R ,~,~ ~ J 7626 3,J~~~~`~`~.~1992 ~, 563 r ti~~ J~~~~o~ ~~p~pp~,``~~~~~~Qp5 hpG ~~~ IIphIIInII IIIIII III IIIIIIInI~A nlnllulul OPTIMIZATION OF POLLING SYSTIIKS WITH BERNOULLI SCHEDULES ~i3~ J.P.C. Blanc R.D, van der Mei FEw 563 ~Ccecc~~ .rQ~a2 y l ~ ~~~~ e,~~~ O,(,,~1~~~~e.c 2Y~d Cs~Z4 Communicated by O.J. Boxma OPTIMIZATION OF POLLING SYSTEMS WITH BERNOULLI SCHEDULES J.P.C. Blanc R.D. van der Mei Tilburg University, Faculty of Economics P.O. Box 90153, 5000 LE Tilburg, The Netherlands Abstract In this paper optimization of cyclic polling systems with Bernoulli schedules is considered. An arbitrary weighted sum of the steady-state mean waiting times at the queues is to be minimized with respect to the Bernoulli parameters. Light- and heavy-traffic asymptotes of the optimal schedule are presented. A partial solution of the optimiaation problem is obtained by means of monotonicity of the mean waiting times as function of the Bernoulli parameters. A numerical approach to compute the optimal schedule, based on the use of the power-series algorithm, is discussed. 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. Keywords: polling systems, optimization, Bernoulli schedules, power-series algorithm z 1. Introduction A polling system is a multi-queue model, attended to by a single server. Polling models arise naturally in the modelíng of many computer-communication and production networks, where several users compete for access to a common resource, e.g., a central computer or a transmission channel. The reader is referred to [20] and [28] for overviews of the large variety of applications. In this paper optimization of continuous-time cyclic polling systems with a so-called Bernoulli service strategy at all queues will be considered. A Bernoulli service strategy, with parameter q, (Osq,s 1) for queue i, works as follows: if there

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