Large Deviations estimates for Polling and Weighted Fair Queueing service systems

Abstract

: In this paper we consider a single server system with an arbitrary number of tra#c classes employing either Weighted Fair Queueing or Weighted Round Robin service policy among classes. By using sample path Large Deviations techniques we derive logarithmic equivalents of the quantities P(W i > x) as x # #, where W i is the stationary amount of class i tra#c backlogged. This generalizes previous results of Weber [18], O'Connell [11] and Bertsimas et al. [1] who derived these equivalents in the case of only two customer classes. The results are illustrated in the case of Poisson tra#c. It is shown, in particular, that for such tra#c and in a symmetric case huge backlogs for a given class are more likely with Fair Queueing rather than with FIFO scheduling. 1 Introduction The present paper is motivated by the performance evaluation of the following polling system: a single server processes customers arriving in K distinct queues, visiting the queues cyclically with zero walk time; the ...

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