Large Deviations estimates for Polling and Weighted Fair Queueing service systems

In this paper we consider a single server system with an arbitrary number of traffic 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(Wi > x) as x → ∞, where Wi is the stationary amount of class i traffic 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 traffic. It is shown, in particular, that for such traffic and in a symmetric case huge backlogs for a given class are more likely with Fair Queueing rather than with FIFO scheduling.