LARGE DEVIATIONS AND OVERFLOW PROBABILITIES FOR THE GENERAL SINGLE-SERVER QUEUE, WITH APPLICATIONS Academic Article uri icon

abstract

  • AbstractWe consider queueing systems where the workload process is assumed to have an associated large deviation principle with arbitrary scaling: there exist increasing scaling functions (at, vt, tR+) and a rate function I such that if (Wt, tR+) denotes the workload process, thenon the continuity set of I. In the case that at = vt = t it has been argued heuristically, and recently proved in a fairly general context (for discrete time models) by Glynn and Whitt[8], that the queue-length distribution (that is, the distribution of supremum of the workload process Q = supt0Wt) decays exponentially:and the decay rate is directly related to the rate function I. We establish conditions for a more general result to hold, where the scaling functions are not necessarily linear in t: we find that the queue-length distribution has an exponential tail only if limtat/vt is finite and strictly positive; otherwise, provided our conditions are satisfied, the tail probabilities decay like

published proceedings

  • MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY

author list (cited authors)

  • DUFFIELD, N. G., & OCONNELL, N.

citation count

  • 317

complete list of authors

  • DUFFIELD, NG||OCONNELL, N

publication date

  • September 1995