Large deviations and overflow probabilities for the general single-server queue, with applications

Abstract

Abstract We 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, t∈R+) and a rate function I such that if (Wt, t∈R+) denotes the workload process, then on 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 = supt≥0Wt) decays exponentially: and the decay rate δ 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 limt→∞at/vt is finite and strictly positive; otherwise, provided our conditions are satisfied, the tail probabilities decay like

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 431 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.