Light traffic equivalence in single-server queues. (English) Zbl 0762.60085

Asmussen, Søren

Ann. Appl. Probab. 2, No. 3, 555-574 (1992).

The behaviour of the steady-state waiting time of the \(GI/G/1\) queue in light traffic is studied, resulting in rather deep insights. The analysis is based upon a light traffic limit theorem for random walks in a triangular array setting, which is proved at the outset. The special case of phase-type distributions is shown to allow more explicit and computationally tractable results.

Reviewer: R.Schassberger (Brauschweig)

MSC:

60K25	Queueing theory (aspects of probability theory)
90B22	Queues and service in operations research

Keywords:

waiting time; steady-state waiting time; light traffic limit; random walks; phase-type distributions