Theory of Probability and Mathematical Statistics

On a busy period in one-channel queues

A. V. Mistryukov

Lomonosov Moscow State University, Moscow

Abstract: In this paper we study properties of a busy period of a single server queue, where server enters sleep mode once busy period is finished. When a new job arrives in empty queue, server initializes itself for some time and only then starts to serve jobs. Service time and initialization time have arbitrary continuous distribution, and interarrival times have either Erlang or hyperexponential distribution.

Keywords: single server queues, busy period, hyperexponential interarrival times, Erlang interarrival times.

UDC: 510.676, 519.217

Received: 30.04.2020
Revised: 20.06.2020

DOI: 10.26456/vtpmk562

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