Subject: blocking time, breakdowns, discrete-time single-server unreliable queueing system, geometric distribution, minimization, service discipline
Year: 1999
Type: Journal Article
Title: Minimization of the blocking time of the unreliable Geo/G_D/1 queueing system
Author: Bakeva, Verica
Author: Kolev, Nikolai
Abstract: In this paper we study the blocking time of an unreliable single-server queueing system Geo/GD/1. The service can be interrupted upon explicit or implicit breakdowns. For the successful finish of the service we use a special service discipline dividing the pure service time X (assumed to be a random variable with known distribution) in subintervals with deterministically selected time-points 0 = t0 < t1 < ... < tk < tk+1; tk < X ≤ tk+1, and making a copy at the end of each subinterval (if no breakdowns occur during it) we derive the probability generating function of the blocking time of the server by a customer. As an application, we consider an unreliable system Geo/D/1 and the results is that the expected blocking time is minimized when the timepoints t0, t1,... are equidistant. We determine the optimal number of copies and the length of the corresponding interval between two consecutive copies.
Publisher: Odjel za matematiku, Sveučilište JJ Strossmayera u Osijeku
Relation: Mathematical Communications
Identifier: oai:repository.ukim.mk:20.500.12188/23986
Identifier: http://hdl.handle.net/20.500.12188/23986
