Title: In the search for the infinite servers queue with Poisson arrivals busy period distribution exponential behaviour

Authors: Manuel Alberto M. Ferreira; José António Filipe

Addresses: BRU-IUL, ISTAR-IUL, Instituto Universitário de Lisboa, Av. das Forças Armadas, 1649-026, LISBOA, Portugal ' BRU-IUL, ISTAR-IUL, Instituto Universitário de Lisboa, Av. das Forças Armadas, 1649-026, LISBOA, Portugal

Abstract: The purpose of this paper is to investigate exponential behaviour conditions for the M|G|∞ queue busy period length distribution. It is presented a general theoretical result that is the basis of this work. The complementary analysis rely on the M|G|∞ queue busy period length distribution moments computation. In M|G+∞ queue practical applications - in economic, management and business areas - the management of the effective number of servers is essential since the physical presence of infinite servers is not viable and so it is necessary to create that condition through an adequate management of the number of servers during the busy period.

Keywords: M|G|∞ queue system; busy period; arrivals; customer; server; Poisson process; exponential distribution; moments.

DOI: 10.1504/IJBSR.2017.087094

International Journal of Business and Systems Research, 2017 Vol.11 No.4, pp.453 - 467

Received: 13 Oct 2015
Accepted: 04 Jan 2016

Published online: 23 Aug 2017 *

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