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Waiting Time in M/G/1 Queues with Impolite Arrival Disciplines

Published online by Cambridge University Press:  27 July 2009

Süleyman Òzekici ,
Jingwen Li  and
Fee Seng Chou
Süleyman Òzekici
Affiliation:
Department of Industrial Engineering, Boǵaziçi University, 80815 Bebek, Istanbul, Turkey
Jingwen Li
Affiliation:
Department of Decision Sciences, National University of Singapore, 10 Kent Ridge Crescent, Singapore, 0511
Fee Seng Chou
Affiliation:
Department of Decision Sciences, National University of Singapore, 10 Kent Ridge Crescent, Singapore, 0511
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Abstract

We consider a queueing system where arriving customers join the queue at some random position. This constitutes an impolite arrival discipline because customers do not necessarily go to the end of the line upon arrival. Although mean performance measures like the average waiting time and average number of customers in the queue are the same for all such disciplines, we show that the variance of the waiting time increases as the arrival discipline becomes more impolite, in the sense that a customer is more likely to choose a position closer to the server. For the M/G/1 model, we also provide an iterative procedure for computing the moments of the waiting time distribution. Explicit computational formulas are derived for an interesting special model where a customer joins the queue either at the head or at the end of the line.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 9 , Issue 2 , April 1995 , pp. 255 - 267
Copyright
Copyright © Cambridge University Press 1995

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