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On the serial correlation for number in system in the stationary GI/M/1 bulk arrival and GI/Em/1 queues

Part of: Computer system organization Operations research and management science Special processes Multivariate analysis

Published online by Cambridge University Press:  14 July 2016

D. A. Stanford  and
B. Pagurek
D. A. Stanford*
Affiliation:
University of Western Ontario
B. Pagurek*
Affiliation:
Carleton University
*
∗Postal address: Department of Statistical and Actuarial Sciences, The University of Western Ontario, London, Canada N6A 5B9.
∗∗Postal address: Department of Systems and Computer Engineering, Carleton University, Ottawa, Canada.
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Abstract

The generating functions for the serial covariances for number in system in the stationary GI/M/1 bulk arrival queue with fixed bulk sizes, and the GI/Em/1 queue, are derived. Expressions for the infinite sum of the serial correlation coefficients are also presented, as well as the first serial correlation coefficient in the case of the bulk arrival queue. Several numerical examples are considered.

Keywords

MODULO PROBABILITIESCORRELATION COEFFICIENT SUMSCORRELATION COEFFICIENT GENERATING FUNCTIONS

MSC classification

Primary: 60K25: Queueing theory
Secondary: 62H20: Measures of association (correlation, canonical correlation, etc.) 90B22: Queues and service 68U20: Simulation 68M20: Performance evaluation; queueing; scheduling
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 2 , June 1992 , pp. 404 - 417
Copyright
Copyright © Applied Probability Trust 1992 

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