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On the severity of M/M/∞ congested episodes

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

J. Preater
J. Preater*
Affiliation:
Keele University
*
∗ Postal address: Department of Mathematics, Keele University, Keele, Staffordshire, ST5 5BG, UK. Email address: [email protected]
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Abstract

The Laplace transform is obtained for the joint length and height of an M/M/∞ queue excursion above occupancy level C.

Keywords

M/M/∞ queueexcursion

MSC classification

Primary: 60K25: Queueing theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 39 , Issue 1 , March 2002 , pp. 228 - 230
Copyright
Copyright © Applied Probability Trust 2002 

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References

[1]. Guillemin, F., and Pinchon, D. (1998). Continued fraction analysis of the duration of an excursion in an M/M/∞ system. J. Appl. Prob. 35, 165–183.Google Scholar
[2]. Guillemin, F., and Pinchon, D. (1999). On a random variable associated with excursions in an M/M/∞ system. Queueing Systems 32, 305–318.Google Scholar
[3]. Guillemin, F., and Simonian, A. (1995). Transient characteristics of an M/M/∞ system. Adv. Appl. Prob. 27, 862–888.CrossRefGoogle Scholar
[4]. Preater, J. (1997). M/M/∞ transience revisited. J. Appl. Prob. 34, 1061–1067.Google Scholar