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On Heavy Traffic Approximations for Transient Characteristics of M/M/∞ Queues

Fabrice M. Guillemin, Ravi R. Mazumdar and Alain D. Simonian
Journal of Applied Probability
Vol. 33, No. 2 (Jun., 1996), pp. 490-506
DOI: 10.2307/3215073
Stable URL: http://www.jstor.org/stable/3215073
Page Count: 17
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On Heavy Traffic Approximations for Transient Characteristics of M/M/∞ Queues
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Abstract

In this paper, transient characteristics related to excursions of the occupation process of M/M/∞ queues are studied, when the excursion level is large and close to the mean offered load. We show that the classical diffusion approximation by an Ornstein-Uhlenbeck (OU) process captures well the average values of the transient variables considered, while the asymptotic distributions of these variables depart from those corresponding to the OU process. They exhibit, however, equivalent tail behaviour at infinity and numerical evidence shows that they are amazingly close to each other over the whole half-line.

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