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On some diffusion approximations to queueing systems

Published online by Cambridge University Press:  01 July 2016

V. Giorno ,
A. G. Nobile  and
L. M. Ricciardi
V. Giorno*
Affiliation:
University of Salerno
A. G. Nobile*
Affiliation:
University of Salerno
L. M. Ricciardi*
Affiliation:
University of Naples
*
∗∗ Postal address: Dipartimento di Informatica e Applicazioni, Facoltà de Scienze, Università di Salerno, 84100 Salerno, Italy.
∗∗ Postal address: Dipartimento di Informatica e Applicazioni, Facoltà de Scienze, Università di Salerno, 84100 Salerno, Italy.
∗Postal address: Dipartimento di Matematica e Applicazioni, Università di Napoli, Via Mezzocannone 8, 80134 Napoli, Italy.
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Abstract

For a class of models of adaptive queueing systems an exact diffusion approximation is derived with the aim of obtaining information on the evolution of the systems. Our approximating diffusion process includes the Wiener and the Ornstein–Uhlenbeck processes with reflecting boundaries at 0. The goodness of the approximations is thoroughly discussed and the closed-form solutions obtained for the diffusion processes are compared with those holding for the queueing system in order to investigate the conditions under which reliable information can be obtained from the approximating continuous models. For the latter the transient behaviour is quantitatively analysed and the distribution of the busy period is determined in closed form.

Keywords

ADAPTIVE QUEUEING SYSTEMSM/M/1 MODELWIENER PROCESSORNSTEIN–UHLENBECK PROCESSFIRST-PASSAGE TIMEBUSY PERIOD
Type
Research Article
Information
Advances in Applied Probability , Volume 18 , Issue 4 , December 1986 , pp. 991 - 1014
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

Work performed under CNR-JSPS Scientific Cooperation Programme, Contracts no. 83.00032.01 and no. 84.00227.01, CNR Contract no. 85.00002.01 and under MPI financial support.

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