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On some time-non-homogeneous 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, Università di Salerno, 84100 Salerno, Italy.
∗Postal address: Dipartimento di Informatica e Applicazioni, 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

Time-non-homogeneous diffusion approximations to single server–single queue–FCFS discipline systems are considered. Under various assumptions on the nature of the time-dependent functions appearing in the infinitesimal moments the transient and the regime behaviour of the approximating diffusions are analysed in some detail. Special attention is then given to the study of a diffusion approximation characterized by a linear drift and by a periodically time-varying infinitesimal variance. Unlike the behaviour of transition functions and moments, the p.d.f. of the busy period is seen to be unaffected by the presence of such periodicity.

Keywords

M/M/1 MODELWIENER PROCESSORNSTEIN–UHLENBECK PROCESSFIRST-PASSAGE TIMEBUSY PERIOD
Type
Research Article
Information
Advances in Applied Probability , Volume 19 , Issue 4 , December 1987 , pp. 974 - 994
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

Research carried out under CNR-JSPS Scientific Cooperation Programme, Contracts No. 83.00002.01 and No. 84.00227.01, and with MPI financial support.

References

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