Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-15T06:07:04.870Z Has data issue: false hasContentIssue false
  • English
  • Français

On a generalization of the preemptive resume priority

Published online by Cambridge University Press:  01 July 2016

Philippe Nain
Philippe Nain*
Affiliation:
Inria
*
∗Postal address: INRIA Centre de Sophia Antipolis, Route des Lucioles, 06565 Valbonne Cedex, France.
Get accessRights & Permissions [Opens in a new window]

Abstract

This paper considers a queueing system with two classes of customers and a single server, where the service policy is of threshold type. As soon as the amount of work required by the class 1 customers is greater than a fixed threshold, the class 1 customers get the server's attention; otherwise the class 2 customers have the priority. Service interruptions can occur for both classes of customers on the basis of the above description of the service mechanism, and in this case the service interruption discipline is preemptive resume priority (PRP). This model, which turns out to be a generalization of the PRP queueing system, has potential applications in computer systems and in communication networks. For Poisson inputs, exponential (arbitrary) servicetime distribution for class 1 (class 2) customers, we derive the Laplace–Stieltjes transform of the stationary joint distribution of the workload of the server, by reducing the analysis to the resolution of a boundary value problem. Explicit formulas are obtained.

Keywords

QUEUESMARKOV PROCESSRIEMANN-HILBERT BOUNDARY-VALUE PROBLEM

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 18 , Issue 1 , March 1986, pp. 255 - 273
Copyright
Copyright © Applied Probability Trust 1986 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1. Baccelli, F. and Fayolle, G. (1982) Two dimensional diffusion processes with boundary and jumps. Applications to coupled queues. Rapport de Recherche INRIA, No. 160.Google Scholar
2. Blanc, J. P. C. (1982) Application of the Theory of Boundary Value Problems in the Analysis of a Queueing Model with Paired Services. Mathematical Centre Tract 153, Amsterdam.Google Scholar
3. Cohen, J. W. (1982) The Single Server Queue , 2nd edn. North-Holland, Amsterdam.Google Scholar
4. Cohen, J. W. and Boxma, O. J. (1983) Boundary Value Problems in Queueing System Analysis. Mathematical Studies 79, North-Holland, Amsterdam.Google Scholar
5. Fayolle, G. (1979) Méthodes analytiques pour les files d'attente couplées. Thèse, Université Paris VI.Google Scholar
6. Fayolle, G. and Iasnogorodski, R. (1979) Two coupled processors: the reduction to a Riemann-Hilbert problem. Z. Wahrscheinlichkeitsth. 47, 325–351.CrossRefGoogle Scholar
7. Fayolle, G., Iasnogorodski, R. and Mitrani, I. (1983) Distribution of sojourn times in a queueing network with overtaking. Proc. 9th Internat. Conf. Performance Evaluation, Maryland. Google Scholar
8. Fayolle, G., King, P. J. B. and Mitrani, I. (1982) The solution of certain twodimensional Markov models. Adv. Appl. Prob. 14, 295–308.Google Scholar
9. Ghakov, F. D. (1966) Boundary Value Problems. Pergamon Press, Oxford.Google Scholar
10. Iasnogorodski, R. (1979) Problèmes-frontières dans les files d'attente. Thèse, Université Paris VI.Google Scholar
11. JaiswAl, N. K. (1968) Priority Queues. Academie Press, New York.Google Scholar
12. Mikou, N. (1981) Modèles de réseaux de files d'attente avec pannes. Thèse, Université Paris XI, Orsay.Google Scholar
13. Muskhelishvili, N. I. (1946) Singular Integral Equations. Noordhoff, Groningen.Google Scholar
14. Nain, Ph. (1984) Workload analysis of a two-queue system by formulating a boundary value problem. In Proc. Internat. Seminar on Modelling and Performance Evaluation Methodology, Paris, 24-26 January 1983. Lecture Notes in Control and Information Science 60, Springer-Verlag, Berlin.Google Scholar
15. Nehari, Z. (1975) Conformal Mapping. Dover, New York.Google Scholar
16. Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar