Exact analysis of a priority queue with finite source

  • Michel Veran
Queues And Networks 3
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 60)


This paper presents a method to evaluate the exact stationary solution of a single queue with preemptive-resume priorities and finite source. In the case of an infinite source (Poisson arrivals) the solution is given by a well-known simple formula. Models requiring finite customer populations are frequently used for computer performance evaluation (i.e. a processor shared by real time applications), for which the infinite source hypothesis may cause unacceptable errors.

Such a model has already been fully analysed by Jaiswal, but this may yield to very complex computations when applied to real case problems. The same limitation occurs when using a numerical approach. Various approximate solutions have also been proposed.

An exact expression of the utilization factor for each customer population is first proved. A simple iterative algorithm is derived and a PASCAL implementation is described. Several examples are presented.


Priority Queue Utilization Factor Preemptive Priority Finite Source Schedule Discipline 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Jaiswal, N., "Priority queues", New-York: Academic Press, 1968.Google Scholar
  2. [2]
    Merle D.; Potier D.; Véran M. "QNAP: a software tool for computer system evaluation", Int. Conf. on Performance of Computer Installations, North-Holland, 1978.Google Scholar
  3. [3]
    Wallace, V.L.; Rosenberg, R.S. "Markovian models and numerical analysis of computer system behavior", Proc. 1966 AFIPS Spring Jt. Conf., Vol. 28.Google Scholar
  4. [4]
    Sevcik, K.C. "Priority scheduling disciplines in queueing network models of computer systems", Proc. IFIP Congress 77, North-Holland Publ. Co., Amsterdam.Google Scholar
  5. [5]
    Sauer, C.H.; Chandy, K.M. "Approximate analysis of central server models", IBM J. Res. Dev. 19, May 75.Google Scholar
  6. [6]
    Bard, Y. "Some extensions to multiclass queueing network analysis", 4th Int. Symp. on modelling and performance evaluation of computer systems, Vienna, Feb. 79.Google Scholar
  7. [7]
    Buzen, J.P.; Goldberg, P.S. "Guidelines for the user of infinite source queueing models in the analysis of computer system performance", Proc. of the NCC, pg. 371–374, 1974.Google Scholar
  8. [8]
    Jacobson, P.A., Lazowska E.D. "The Method of Surrogate Delays: Simultaneous Resource Possession in Analytic Models of Computer Systems"; Proc. ACM SIGMETRICS Conference on Measurement and Modelling of Computer Systems, Las Vegas, Sept. 1981.Google Scholar
  9. [9]
    Véran M. " Résolution d'un réseau de files d'attente avec partage de ressource"; Rapport de Recherche, Centre de Recherches CII-HB, Décembre 81.Google Scholar
  10. [10]
    Chow We-Min "M/M/1 Priority Queues with State Dependent Arrival and Service Rates", RC8570, IBM, Thomas J. Watson Research Center, Yorktown Heights, NY.Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Michel Veran
    • 1
  1. 1.Centre de Recherches CII Honeywell BullGrenoble CedexFrance

Personalised recommendations