Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-22T16:49:50.220Z Has data issue: false hasContentIssue false
  • English
  • Français

Queueing systems with restricted workload: an explicit solution

Published online by Cambridge University Press:  14 July 2016

Nico M. Van Dijk
Nico M. Van Dijk*
Affiliation:
Free University, Amsterdam
*
∗Postal address: Faculty of Economics and Econometrics, Free University, Postbus 7161, 1007 MC Amsterdam, The Netherlands.
Get access Rights & Permissions [Opens in a new window]

Abstract

Queueing systems with non-exponential service distributions and a capacity restriction on the total residual service requirement (workload) are studied. Closed-form expressions of geometric form in the LCFS case and recursive representations in the FCFS case are obtained for the steady state workload distribution. The proof is of interest in itself and directly leads to extensions.

Keywords

RECURSIVE REPRESENTATIONPARTIAL BALANCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 2 , June 1990 , pp. 393 - 400
Copyright
Copyright © Applied Probability Trust 1990 

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.)

References

[1] Asmussen, S. (1987) Applied Probability and Queues. Wiley, New York.Google Scholar
[2] Barbour, A. (1976) Networks of queues and the method of stages. Adv. Appl. Prob. 8, 584–591.CrossRefGoogle Scholar
[3] Cohen, J. W. (1982) The Single-server Queue. North-Holland, Amsterdam.Google Scholar
[4] Cohen, J. W. (1979) The multiple phase service network with generalized processor sharing. Acta Informatica 2, 245–284.Google Scholar
[5] Cohen, J. W. (1969) Single server queues with restricted accessibility. J. Eng. Math. 3, 265–284.Google Scholar
[6] De Kok, A. G. and Tijms, H. C. (1985) A two-moment approximation for a buffer design problem requiring a small rejection probability. Performance Evaluation 5, 77–84.Google Scholar
[7] Dynkin, E. B. (1965) Markov Processes I. Springer-Verlag, Berlin.Google Scholar
[8] Gavish, B. and Schweitzer, P. J. (1977) The Markovian queue with bounded waiting time. Management Sci. 23, 1349–1357.Google Scholar
[9] Geish, K. and Kobayashi, H. (1982) Bounds on the overflow probabilities in communication systems. Performance Evaluation 2, 149–160.Google Scholar
[10] Horduk, A. and Van Dijk, N. M. (1983) Adjoint processes job-local-balance and insensitivity of stochastic networks. Bull. 44th Session Int. Statist. Inst. 50, 776–788.Google Scholar
[11] Iglehart, D. L. (1972) Extreme values in the GI/G/1 queue. Ann. Math. Statist. 43, 627–635.Google Scholar
[12] Keilson, J. (1963) A gambler's ruin type problem in queueing theory. Operat. Res. 11, 570–576.Google Scholar
[13] Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
[14] Ross, S. M. (1974) Bounds on the delay distribution in GI/G/1 queues. J. Appl. Prob. 11, 417–421.Google Scholar
[15] Schassberger, R. (1978) The insensitivity of stationary probabilities in networks of queues. Adv. Appl. Prob. 10, 906–912.CrossRefGoogle Scholar
[16] Tijms, H. C. (1985) Stochastic Modelling and Analysis. Wiley, New York.Google Scholar
[17] Van Ommeren, J. C. W. (1987) Exponential bounds for excess probabilities in systems with a finite capacity. Stoch. Proc. Appl. 24, 143–149.Google Scholar
[18] Van Ommeren, J. C. W. and De Kok, A. G. (1987) Asymptotic results for buffer systems under heavy load. Prob. Eng. Inf. Sci. 1, 327–348.Google Scholar
[19] Wyner, A. D. (1974) On the probability of buffer overflow under an arbitrary bounded input output distribution. SIAM J. Appl. Math. 27, 544–570.Google Scholar