Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-05T11:58:05.087Z Has data issue: false hasContentIssue false
  • English
  • Français

An LCFS finite buffer model with finite source batch input

Published online by Cambridge University Press:  14 July 2016

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

Abstract

Queueing systems are studied with a last-come, first-served queueing discipline and batch arrivals generated by a finite number of non-exponential sources. A closed-form expression is derived for the steady-state queue length distribution. This expression has a scaled geometric form and is insensitive to the input distribution. Moreover, an algorithm for the recursive computation of the normalizing constant and the busy source distribution is presented. The results are of both practical and theoretical interest as an extension of the standard Poisson batch input case.

Keywords

QUEUEINGLAST-COME FIRST-SERVEDCLOSED-FORM EXPRESSIONINSENSITIVITYNORMALIZING CONSTANT
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 2 , June 1989 , pp. 372 - 380
Copyright
Copyright © Applied Probability Trust 1989 

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

Barbour, A. (1976) Networks of queues and the method of stages. Adv. Appl. Prob. 8, 584–591.Google Scholar
Burke, P. J. (1975) Delays in single-server queues with batch input. Operat. Res. 23, 830–833.Google Scholar
Chaudhry, M. L. and Templeton, J. G. C. (1983) A First Course in Bulk Queues. Wiley, New York.Google Scholar
Cohen, J. W. (1976) On a single server queue with group arrivals. J. Appl. Prob. 13, 619–622.Google Scholar
Cohen, J. W. (1979) The multiple phase service network with generalized processor sharing. Acta Informatica 2, 245–284.Google Scholar
Eikeboom, A. M. and Tijms, H. C. (1987) Waiting time percentiles in the multiserver Mx/G/c queue with batch arrivals. Prob. Eng. Inf. Sci. 1, 163–174.Google Scholar
Hordijk, A. and Schassberger, R. (1982) Weak convergence of generalized semi-Markov processes. Stoch. Proc. Appl. 12, 271–291.Google Scholar
Hordijk, A. and Van Dijk, N. M. (1983a) Networks of queues. Part I: Job-local-balance and the adjoint process. Part II: General routing and service characteristics. Lecture Notes in Control and Informational Sciences 60, Springer-Verlag, Berlin, 158–205.Google Scholar
Hordijk, A. and Van Dijk, N. M. (1983b) Adjoint processes, job-local-balance and insensitivity of stochastic networks. Bull. 44th Session Internat. Stat. Inst. 50, 776–788.Google Scholar
Kabak, I. W. (1970) Blocking and delays in M (x)/M/c- bulk arrival queueing systems. Management Sci. 17, 112–115.Google Scholar
Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
Kohlas, J. (1982) Stochastic Methods of Operations Research. Cambridge University Press.Google Scholar
Mansfield, D. R. and Tran-Gia, P. (1982) Analysis of a finite storage system with batch input arising out of message packetization. IEEE Trans. Comm. 30, 456–463.Google Scholar
Nobel, R. (1987) Practical approximations for finite buffer queueing models with batch arrivals. Research Report, Free University, Amsterdam.Google Scholar
Van Ommeren, J. C. W. (1988) Exponential expansion for the tail of the waiting time probability in the single server queue with batch arrivals. Adv. Appl. Prob. 20, 880–895.Google Scholar
Schassberger, R. (1978) The insensitivity of stationary probabilities in networks of queues. Adv. Appl. Prob. 10, 906–912.Google Scholar
Takahashi, Y. and Katayama, T. (1985) Multi-server system with batch arrivals of queueing and non-queueing calls. ITC 11, Elsevier, Amsterdam, 3.2 A. 4.1–4.7.Google Scholar
Whitt, W. (1980) Continuity of generalized semi-Markov processes. Math. Operat. Res. 5, 494–501.Google Scholar