Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T08:05:22.298Z Has data issue: false hasContentIssue false
  • English
  • Français

Simple Bounds and Monotnicity the Call Congestion of Finite Multiserver Delay Systems

Published online by Cambridge University Press:  27 July 2009

Nico M van Dijk ,
Pantelis Tsoucas  and
Jean Walrand
Nico M van Dijk
Affiliation:
Department of Actuarial Sciences and Econometrics Free University, Amsterdam, The Netherlands
Pantelis Tsoucas
Affiliation:
Department of Electrical Engineering and Computer Sciences and Electronics Research LaboratoryUniversity of California, Berkeley Berkeley, California 94720
Jean Walrand
Affiliation:
Department of Electrical Engineering and Computer Sciences and Electronics Research LaboratoryUniversity of California, Berkeley Berkeley, California 94720
Get access Rights & Permissions [Opens in a new window]

Abstract

Simple and insensitive lower and upper bounds are proposed for the call congestion of M/GI/c/n queues. To prove them we establish the general monotonicity property that increasing the waiting room and/or the number of servers in a /GI/c/n queue increases the throughput. An asymptotic result on the number of busy servers is obtained as a consequence of the bounds. Numerical evidence as well as an application to optimal design illustrates the potential usefulness for engineering purposes. The proof is based on a sample path argument.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 2 , Issue 1 , January 1988 , pp. 129 - 138
Copyright
Copyright © Cambridge University Press 1988

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

Borovkov, A.A. (1984). Asymptotic methods in queueing theory. Wiley (1984).Google Scholar
Groenevelt, H., van, Hoorn M.H. & Turns, H.C. (1984). Tables for M/G/c queueing systems with phase-type service. European Journal of Operations Research 16: 257–269.CrossRefGoogle Scholar
Heyman, D.P. (1980). Comments on a queueing inequality. Management Science 26: 956–959.CrossRefGoogle Scholar
Halachmi, B. & Franta, W.R. (1978). A diffusion approximation to the multiserver queue. Management Science 24: 522–529.CrossRefGoogle Scholar
Neuts, M.F. (1981). Matrix-geometric solutions in stochastic models. Baltimore, Maryland: The Johns Hopkins University Press.Google Scholar
Seelen, L.P., Tijms, H.C. & van, Hoorn M.H. (1985). Tables for multiserver queues. Amsterdam: North-Holland.Google Scholar
Sobel, M.J. (1980). Simple inequalities for multiserver queues. Management Science 26: 951–956.CrossRefGoogle Scholar
Takahashi, Y. & Takarni, Y. (1981). A numerical method for the steady-state probabilities of a G1/G/c-queueing system in a general class. Journal of the Operational Research Society (Japan) 19: 147–157.Google Scholar
Tijms, H.C., van, Hoorn M.H. & Federgruen, A. (1981). Approximations for the steady-state probabilities in the M/G/c queue. Advances in Applied Probability 13: 186–206.CrossRefGoogle Scholar
van, Dijk N.M. (1986). Quick and insensitive performance bounds for nonproduct-form queueing systems. Research Report, Twente University of Technology, Submitted for publication.Google Scholar
van, Dijk N.M. (1985). Simple bounds for the call congestion of multiserver queues. Research Report, Free University.Google Scholar
van, Dijk N.M. (1987). A formal proof of simple and insensitive bounds for finite multiserver tandem queues. Research Report, Twente University of Technology, To appear in Advances in Applied Probability.Google Scholar
van, Dijk N.M. & Lamond, B.F. (1987). Bounds for the call congestion in tandem queues. Working Paper 1078, University of British Columbia, Canada. To appear in Operations Research.Google Scholar
Whitt, W. (1982). Refining diffusion approximation for queues. Operational Research Letters 1: 165–169.CrossRefGoogle Scholar