Hostname: page-component-74656f9884-c52kr Total loading time: 0 Render date: 2026-11-08T14:36:52.699Z Has data issue: false hasContentIssue false
  • English
  • Français

The Equilibrium Distribution for a Clocked Buffered Switch

Published online by Cambridge University Press:  27 July 2009

Steven Jaffe
Steven Jaffe*
Affiliation:
Department of Mathematics University of Southern California Los angeles, California 90089-1113
*
Current address: Department of Mathematics, Vassar College, Poughkeepsie, New York 12601.
Get access Rights & Permissions [Opens in a new window]

Abstract

A 2-by-2 buffered switch is the basic element of certain parallel data-processing networks. For a switch fed by two independent Bernoulli input streams, we find the joint distribution of the number of messages waiting in the two buffers at equilibrium, in the form of a bivariate generating function. The derivation uses complex-variable techniques developed by Kingman and by Flatto and McKean for the “shortest queue problem.” A number of asymptotic results are given, the principal one being the variance of the total number of waiting messages in the heavy-traffic limit.

Information

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 6 , Issue 4 , October 1992 , pp. 425 - 438
Copyright
Copyright © Cambridge University Press 1992

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

Chung, K.L. (1967). Markov chains with stationary transition probabilities, 2nd ed.Berlin: Springer-Verlag.Google Scholar
Cohen, J.W. & Boxma, O. J. (1983). Boundary value problems in queueing system analysis. Amsterdam: Elsevier North-Holland.Google Scholar
Flatto, L. & McKean, H.P. (1977). Two queues in parallel. Communications on Pure and Applied Mathematics 30: 255–263.CrossRefGoogle Scholar
Jaffe, S. (1989). Equilibrium results for a pair of coupled discrete-time queues. Ultracomputer Note #160, NYU Ultracomputer Research Lab, Courant Institute of Mathematical Sciences, New York.Google Scholar
Kingman, J.F.C. (1961). Two similar queues in parallel. Annals of Mathematical Statistics 32:1314–1323.CrossRefGoogle Scholar
Kruskal, C.P., Snir, M., & Weiss, A. (1986). The distribution of waiting times in clocked multistage interconnection networks. In Proceedings of the 1986 International Conference on Parallel Processing, pp. 12–19. Washington, DC: IEEE Computer Society Press.Google Scholar
Percus, O.E. & Percus, J.K. (1990). Elementary properties of clock-regulated queues. SIAM Journal on Applied Mathematics 50: 1166–1175.CrossRefGoogle Scholar
Percus, O.E. & Percus, J.K. (1990). Models for queue length in clocked queueing networks. Communications on Pure and Applied Mathematics 43: 273–289.CrossRefGoogle Scholar
Percus, O.E. & Percus, J.K. (1990). Queue length distributions in a Markov model of a multistage clocked queueing network. Communications on Pure and Applied Mathematics 43: 685–693.CrossRefGoogle Scholar