Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-22T03:34:08.011Z Has data issue: false hasContentIssue false
  • English
  • Français

Stationary and stability of fork-join networks

Published online by Cambridge University Press:  14 July 2016

Panagiotis Konstantopoulos  and
Jean Walrand
Panagiotis Konstantopoulos
Affiliation:
University of California, Berkeley
Jean Walrand*
Affiliation:
University of California, Berkeley
*
∗Postal address for both authors: Department of Electrical Engineering and Computer Sciences and Electronics Research Laboratory, University of California, Berkeley CA 94720, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider a fork-join network with arrival and service times forming a stationary and ergodic process. The usual stability condition, namely that the input rate is strictly less than all the service rates, is proved to be valid in this general case. Finally we extend the result to the case where there is random routing.

Keywords

STATIONARY POINT PROCESSESPALM TRANSFORMATIONQUEUEING NETWORKS
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 3 , September 1989 , pp. 604 - 614
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

Baccelli, F. and Bremaud, P. (1987) Palm Probabilities and Stationary Queues. Lecture Notes in Statistics 41, Springer-Verlag, Berlin.Google Scholar
Baccelli, F. and Massey, W. A. (1986) Series-parallel, fork-join queueing networks and their stochastic ordering. Rapport de Recherche No. 488, INRIA-Rocquencourt, France.Google Scholar
Baccelli, F., Makowski, A. M. and Schwartz, A. (1987a) The fork-join queue and related systems with synchronization constraints: Stochastic ordering, approximations and computable bounds. Technical Research Report, SRC, Univ. of Maryland.Google Scholar
Baccelli, F., Massey, W. and Towsley, D. (1987b) COINS Technical Report 87–40, University of Massachusetts.Google Scholar
Franken, P., König, D., Arndt, U. and Schmidt, V. (1982) Queues and Point Processes. Academie-Verlag, Berlin.Google Scholar
Loynes, R. M. (1962) The stability of a queue with non-independent inter-arrival and service times. Proc. Camb. Phil. Soc. 58, 497–520.Google Scholar
Neveu, J. (1976) Sur les measures de Palm de deux processus ponctuels stationnaires. Z. Wahrscheinlichkeitsth. 34, 199–203.Google Scholar
Neveu, J. (1977) Processus ponctuelles. In Lecture Notes in Mathematics 598, Springer-Verlag, Berlin, 249–447.Google Scholar
Walrand, J. (1988) An Introduction to Queueing Networks. Prentice-Hall, Englewood Cliffs. NJ.Google Scholar