Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-23T06:14:42.579Z Has data issue: false hasContentIssue false
  • English
  • Français

Passage times for overtake-free paths in Gordon–Newell networks

Published online by Cambridge University Press:  01 July 2016

Hans Daduna
Hans Daduna*
Affiliation:
Technische Universität Berlin
*
∗Postal address: Technische Universität Berlin, Fachbereich 3-Mathematik, Strasse des 17. Juni 135, 1000 Berlin 12, Germany.
Get access Rights & Permissions [Opens in a new window]

Abstract

Consider a path in a multiclass Gordon–Newell network such that a customer present in a node of this path cannot be overtaken by any other customer behind him in a node of this path or by probabilistic influences created by such customers. The passage time through such a path is a mixture of Erlangian distributions, where the mixing distribution is given by the steady state of the network.

Keywords

GORDON–NEWELL NETWORKSPASSAGE TIMESSOJOURN TIMESJACKSON NETWORKSOVERTAKE-FREE PATH
Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 3 , September 1982 , pp. 672 - 686
Copyright
Copyright © Applied Probability Trust 1982 

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] Baskett, F., Chandy, K. M., Muntz, R. R. and Palacios, F. G. (1975) Open, closed and mixed networks of queues with different classes of customers. J. Assoc. Comput. Mach. 22, 248–260.CrossRefGoogle Scholar
[2] Chow, W. M. (1981) The cycle time distribution of exponential cyclic queues. J. Assoc. Comput. Mach. 27, 281–286.Google Scholar
[3] Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
[4] Lemoine, A. (1979) On total sojourn time in acyclic Jackson networks.CrossRefGoogle Scholar
[5] Melamed, B. (1979) Sojourn times in queueing networks.Google Scholar
[6] Reich, E. (1957) Waiting times when queues are in tandem. Ann. Math. Statist. 28, 768–773.Google Scholar
[7] Reich, E. (1963) Note on queues in tandem. Ann. Math. Statist. 34, 338–341.Google Scholar
[8] Schassberger, R. and Daduna, H. (1980) The time for a round-trip in a cycle of exponential queues.Google Scholar
[9] Walrand, J. and Varaiya, P. (1980) Sojourn times and the overtaking condition in Jacksonian networks. Adv. Appl. Prob. 12, 1000–1018.Google Scholar