Hostname: page-component-6898cfcb55-th4rj Total loading time: 0 Render date: 2026-11-11T20:13:49.270Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on cycle times in tree-like queueing networks

Published online by Cambridge University Press:  01 July 2016

P. G. Harrison
P. G. Harrison*
Affiliation:
Imperial College, London
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Cycle-time distribution is shown to take the form of a linear combination of M Erlang-N density functions in a cyclic queueing network of M servers and N customers. For paths of m servers in tree-like networks, the components in the more complex linear combination are convolutions of Erlang-N with at most m − 1 negative exponentials.

Information

Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 16 , Issue 1 , March 1984, pp. 216 - 219
Copyright
Copyright © Applied Probability Trust 1984 

References

[1] Buzen, J. P. (1973) Computational algorithms for closed queueing networks with exponential servers. Comm. Assoc. Comput. Mach. 16, 527–531.Google Scholar
[2] Chow, W. M. (1980) The cycle-time distribution of exponential cyclic queues. J. Assoc. Comput. Mach. 27, 281–286.Google Scholar
[3] Daduna, H. (1982) Passage times for overtake-free paths in Gordon-Newell networks. Adv. Appl. Prob. 14, 672–686.Google Scholar
[4] Gordon, W. J. and Newell, G. F. (1967) Closed queueing systems with exponential servers. Operat. Res. 15, 254–265.CrossRefGoogle Scholar
[5] Harrison, P. G. (1979) Cycle time distribution in tree-like queueing networks. Research Report 79/50, Imperial College, London.Google Scholar
[6] Kelly, F. P. and Pollett, P. K. (1983) Sojourn times in closed queuing networks. Adv. Appl. Prob. 15, 638–656.Google Scholar
[7] Schassberger, R. and Daduna, H. (1983) The time for a round trip in a cycle of exponential queues. J. Assoc. Comput. Mach. 30, 146–150.Google Scholar
[8] Walrand, J. and Varaiya, P. (1980) Sojourn times and the overtaking condition in Jacksonian networks. Adv. Appl. Prob. 12, 1000–1018.Google Scholar