Hostname: page-component-7b7567c8c-7pwfn Total loading time: 0 Render date: 2026-11-15T11:42:23.379Z Has data issue: false hasContentIssue false
  • English
  • Français

Inequalities for queues with dependent interarrival and service times

Published online by Cambridge University Press:  14 July 2016

G. L. O'Brien
G. L. O'Brien*
Affiliation:
York University, Downsview, Ontario
Get accessRights & Permissions [Opens in a new window]

Abstract

Consider two queues with k servers. Inequalities between their sample paths and thence between the distribution functions of their waiting times and queue sizes are deduced from inequalities between the conditional distribution functions, given previous interarrival and service times, for the two queues.

Keywords

QUEUESWAITING TIMESSTOCHASTIC ORDERING

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 3 , September 1975, pp. 653 - 656
Copyright
Copyright © Applied Probability Trust 1975 

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

[1] Benes, V. E. (1968) General Stochastic Processes in the Theory of Queues. Addison-Wesley, Reading, Mass.Google Scholar
[2] Daley, D. J. and Moran, P. A. P. (1968) Two-sided inequalities for waiting time and queue size distributions in GI/G/1. Theor. Prob. Appl. 13, 338–341.Google Scholar
[3] Jacobs, D. R. and Schach, S. (1972) Stochastic order relationships between GI/G/k systems. Ann. Math. Statist. 43, 1623–1633.Google Scholar
[4] Loynes, R. M. (1962) Stationary waiting time distributions for single-server queues. Ann. Math. Statist. 33, 1323–1339.Google Scholar
[5] Neuts, M. F. and Chen, S.-Z. (1972) The infinite server queue with semi-Markovian arrivals and negative exponential services. J. Appl. Prob. 9, 178–184.Google Scholar
[6] O'brien, G. L. (1975) The comparison method for stochastic processes. Ann. Prob. 3, 80–88.Google Scholar
[7] Runnenberg, J. Th. (1961) An example illustrating the possibilities of renewal theory and waiting-time theory for Markov-dependent arrival-intervals. Indag. Math. 23, 560–576.CrossRefGoogle Scholar