Hostname: page-component-848d4c4894-nmvwc Total loading time: 0 Render date: 2024-06-28T17:36:19.238Z Has data issue: false hasContentIssue false
  • English
  • Français

Bounds for the expected delays in some tandem queues

Published online by Cambridge University Press:  14 July 2016

Shun-Chen Niu
Shun-Chen Niu*
Affiliation:
Cleveland State University
*
∗Postal address: James J. Nance College of Business Administration, Cleveland State University, Cleveland, OH 44115, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

Tandem queues are analyzed. An upper bound for the stationary expected delay in front of the second server is found for a sequence of two queues in tandem where the first server has deterministic service times, the second server has general service distribution, and the arrival process is an arbitrary renewal process. The result is extended to the case of n queues in tandem where all the servers except the last one have constant service times.

Keywords

TANDEM QUEUESBOUNDSASSOCIATED RANDOM VARIABLES
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 3 , September 1980 , pp. 831 - 838
Copyright
Copyright © Applied Probability Trust 1980 

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] Burke, P. J. (1956) The output of a queueing system. Operat. Res. 4, 699–704.Google Scholar
[2] Burke, P. J. (1968) The output process of a stationary M/M/S queueing system. Ann. Math. Statist. 39, 1144–1152.Google Scholar
[3] Esary, J. D., Proschan, F. and Walkup, D. W. (1967) Association of random variables, with applications. Ann. Math. Statist. 38, 1466–1474.CrossRefGoogle Scholar
[4] Friedman, H. D. (1965) Reduction methods for tandem queueing systems. Operat. Res. 13, 121–131.CrossRefGoogle Scholar
[5] Kingman, J. F. C. (1962) Some inequalities for the GI/G/1 queue. Biometrika 49, 315–324.CrossRefGoogle Scholar
[6] Kingman, J. F. C. (1970) Inequalities in the theory of queues. J. R. Statist. Soc. B 32, 102–110.Google Scholar
[7] Marshall, K. T. (1968) Some inequalities in queueing. Operat. Res. 16, 651–665.CrossRefGoogle Scholar
[8] Reich, E. (1957) Waiting times when queues are in tandem. Ann. Math. Statist. 28, 768–773.CrossRefGoogle Scholar
[9] Reich, E. (1963) Notes on queues in tandem. Ann. Math. Statist. 34, 338–341.Google Scholar
[10] Tembe, S. V. and Wolff, R. W. (1974) Optimal order of service in tandem queues. Operat. Res. 22, 824–832.CrossRefGoogle Scholar