Hostname: page-component-77c89778f8-n9wrp Total loading time: 0 Render date: 2024-07-20T20:11:53.189Z Has data issue: false hasContentIssue false
  • English
  • Français

Tandem queues with bulk arrivals, infinitely many servers and correlated service times

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Ushio Sumita  and
Yasushi Masuda
Ushio Sumita*
Affiliation:
International University of Japan
Yasushi Masuda*
Affiliation:
Keio University
*
∗Postal address: International University of Japan, Yamato-machi, Minamiuonuma-gun, Niigata-ken, 949–72, Japan.
∗∗Postal address: Faculty of Science and Technology, Keio University, 3–14–1, Hiyoshi, Kohoku-ku, Yokohama 223, Japan.
Get access Rights & Permissions [Opens in a new window]

Abstract

A system of GIx/G/∞ queues in tandem is considered where the service times of a customer are correlated but the service time vectors for customers are independently and identically distributed. It is shown that the binomial moments of the joint occupancy distribution can be generated by a sequence of renewal equations. The distribution of the joint occupancy level is then expressed in terms of the binomial moments. Numerical experiments for a two-station tandem queueing system demonstrate a somewhat counterintuitive result that the transient covariance of the joint occupancy level decreases as the covariance of the service times increases. It is also shown that the analysis is valid for a network of GIx/SM/∞ queues.

Keywords

TANDEM QUEUESBULK ARRIVALSINFINITELY MANY SERVERSCORRELATED SERVICE TIMES

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 1 , March 1997 , pp. 248 - 257
Copyright
Copyright © Applied Probability Trust 1997 

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.)

Footnotes

This paper has been partially supported by the NTT research fund.

References

[1] Barlow, E. R. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.Google Scholar
[2] Baskett, F., Chandy, M., Muntz, R. and Palacios, J. (1975) Open, closed and mixed networks and queues with different classes of customers. J. Assoc. Computing Machinery 22, 248–260.Google Scholar
[3] Brown, M. and Ross, S. M. (1969) Some results for infinite server queues. J. Appl. Prob. 6, 604–611.CrossRefGoogle Scholar
[4] Buzacott, J. A. and Shanthikumar, J. G. (1993) Stochastic Models of Manufacturing Systems. Prentice-Hall, New Jersey.Google Scholar
[5] Keilson, J. and Seidmann, A. (1988) M/G/8 with batch arrivals. Operat. Res. Lett. 7, 219–222.Google Scholar
[6] Keilson, J. and Servi, L. D. (1994) Networks of non-homogeneous M(t)/G/8 systems. J. Appl. Prob. 31A, 157–168.Google Scholar
[7] Lazowska, E. D., Zahorjan, Graham, G. S. and Sevcik, K. C. (1984) Quantitative System Performance. Prentice-Hall, New Jersey.Google Scholar
[8] Liu, L., Kashyap, B. R. K. and Templeton, J. G. C. (1990) On the GIX/G/8 system. J. Appl. Prob. 27, 671–683.Google Scholar