Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-27T07:38:28.446Z Has data issue: false hasContentIssue false
  • English
  • Français

Two Extremal Autocorrelated Arrival Processes

Published online by Cambridge University Press:  27 July 2009

Hiroshi Toyoizumi ,
J. George Shanthikumar  and
Ronald W. Wolff
Hiroshi Toyoizumi
Affiliation:
NTT Multimedia Networks Laboratories, Midori-cho 3-9-11 Musashino-shi, Tokyo 180, Japan
J. George Shanthikumar
Affiliation:
Department of Industrial Engineering and Operations Research, University of California at Berkeley, Berkeley, California 94720
Ronald W. Wolff
Affiliation:
Faculty of Economics, Tokyo Metropolitan University, 1-1 Minami Oosawa, Hachioji-shi, Tokyo, 192-03, Japan and Department of Industrial Engineering and Operations Research, University of California at Berkeley, Berkeley, California 94720
Get access Rights & Permissions [Opens in a new window]

Abstract

Extremal arrival processes, in the sense of increasing convex order of waiting time of queueing systems, are investigated. Two types of extremal processes are proposed: one in the class of processes that have identical marginal distributions and the other in the class of bounded stochastic processes that have the same mean and covariance structure. The worst performance with regard to waiting time in the sense of increasing convex order is guaranteed when these extremal processes are fed into a first in-first out single-server queue.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 11 , Issue 4 , October 1997 , pp. 441 - 450
Copyright
Copyright © Cambridge University Press 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.)

References

1.Meester, L.E. & Shanthikumar, J.G. (1993). Regularity of stochastic processes. Probability in the Engineering and Informational Sciences 7: 343–360.CrossRefGoogle Scholar
2.Shaked, M. & Shanthikumar, J.G. (1990). Parametric stochastic convexity and concavity of stochastic processes. Annals of the Institute of Statistical Mathematics 42(3): 509–553.CrossRefGoogle Scholar
3.Shaked, M. & Shanthikumar, J.G. (1994). Stochastic orders and their applications. London: Academic Press.Google Scholar
4.Shanthikumar, J.G. & Yao, D.D. (1992). Spatiotemporal convexity of stochastic processes and applications. Probability in the Engineering and Informational Sciences 6: 1–16.CrossRefGoogle Scholar
5.Tchen, A.H. (1980). Inequalities for distributions with given marginals. Annals of Probability 8(4): 814–827.CrossRefGoogle Scholar
6.Toyoizumi, H., Shanthikumar, J.G., & Wolff, R. (1996). A new modeling of auto-correlated arrival processes. Preprint.Google Scholar