Hostname: page-component-cb9f654ff-5jtmz Total loading time: 0 Render date: 2025-08-26T12:17:27.299Z Has data issue: false hasContentIssue false
  • English
  • Français

Approximating a Cumulative Distribution Function by Generalized Hyperexponential Distributions

Published online by Cambridge University Press:  27 July 2009

Jihong Ou ,
Jingwen Li  and
Süleyman Özekici
Jihong Ou
Affiliation:
Department of Decision Sciences, National University of Singapore, 10 Kent Ridge Crescent, Singapore, 11926O
Jingwen Li
Affiliation:
Department of Decision Sciences, National University of Singapore, 10 Kent Ridge Crescent, Singapore, 11926O
Süleyman Özekici
Affiliation:
Department of Industrial Engineering, Boḡaziçi University, 80815 Bebek-lstanbul, Turkey
Get access Rights & Permissions [Opens in a new window]

Abstract

Recent developments in stochastic modeling show that enormous analytical advantages can be gained if a general cumulative distribution function (c.d.f.) can be approximated by generalized hyperexponential distributions. In this paper, we introduce a procedure to explicitly construct such approximations of an arbitrary c.d.f. Although our approach can be used in different types of stochastic models, the main motivation comes from queueing theory in obtaining approximations of the idle-period distribution and other performance measures in GI/G/1 queues.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 11 , Issue 1 , January 1997 , pp. 11 - 18
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.)

Article purchase

Temporarily unavailable

References

1.Botta, R.F. & Harris, C.M. (1986). Approximation with generalized hyperexponential distributions: Weak convergence results. Queueing Systems 2: 169–190.CrossRefGoogle Scholar
2.Feller, W. (1971). An Introduction to Probability Theory and Its Applications, Vol. 2, 2nd ed.New York: Wiley.Google Scholar
3.Jensen, A. (1954). A Distribution Model Applicable to Economics. Copenhagen: Munksgaard.Google Scholar
4.Kennedy, D.P. (1972). The continuity of the single server queue. Journal of Applied Probability 9: 370–381.CrossRefGoogle Scholar
5.Li, J. (1997). An approximation method for the analysis of GI/G/1 queues. Operations Research (to appear).CrossRefGoogle Scholar
6.Li, J. & Ou, J. (1995). Characterizing the idle-period distribution of GI/G/1 queues. Journal of Applied Probability 32: 247–255.CrossRefGoogle Scholar
7.Neuts, M.F. (1981). Matrix-Geometric Solutions in Stochastic Models. Baltimore, MD: Johns Hopkins University Press.Google Scholar
8.Neuts, M.F. (1989). Structured Stochastic Matrices of M/G/1 Type and Their Applications. New York: Marcel Dekker.Google Scholar
9.Schassberger, R. (1970). On the waiting time in the queueing system GI/G/1. Annals of Mathematical Statistics 41: 182–187.CrossRefGoogle Scholar