Hostname: page-component-8448b6f56d-m8qmq Total loading time: 0 Render date: 2024-04-24T12:20:20.974Z Has data issue: false hasContentIssue false
  • English
  • Français

A machine interference model with threshold effect

Published online by Cambridge University Press:  14 July 2016

Karmeshu  and
N. K. Jaiswal
Karmeshu*
Affiliation:
University of Waterloo
N. K. Jaiswal*
Affiliation:
Indian Statistical Institute
*
∗Postal address: Department of Physics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1.
∗∗Postal address: Indian Statistical Institute, 7, S.J.S. Sansanwal Marg, New Delhi–110029, India.
Get access Rights & Permissions [Opens in a new window]

Abstract

A non-linear stochastic model for the single-server machine interference problem is investigated. The service rate is a rational function of the number of failed machines, the numerator as well as the denominator of the function being linear in n. Depending on the relative values of the parameters involved, the service rate may increase or decrease with n, exhibiting the incentive or disincentive effect. The analysis is carried out by the usual diffusion approximation technique. A notable feature of this model is the threshold effect exhibited in the mean queue size.

Keywords

DIFFUSION APPROXIMATIONFOKKER-PLANCK EQUATIONMACHINE INTERFERENCE MODELTHRESHOLD EFFECT
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 2 , June 1981 , pp. 491 - 498
Copyright
Copyright © Applied Probability Trust 

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

Arnold, L. (1974) Stochastic Differential Equations. Wiley, New York.Google Scholar
Bailey, N. T. J. (1975) The Mathematical Theory of Infectious Diseases and its Applications, 2nd edn. Griffin, London.Google Scholar
Barbour, A. D. (1976) Quasi-stationary distributions in Markov population processes. Adv. Appl. Prob. 8, 296–314.Google Scholar
Bartholomew, O. J. (1976) Continuous time diffusion models with random duration of interest. J. Math. Sociol. 4, 187–197.Google Scholar
Gaver, D. P. and Lehoczky, J. P. (1977) A diffusion approximation solution for a repairman problem with two types of failure. Management Sci. 24, 71–81.Google Scholar
Haken, H. (1977) Synergetics. Springer-Verlag, New York.Google Scholar
Jaiswal, N. K. (1968) Priority Queues. Academic Press, New York.Google Scholar
Karmeshu, and Pathria, R. K. (1979) Cooperative behaviour in a nonlinear model of diffusion of information. Canad. J. Phys. 57, 1572–1578.Google Scholar
McNeil, D. R. (1973) Diffusion models for congestion models. J. Appl. Prob. 10, 368–376.Google Scholar
Rosen, R. (1970) Dynamical System Theory in Biology Vol. 1 — Stability Theory and its Applications. Academic Press, New York.Google Scholar