Hostname: page-component-8448b6f56d-wq2xx Total loading time: 0 Render date: 2024-04-19T14:18:59.059Z Has data issue: false hasContentIssue false
  • English
  • Français

Distribution of the busy period in a controllable M/M/2 queue operating under the triadic (0, K, N, M) policy

Published online by Cambridge University Press:  14 July 2016

Hahn-Kyou Rhee  and
B. D. Sivazlian
Hahn-Kyou Rhee
Affiliation:
University of Florida
B. D. Sivazlian*
Affiliation:
University of Florida
*
∗Postal address for both authors: Department of Industrial and Systems Engineering, University of Florida, Gainesville FL 32611, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider an M/M/2 queueing system with removable service stations operating under steady-state conditions. We assume that the number of operating service stations can be adjusted at customers' arrival or service completion epochs depending on the number of customers in the system. The objective of this paper is to obtain the distribution of the busy period using the theory of the gambler's ruin problem. As special cases, the distributions of the busy periods for the ordinary M/M/2 queueing system, the M/M/1 queueing system operating under the N policy and the ordinary M/M/1 queueing system are obtained.

Keywords

MARKOVIAN QUEUEING SYSTEMGAMBLER'S RUIN PROBLEMLAPLACE TRANSFORMBUSY PERIOD
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 2 , June 1990 , pp. 425 - 432
Copyright
Copyright © Applied Probability Trust 1990 

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

Bell, C. E. (1971) Characterization and computation of optimal policies for operating an M/G/1 queueing system with removable server. Operat. Res. 19, 208–218.Google Scholar
Bell, C. E. (1975) Turning off a server with customers present: Is this any way to run an M/M/c queue with removable servers. Operat. Res. 23, 571–573.Google Scholar
Bell, C. E. (1980) Optimal operations of an M/M/2 queue with removable servers. Operat. Res. 28, 1189–1204.Google Scholar
ÇInlar, E. (1975) Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
Conolly, B. (1975) Lecture Notes on Queueing Systems. Halsted, London.Google Scholar
Feller, W. (1968) An Introduction to Probability Theory and its Applications. Vol. I, Wiley, New York.Google Scholar
Heyman, D. (1968) Optimal operating policies for M/G/1 queueing systems. Operat. Res. 16, 362–382.Google Scholar
Kimura, T. (1981) Optimal control of an M/G/1 queueing system with removable server via diffusion approximation. Eur. J. Operat. Res. 00, 390–398.Google Scholar
Kleinrock, L. (1975) Queueing System Vol. 1: Theory. Wiley, New York.Google Scholar
Mcgill, J. T. (1969) Optimal control of queueing system with variable number of exponential servers. Technical Report No. 13, Department of Operations Research, Stanford University.Google Scholar
Prabhu, N. V. (1980) Stochastic Storage Processes. Springer-Verlag, New York.Google Scholar
Sobel, M. J. (1969) Optimal average-cost policy for a queue with start-up and shut-down costs. Operat. Res. 17, 145–162.Google Scholar
Taylor, H. M. and Karlin, S. (1984) An Introduction to Stochastic Modeling. Academic Press, New York.Google Scholar
Teghem, J. Jr. (1986) Control of the service process in a queueing system. Eur. J. Operat. Res. 141–158.Google Scholar
Yadin, M. and Naor, P. (1963) Queueing system with a removable service station. Operat. Res. Quart. 14, 393–405.Google Scholar