Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-27T21:21:00.390Z Has data issue: false hasContentIssue false
  • English
  • Français

Parallel fluid queues with constant inflows and simultaneous random reductions

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Offer Kella  and
Masakiyo Miyazawa
Offer Kella*
Affiliation:
The Hebrew University of Jerusalem
Masakiyo Miyazawa*
Affiliation:
Science University of Tokyo
*
∗ Postal address: Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel.
∗∗ Postal address: Department of Information Sciences, Science University of Tokyo, Noda-City, Chiba 278-8510, Japan. Email address: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider I fluid queues in parallel. Each fluid queue has a deterministic inflow with a constant rate. At a random instant subject to a Poisson process, random amounts of fluids are simultaneously reduced. The requested amounts for the reduction are subject to a general I-dimensional distribution. The queues with inventories that are smaller than the requests are emptied. Stochastic upper bounds are considered for the stationary distribution of the joint buffer contents. Our major interest is in finding exponential product-form bounds, which turn out to have the appropriate decay rates with respect to certain linear combinations of buffer contents.

Keywords

Parallel fluid queuesmultidimensional stationary distributionstochastic upper boundexponential product formdecay rate

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B15: Network models, stochastic
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 3 , September 2001 , pp. 609 - 620
Copyright
Copyright © by the Applied Probability Trust 2001 

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

Asmussen, S. (1987). Applied Probability and Queues. John Wiley, Chichester.Google Scholar
Baccelli, F. and Brémaud, P. (1994). Elements of Queueing Theory. Springer, New York.Google Scholar
Bazaraa, M. S., Sherali, H. D., and Shetty, C. M. (1993). Nonlinear Programming: Theory and Algorithms, 2nd edn. John Wiley, Chichester.Google Scholar
Chao, X., and Miyazawa, M. (2000). Queueing networks with instantaneous movements: a unified approach by quasi-reversibility. Adv. Appl. Prob. 32, 284–313.CrossRefGoogle Scholar
Chao, X., Miyazawa, M., and Pinedo, M. (1999). Queueing Networks: Customers, Signals, and Product Form Solutions. John Wiley, Chichester.Google Scholar
Feller, W. (1971). An Introduction to Probability Theory and Its Applications, Vol. II, 2nd edn. John Wiley, Chichester.Google Scholar
Kella, O. (1997). Stochastic storage networks: stationarity and the feedforward case. J. Appl. Prob. 34, 498–507.CrossRefGoogle Scholar
Marshal, A. W., and Olkin, I. (1979). Inequalities: Theory of Majorization and Its Applications. Academic Press, London.Google Scholar
Rockafellar, R. T. (1970). Convex Analysis. Princeton University Press.CrossRefGoogle Scholar
Wolff, R. W. (1989). Stochastic Modeling and the Theory of Queues. Prentice Hall, Englewood Cliffs, NJ.Google Scholar
Yamashita, H., and Miyazawa, M. (1998). Product form queueing networks with concurrent movements. Adv. Appl. Prob. 30, 1111–1129.CrossRefGoogle Scholar