Hostname: page-component-848d4c4894-2xdlg Total loading time: 0 Render date: 2024-06-28T22:03:31.135Z Has data issue: false hasContentIssue false
  • English
  • Français

Moments of a Markov-modulated, irreducible network of fluid queues

Part of: Special processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Landy Rabehasaina
Landy Rabehasaina*
Affiliation:
ENSSAT
*
∗Postal address: ENSSAT, 6 rue de Kerampont, BP 805, 22305 Lannion, France. Email address: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study a network of fluid queues in which exogenous arrivals are modulated by a continuous-time Markov chain. Service rates in each queue are proportional to the queue size, and the network is assumed to be irreducible. The queue levels satisfy a linear, vector-valued differential equation. We obtain joint moments of the queue sizes recursively, and deduce the Laplace transform of the queue sizes in the stationary regime.

Keywords

Linear fluid networkMarkov modulation

MSC classification

Primary: 60K25: Queueing theory 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Secondary: 60J25: Continuous-time Markov processes on general state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 2 , June 2006 , pp. 510 - 522
Copyright
© Applied Probability Trust 2006 

References

Asmussen, S. and Kella, O. (1996). Rate modulation in dams and ruin problem. J. Appl. Prob. 33, 523–535.Google Scholar
Chen, H. and Yao, D. D. (2001). Fundamentals of Queueing Networks. Springer, New York.CrossRefGoogle Scholar
Graham, A. (1981). Kronecker Product and Matrix Calculus: with Applications. Halsted Press, New York.Google Scholar
Kaspi, H. and Kella, O. (1996). Stability of feed-forward fluid networks with Lévy input. J. Appl. Prob. 33, 513–522.Google Scholar
Kella, O. and Stadje, W. (2002). Exact results for a fluid model with state-dependent flow rates. Prob. Eng. Inf. Sci. 16, 389–402.CrossRefGoogle Scholar
Kella, O. and Stadje, W. (2002). Markov-modulated linear fluid networks with Markov additive input. J. Appl. Prob. 39, 413–420.Google Scholar
Kella, O. and Whitt, W. (1996). Stability and structural properties of stochastic fluid networks. J. Appl. Prob. 33, 1169–1180.Google Scholar
Kella, O. and Whitt, W. (1999). Linear stochastic fluid networks. J. Appl. Prob. 36, 244–260.Google Scholar
Neuts, M. F. (1981). Matrix-Geometric Solutions in Stochastic Models. An Algorithmic Approach. Johns Hopkins University Press, Baltimore, MD.Google Scholar
Rabehasaina, L. and Sericola, B. (2004). A second-order Markov-modulated fluid queue with linear service rate. J. Appl. Prob. 41, 758–777.Google Scholar
Rabehasaina, L. and Sericola, B. (2003). Transient analysis of a Markov modulated fluid queue with linear service rate. In Proc. 10th Conf. Anal. Stoch. Modelling Tech. Appl. (ASMTA'03, Nottingham, June 2003), ed. Al-Dabass, D., SCS European Publishing House, pp. 234–239.Google Scholar