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Title

Large closed queueing networks in semi-Markov environment and their application

Author(s)

Abramov, V. M.

Abstract

The paper studies closed queueing networks containing a server station and k client stations. The server station is an infinite server queueing system, and client stations are single-server queueing systems with autonomous service, i.e. every client station serves customers (units) only at random instants generated by a strictly stationary and ergodic sequence of random variables. The total number of units in the network is N. The expected times between departures in client stations are (N μ j )-1. After a service completion in the server station, a unit is transmitted to the jth client station with probability p j (j=1,2,...,k), and being processed in the jth client station, the unit returns to the server station. The network is assumed to be in a semi-Markov environment. A semi-Markov environment is defined by a finite or countable infinite Markov chain and by sequences of independent and identically distributed random variables. Then the routing probabilities p j (j=1,2,...,k) and transmission rates (which are expressed via parameters of the network) depend on a Markov state of the environment. The paper studies the queue-length processes in client stations of this network and is aimed to the analysis of performance measures associated with this network. The questions risen in this paper have immediate relation to quality control of complex telecommunication networks, and the obtained results are expected to lead to the solutions to many practical problems of this area of research.

Publication type

Journal article

Source

Acta Applicandae Mathematicae, Vol. 100, no. 3 (2008), pp. 201-226

Publication year

2008

FOR Code(s)

0102 Applied Mathematics

Keyword(s)

Closed queueing network;  Martingales and semimartingales;  Random environment;  Skorokhod reflection principle;  Probability distributions;  Queueing networks;  Servers;  Telecommunication networks;  Autonomous services;  Client stations;  Ergodic sequences;  Infinite server queueing systems;  Semi-Markov environment;  Skorokhod reflection principles;  Markov processes

Publisher

Springer

ISSN

0167-8019

Publisher URL

http://dx.doi.org/10.1007/s10440-007-9180-4

Copyright

Copyright © 2007 Springer Science+Business Media B.V. The accepted manuscript is reproduced in accordance with the copyright policy of the publisher. The definitive version is available at www.springer.com.

Full text

Peer reviewed