MacPhee, I. M. and Müller, L. J. (2006) 'Stability criteria for controlled queueing systems.', Queueing systems : theory and applications., 52 (3). pp. 215-229.
We give an almost complete classification of ergodicity and transience conditions for a general multi-queue system with the following features: arrivals form Poisson streams and there are various routing schemes for allocating arrivals to queues; the servers can be configured in a variety of ways; completed jobs can feed back into the system; the exponential service times and feedback probabilities depend upon the configuration of the servers (this model includes some types of multi-class queueing system); switching between service regimes is instantaneous. Several different levels of control of the service regimes are considered. Our results for the N-queue system require randomisation of service configurations but we have studied the two queue system in situations where there is less control. We use the semi-martingale methods described in Fayolle, Malyshev and Menshikov  and our results generalise Kurkova  and complement Foley and McDonald  and .
|Keywords:||Queueing network, Control, Ergodicity, Transience.|
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|Publisher Web site:||http://dx.doi.org/10.1007/s11134-006-5555-x|
|Record Created:||01 May 2007|
|Last Modified:||08 Apr 2009 16:30|
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