Stability criteria for controlled queueing systems

MacPhee, I.M.; Müller, L.J.

Abstract

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 [3] and our results generalise Kurkova [8] and complement Foley and McDonald [4] and [5].

Citation

MacPhee, I., & Müller, L. (2006). Stability criteria for controlled queueing systems. Queueing Systems, 52(3), 215-229. https://doi.org/10.1007/s11134-006-5555-x

• Journal Article Type: Article
• Publication Date: Mar 1, 2006
• Deposit Date: May 1, 2007
• Journal: Queueing Systems
• Print ISSN: 0257-0130
• Electronic ISSN: 1572-9443
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 52
• Issue: 3
• Pages: 215-229
• DOI: https://doi.org/10.1007/s11134-006-5555-x
• Keywords: Queueing network, Control, Ergodicity, Transience.
• Public URL: https://durham-repository.worktribe.com/output/1593852
• Publisher URL: http://www.maths.dur.ac.uk/~dma0imm/macpheemuller.ps