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].
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AMS 2000 subject classification: Primary: 90B22; Secondary: 60J10 90B15
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MacPhee, I.M., Müller, L.J. Stability criteria for controlled queueing systems. Queueing Syst 52, 215–229 (2006). https://doi.org/10.1007/s11134-006-5555-x
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DOI: https://doi.org/10.1007/s11134-006-5555-x