Stability and instability of fluid models for reentrant lines
Mathematics of Operations Research
ON THE STABILITY OF A BANDWIDTH PACKING ALGORITHM
Probability in the Engineering and Informational Sciences
Stability of flow-level scheduling with Markovian time-varying channels
Performance Evaluation
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A ring of I cells rotates past I queues, carrying customers from their origins to their destinations. The system is modelled as a Markov chain, and the exact ergodicity conditions are given. They are shown to depend on the precise travel lengths distributions, that is, not only on their means. Ergodicity is proven through the stability analysis of the associated fluid limits. The arrivals distributions, which in the ergodicity conditions appear only through their means, are more subtly involved in the fluid limits behaviour, in that they determine the probabilities of random bifurcations that occur infinitely often in a simple system of I=2 queues.