Abstract
We consider networks where at each node there is a single exponential server with a service rate which is a non-decreasing function of the queue length. The asymptotic profile of a sequence of networks consists of the set of persistent service rates, the limiting customer-to-node ratio, and the limiting service-rate measure. For a sequence of cyclic networks whose asymptotic profile exists, we compute upper and lower bounds for the limit points of the sequence of throughputs as functions of the limiting customer-to-node ratio. We then find conditions under which the limiting throughput exists and is expressible in terms of the asymptotic profile. Under these conditions, we determine the limiting queue-length distributions for persistent service rates. In the absence of these conditions, the limiting throughput need not exist, even for increasing sequences of cyclic networks.
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Daduna, H., Pestien, V. & Ramakrishnan, S. Throughput limits from the asymptotic profile of cyclic networks with state-dependent service rates. Queueing Syst 58, 191–219 (2008). https://doi.org/10.1007/s11134-008-9067-8
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DOI: https://doi.org/10.1007/s11134-008-9067-8