Congestion probabilities in a batched Poisson multirate loss model supporting elastic and adaptive traffic

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The ever increasing demand of elastic and adaptive services, where in-service calls can tolerate bandwidth compression/expansion, together with the bursty nature of traffic, necessitates a proper teletraffic loss model which can contribute to the call-level performance evaluation of modern communication networks. In this paper, we propose a multirate loss model that supports elastic and adaptive traffic, under the assumption that calls arrive in a single link according to a batched Poisson process (a more “bursty” process than the Poisson process, where calls arrive in batches). We assume a general batch size distribution and the partial batch blocking discipline, whereby one or more calls of a new batch are blocked and lost, depending on the available bandwidth of the link. The proposed model does not have a product form solution, and therefore we propose approximate but recursive formulas for the efficient calculation of time and call congestion probabilities, link utilization, average number of calls in the system, and average bandwidth allocated to calls. The consistency and the accuracy of the model are verified through simulation and found to be quite satisfactory.