A Batched Poisson Multirate Loss Model Supporting Elastic Traffic under the Bandwidth Reservation Policy

Abstract

We present a new loss model for the call-level analysis of a single link, which accommodates calls of different service-classes with elastic bandwidth requirements. Calls arrive in the link according to a Batch Poisson process, a process that can be used to model traffic, which is more 'peaked' and 'bursty' than the Poisson process. The available link bandwidth is shared to calls according to the Bandwidth Reservation policy, whereby we can guarantee certain Quality-of-Service for each service-class. In the proposed model, we assume a general batch size distribution and the Partial Batch Blocking discipline. According to this discipline, one or more calls of an arriving batch can be accepted, while the rest can be discarded, depending on the available link bandwidth. New and in-service calls tolerate bandwidth compression/expansion. The analysis of the system is based on Markov chains. Since no Product Form Solution exists, for an efficient solution, we propose an approximate reversible Markov chain. Based on it, we derive a recursive formula for the calculation of link occupancy distribution and consequently time and call congestion probabilities (important call-level performance metrics). The proposed model's accuracy and its consistency are verified by simulation and found to be quite satisfactory.

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