Blocking probabilities of elastic and adaptive calls in the Erlang multirate loss model under the threshold policy

In this paper, we propose a new multirate teletraffic loss model of a single link with certain bandwidth capacity that accommodates Poisson arriving calls, which can tolerate bandwidth compression, under the threshold policy of admission control. When compression occurs, the service time may increase (elastic calls) or not (adaptive calls). The threshold policy can provide different QoS among service-classes by limiting the number of calls of a service-class up to a predefined threshold, which can be different for each service-class. The proposed model does not have a product form solution for the determination of the steady state probabilities. However, we approximate the model by a reversible Markov chain, and provide recursive formulas for the efficient calculation of the call-level performance metrics, such as call blocking probabilities and link utilization. In addition, we provide similar formulas when the threshold policy co-exists with the bandwidth reservation policy. The latter reserves part of the available link bandwidth to benefit calls of high bandwidth requirements. The accuracy of the proposed formulas is verified through simulation and found to be quite satisfactory. We also show the necessity and consistency of the proposed models.