Congestion probabilities of elastic and adaptive calls in Erlang-Engset multirate loss models under the threshold and bandwidth reservation policies

In this paper, we consider a single link of fixed capacity that accommodates calls of different service-classes with different bandwidth-per-call requirements. The link behaves as a multirate loss system. Calls of each service-class arrive in the link according to a Poisson (random) or a quasi-random process and have an exponentially distributed service time. Poisson or quasi-random arriving calls are generated by an infinite or finite number of traffic sources, respectively. Service-classes are also distinguished according to the behavior of in-service calls, in elastic and adaptive service-classes. Elastic calls can compress their bandwidth by simultaneously increasing their service time. Adaptive calls tolerate bandwidth compression without affecting their service time. All calls compete for the available link bandwidth under the combination of the Threshold (TH) and the Bandwidth Reservation (BR) policies. The TH 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 BR policy reserves part of the available link bandwidth to benefit calls of high bandwidth requirements. The proposed models, for random or quasi-random traffic, do not have a product form solution for the determination of the steady state probabilities. However, we approximate both models by reversible Markov chains, and prove recursive formulas for the efficient calculation of the call-level performance metrics, such as time and call congestion probabilities as well as link utilization. The accuracy of the proposed formulas is verified through simulation and found to be quite satisfactory.