The Erlang multirate loss model with Batched Poisson arrival processes under the bandwidth reservation policy

Abstract

The Erlang Multirate Loss Model (EMLM) has been widely used as a springboard in the study of multirate loss systems. In this paper, we study an extension of the EMLM in order to ensure QoS guarantee per service-class in the heterogeneous environment of telecom networks. The proposed model is named Batched Poisson EMLM under Bandwidth Reservation (BR) policy (BP-EMLM/BR), since its input process is a Batched Poisson arrival process; that is, calls of each service-class arrive to a fixed-capacity link as batches. The distribution of the batch size can be general. The batch blocking discipline is the partial batch blocking, i.e. depending on the available link bandwidth, a part of an arriving batch can be accepted while the rest of it is discarded. The Call Admission Control is based on the BR policy, whereby we can achieve our goal to guarantee specific QoS for each service-class at call-level. In order to apply the BR policy in the BP-EMLM/BR, we examine two methods also used in the EMLM: (a) the Roberts’ method and (b) the Stasiak–Glabowski (S&G) method. The proposed model does not have a product form solution and therefore we propose approximate but recursive formulas for the calculation of various performance measures, such as time and call congestion probabilities as well as link utilization. A comparison between the analytical and simulation results shows that both methods provide satisfactory results when equalization between time congestion probabilities of all service-classes is desired. The S&G method, however, performs much better than the Roberts’ method in the case where more than two service-classes are accommodated in the link.