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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 …