QoS guarantee in the Erlang Multirate Loss Model based on derivatives of blocking probabilities

We consider a single-link loss system of capacity C bandwidth units, accommodating K service-classes of Poisson traffic with different bandwidth-per-call requirements. Calls of all service-classes compete for the available link bandwidth under the bandwidth reservation (BR) policy. The BR policy is used in teletraffic engineering in order to achieve call blocking probability (CBP) equalization among different service classes. Such a single-link loss system has been analytically described by the Erlang Multirate Loss Model under the BR policy (EMLM/BR). In this paper, we focus on the problem of determining, in an efficient analytical way, derivatives of blocking probabilities with respect to offered traffic-load of any service-class under the BR policy. We further show through an analytical formula how CBP derivatives can be used to determine approximate CBP when small variations of offered traffic-load are considered.