Derivatives of blocking probabilities for multi-service loss systems and their applications

Derivatives of blocking probabilities of multi-service loss networks are important for traffic engineering. An explicit formula for the derivatives of blocking probabilities with respect to offered traffics is obtained expressed by stationary probabilities of global state probabilities. The approach is based on the convolution algorithm. It allows us to find expressions for the derivatives in a much more easy way than known so far. It is briefly shown how derivatives can be applied for approximate evaluation of performance measures and for studying the error of performance measures estimation caused by small changes of offered traffic. The results can also be applied for network optimization.