Multi-rate model of the limited-availability group with a finite source population

This paper presents a blocking probability calculation method in a limited-availability group with multi-rate traffic streams generated by a finite population of sources. The basis of the method is an approximation of a multi-dimensional process occurring in the considered group by the appropriately constructed one-dimensional Markov chain. The proposed calculation algorithm is based on an assumption about equality of reverse transition rates in both infinite and finite population models. Such an assumption allows us to determine the number of idle sources of particular traffic classes, which consequently leads to determination of traffic, offered in particular states of service process in the group. The results of analytical calculations of blocking probability have been compared with simulation results.