A simple approximation of the link model with reservation by a one-dimensional Markov chain

This paper presents a new approximate calculation algorithm of the blocking probability in the full-availability group with reservation carrying a mixture of different multi-rate traffic streams. The algorithm is based on transforming multi-dimensional service processes in the system into a one-dimensional discrete Markov chain, which is characterised by a product form solution. Special attention is paid to the method for determining reverse transition rates and state probabilities in this Markov chain. The results of analytical calculations of the blocking probability are compared with the results of digital simulation of systems with bandwidth reservation. This research has shown a better accuracy of the proposed method as compared to the accuracy of other known solutions. The derived formulae can be useful for the analysis of ISDN and B-ISDN switching systems.