A new convolution algorithm for loss probability analysis in multiservice networks

Performance analysis in multiservice loss systems generally focuses on accurate and efficient calculation methods for traffic loss probability. Convolution algorithm is one of the existing efficient numerical methods. Exact loss probabilities are obtainable from the convolution algorithm in systems where the bandwidth is fully shared by all traffic classes; but not available for systems with trunk reservation, i.e. part of the bandwidth is reserved for a special class of traffic. A proposal known as asymmetric convolution algorithm (ACA) has been made to overcome the deficiency of the convolution algorithm. It obtains an approximation of the channel occupancy distribution in multiservice systems with trunk reservation. However, the ACA approximation is only accurate with two traffic flows; increased approximation errors are observed for systems with three or more traffic flows.In this paper, we present a new Permutational Convolution Algorithm (PCA) for loss probability approximation in multiservice systems with trunk reservation. This method extends the application of the convolution algorithm and overcomes the problems of approximation accuracy in systems with a large number of traffic flows. It is verified that the loss probabilities obtained by PCA are very close to the exact solutions obtained by Markov chain models, and the accuracy outperforms the ACA approximation.