An Efficient Convolution Algorithm for the Non-Markovian Two-Node Cyclic Network

Consider a closed cyclic queueing model that consists of two nodes and total M customers. Each node buffer can accommodate all id="M2"> Node 1 has id="M3"> N ≤ servers, each having an exponential service time with rate id="M4"> λ . The second single server general distribution function id="M5"> B . well-known machine repair spares, where set identical machines, id="M6"> , is served by person, key application this model. This several other applications in performance evaluation, manufacturing, computer networks, reliability studies as it be easily used to compute system availability. In article, we give efficient algorithm derive exact solution for the steady state size probabilities. Our approach based on developing polynomial convolution method transition probabilities birth process over 2 times solving imbedded Markov chain at completion epochs. significant improvement given earlier paper. Numerical examples are demonstrate our method.