Individual blocking probabilities in the loss system $$GI + M|\vec M|N|0$$

AbstractIn this paper we investigate anN server loss system, where the input is a superposition of two types of traffics, namely of a renewal process and a Poisson process. The holding times of the two customer types are exponentially distributed with different parameters. For this model, denoted by $$GI + M|\vec M|N|0$$ , we derive a numerical algorithm for computing the individual blocking (loss) probabilities. The analysis is given by constructing a two-dimensional embedded Markov chain and by using the intensity conservation principle as well as point process arguments. The results generalize those of Kuczura [8] and Willie [11]. Finally, for the $$GI + GI + M|\vec M|N|0$$ loss system we give a system of partial differential equations for the densities of the steady state distribution and discuss a special case.