Individual call blocking probabilities in the loss systems SM+M/M/N and G+M/M/N

A method is derived for calculating the individual call blocking probabilities which arise when two independent traffic streams, a Poissonian stream and a stream induced by a semi-Markov point processes, are offered together to a finite number of service stations. Using this procedure and the possibility of approximating every stationary point process by a sequence of stationary semi-Markov point processes and a continuity argument, one can calculate the individual call loss proababilities when a general stationary traffic stream and a Poissonian stream are offered simultaneously to N servers. For N=1, this method or rather an elementary one yields simple, explicit formulas which reveal a modified insensitivity property of the model in question.