Lost customers in <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">M</Emphasis>/1/1 loss system

In this paper, we consider lost customers in the M/M/1/1 Erlang loss system. Here we present an explicit form of the probability that the M/M/1/1 system does not lose any customer in the time interval 0, t) and an iterative procedure to determine the distribution of the total number of losses in 0, t). All these probabilities solve the same second-order differential equation which was used to evaluate the corresponding generating probability function. Finally, the connection between the Erlang’s loss rate and the evaluated probabilities is showed.