TOTAL WAITING TIME DISTRIBUTION FUNCTION AND THE FATE OF A CUSTOMER IN A SYSTEM WITH TWO QUEUES IN SERIES.

This paper is concerned with a system of two unlimited queues in series, when Poisson traffic is offered to the first stage and the service times in the two stages are independent of each other and negative-exponentially distributed. The first stage includes one service unit, while the second stage is allowed to be a multiserver queueing system. By pursuing a particular customer (call or request) at his walk through the whole system, the fate of a customer in the second stage is determined as a function of all possible components of fate in the first stage. Though the flow times (waiting plus service times) of the same customer in the successive stages are independent, other values of fate (e. g. the waiting times) are not independent.