Generating function analysis of some joint distributions for Poisson loss systems
We present a new approach to derive joint distributions for stationary Poisson loss systems. In particular, for M/M/m/0 and M/M/1/n we find the Laplace transforms (with respect to time t) of the probability that at time t there are i customers in the system and during [0,t], j customers are refused admission; for M/M/m/0 we further determine the LT of the probability that the system was full for less than s time units during [0,t] and serves i customers at time t. Explicit formulas for the corresponding moments are also given.
generating function joint distribution poisson loss system stationary laplace transform method of auxiliary functions