Palm's Machine-Repair Model with a Generalised Poisson Input Stream and Constant Service Time

This model belongs to the class of queueing systems with feedback. It is M(g)/D/1/k/S queue with generalised Poisson arrival process, constant service time, single server, limited waiting positions and finite number of customers. We use the generalised input Poisson stream that can be peaked, regular or smooth. This model with quasi-random input stream and constant service time is a non-Markov process (renewal process). An algorithm for the calculation of the state probabilities, the time congestion probability, the average delay and the waiting time distributions are presented. It is shown that the variance of the input stream changes significantly the characteristics of this waiting system