Stationary Characteristics of the two-node Tandem Queueing System with Poisson Arrivals and General Renovation

We consider the two-node tandem queueing system with finite capacity queues in both nodes and Poisson input flows. There is one server in each node and the service times are assumed to be i.i.d. random variables, having Erlang distributions with different parameters. General renovation mechanism is assumed to be implemented in each node. It implies that the queue is controlled upon customers' departure instants. Upon quitting the 1st node a customer pushes out i customers from its queue with the given probability distributioni{qi , 0 ≤ i ≤ N1 - 1}, with N1 being the 1st node capacity. Pushed-out customers leave the system and do not have any further effect on it. Upon quitting the 2nd node a customer pushes out customers from its queue with another given probability distribution {q(2), 0 ≤ i ≤ N2 - 1}, where N2 is the 2nd node capacity. The analytic method, based on well-known matrix analytictechnique, is being briefly discussed, which allows one to compute the main stationary performance characteristics of the model including loss probabilities.