Stationary characteristics of the two-node Markovian tandem queueing system with general renovation

Consideration is given to the Markovian tandem queueing system with two finite-capacity heterogeneous nodes, say node 1 and node 2. The output of node 1 is the input into node 2. Each node is a single-server queue with a Poisson incoming flow of customers and service times having Erlang distribution. The service discipline is FIFO (first in, first out). General renovation is implemented in each node which implies that upon a service completion, a customer may remove a random number of customers from the queue (if any is available), with a given probability distribution; removed customers leave the system. Using the matrix-geometric technique, one derives the joint stationary distribution of the nodes' states. A recursive algorithm for computation of the stationary loss probabilities under the head-of-the-queue renovation is also proposed.