Matrix product-form solution for an LCFS-PR single-server queue with multiple arrival streams governed by a Markov chain.

This paper considers a stationary single-server queue with multiple arrival streams governed by a Markov chain, where customers are served on an LCFS preemptive-resume basis. Service times of customers from each arrival stream are generally distributed and service time distributions for different arrival streams may be different. Under these assumptions, it is shown that the stationary distribution of queue strings representing from which arrival stream each customer in the system arrived has a matrix product-form solution, where rate matrices constituting the matrix product-form solution are given in terms of the infinitesimal generator of a certain Markov chain. Compared with the previous works, the result in this paper is more general in the sense that general service time distributions are allowed, and it has the advantage of computational efficiency