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 joint distribution
of queue strings representing from which arrival stream each customer
in the system arrived and remaining service times of respective
customers in the system has a matrix product-form solution, where
matrices constituting the 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. Note also that the result is a
natural extension of the classical result for the LCFS-PR M/G/1 queue.
Further, utilizing the matrix product-form solution, we derive a new
expression of the vector LST of the stationary distribution of
unfinished work in the work-conserving single-server queue with
multiple arrival streams governed by a Markov chain, which is given in
terms of the sum of matrix-geometric series.