Bulletin of the
Korean Mathematical Society BKMS

We consider a single-server queue with service time distribution of phase type where positive customers, negative customers and disasters arrive according to a Markovian arrival process with marked transitions (MMAP). We derive simple formulae for the stationary queue length distributions. The Laplace-Stieltjes transforms (LST's) of the sojourn time distributions under the combinations of removal policies and service disciplines are also obtained by using the absorption time distribution of a Markov chain.

Keywords: MMAP, negative customers, disasters, queue length, sojourn time, fundamental matrix

MSC numbers: 60K25, 90B22