An $MMAP[3]/PH/1$ queue with negative customers and disasters
Bull. Korean Math. Soc. 2006 Vol. 43, No. 2, 277-292
Published online June 1, 2006
Yang Woo Shin
Changwon National University
Abstract : 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
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