AN MMAP[3]/PH/1 QUEUE WITH NEGATIVE CUSTOMERS AND DISASTERS | Zendy

Yang-Woo Shin | Zendy

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AN MMAP[3]/PH/1 QUEUE WITH NEGATIVE CUSTOMERS AND DISASTERS

Author(s) -

Yang-Woo Shin

Publication year - 2006

Publication title -

bulletin of the korean mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.295

H-Index - 27

eISSN - 2234-3016

pISSN - 1015-8634

DOI - 10.4134/bkms.2006.43.2.277

Subject(s) - mathematics , markov chain , queue , distribution (mathematics) , service (business) , queueing theory , markov process , computer science , computer network , discrete mathematics , mathematical analysis , statistics , business , marketing

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.

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