Multi-server retrial queue with negative customers and disasters |
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Authors: | Yang Woo Shin |
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Institution: | (1) Department of Statistics, Changwon National University, Changwon, Gyeongnam, 641-773, South Korea |
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Abstract: | We consider a multi-server retrial queue with waiting places in service area and four types of arrivals, positive customers,
disasters and two types of negative customers, one for deleting customers in orbit and the other for deleting customers in
service area. The four types of arrivals occur according to a Markovian arrival process with marked transitions (MMAP) which
may induce the dependence among the arrival processes of the four types.
We derive a necessary and sufficient condition for the system to be positive recurrent by comparing sample paths of auxiliary
systems whose stability conditions can be obtained. We use a generalized truncated system that is obtained by modifying the
retrial rates for an approximation of stationary queue length distribution and show the convergence of approximation to the
original model. An algorithmic solution for the stationary queue length distribution and some numerical results are presented.
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Keywords: | Retrial queue Marked Markovian arrival process (MMAP) Negative customers Disasters Queue length Stochastic order Tightness |
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