Geodesic
Analysis of Discrete-time queues with correlated arrivals, negative customers and server interruption
Senthil Vadivu, A.1 ; Arumuganathan, R.2 ; Senthil Kumar, M.3
1 Department of Mathematics, Dr.NGP Institute of Technology, 641048 Coimbatore, India.
2 Department of Mathematics, PSG College of Technology, 641004 Coimbatore, India.
3 Department of Applied Mathematics & Computational Sciences, PSG College of Technology, 641004 Coimbatore, India.
RAIRO - Operations Research - Recherche Opérationnelle, Tome 50 (2016) no. 1, pp. 67-81

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This paper analysis a discrete time infinite capacity queueing system with correlated arrival and negative customers served by two state Markovian server. Positive customers are generated according to the first order Markovian arrival process with geometrically distributed lengths of On periods and Off periods. Further, the geometrically distributed arrival of negative customer removes the positive customers is any, and has no effect when the system is empty. The server state is a two state Markov chain which alternate between Good and Bad states with geometrically distributed service times. Closed-form expressions for mean queue length, unfinished work and sojourn time distributions are obtained. Numerical illustrations are also presented.

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DOI : 10.1051/ro/2015012
Classification : 60K25, 90B22
Keywords: On-OffSource, negative customers, two state Markovian server, sojourn time distribution

Senthil Vadivu, A. 1 ; Arumuganathan, R. 2 ; Senthil Kumar, M. 3

1 Department of Mathematics, Dr.NGP Institute of Technology, 641048 Coimbatore, India.
2 Department of Mathematics, PSG College of Technology, 641004 Coimbatore, India.
3 Department of Applied Mathematics & Computational Sciences, PSG College of Technology, 641004 Coimbatore, India. 
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     author = {Senthil Vadivu, A. and Arumuganathan, R. and Senthil Kumar, M.},
     title = {Analysis of {Discrete-time} queues with correlated arrivals, negative customers and server interruption},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {67--81},
     publisher = {EDP-Sciences},
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     year = {2016},
     doi = {10.1051/ro/2015012},
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Senthil Vadivu, A.; Arumuganathan, R.; Senthil Kumar, M. Analysis of Discrete-time queues with correlated arrivals, negative customers and server interruption. RAIRO - Operations Research - Recherche Opérationnelle, Tome 50 (2016) no. 1, pp. 67-81. doi: 10.1051/ro/2015012

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