Analysis of an M/M/cQueueing System with Impatient Customers and Synchronous Vacations | Zendy

Dequan Yue | Zendy; Wuyi Yue | Zendy; Guoxi Zhao | Zendy

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Analysis of an M/M/cQueueing System with Impatient Customers and Synchronous Vacations

Author(s) -

Dequan Yue,

Wuyi Yue,

Guoxi Zhao

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/893094

Subject(s) - server , queue , queueing system , computer science , queueing theory , limiting , function (biology) , probability generating function , mathematical optimization , mathematics , computer network , probability density function , statistics , cumulative distribution function , mechanical engineering , evolutionary biology , engineering , biology

We consider an M/M/c queueing system with impatient customers and a synchronous vacation policy, where customer impatience is due to the servers’ vacation. Whenever a system becomes empty, all the servers take a vacation. If the system is still empty, when the vacation ends, all the servers take another vacation; otherwise, they return to serve the queue. We develop the balance equations for the steady-state probabilities and solve the equations by using the probability generating function method. We obtain explicit expressions of some important performance measures by means of the two indexes. Based on these, we obtain some results about limiting behavior for some performance measures. We derive closed-form expressions of some important performance measures for two special cases. Finally, some numerical results are also presented

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