AN M/G/1 QUEUE WITH REGULAR AND OPTIONAL PHASE VACATION AND WITH STATE DEPENDENT ARRIVAL RATE

Subject Areas : International Journal of Mathematical Modelling & Computations

Rathinasabapathy  Kalyanaraman ¹ (Professor of Mathematics, Annamalai University India Professor of Mathematics 2nd)
Shanthi  R ² (Assistant professor Annamalai University India Research Scholar)

Received: 2016-04-15 Accepted : 2016-04-15 Published : 2015-03-21

Keywords: Performance Measures, Supplementary variable, Vacation queue, probability generating function,

Abstract :

We consider an M/G/1 queue with regular and optional phase vacation and withstate dependent arrival rate. The vacation policy is after completion of service if there areno customers in the system, the server takes vacation consisting of K -phases, each phaseis generally distributed. Here the first phase is compulsory where as the other phases areoptional. For this model the supplementary variable technique has been applied to obtainthe probability generating functions of number of customers in the queue at the different server states. Some particular models are obtained and a numerical study is also carriedout.

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