Analysis Of The Geom～x/G/1 Queueing Systems With Exhaustive Service Discipline And Vacation

By means of ancestor line, we first derive that the stable system size of Geom^X /G/1 queue with exhaustive service discipline and multiple vacations(denoted by Geomx /G(E,MV)/1 ) has decomposition properties and by compairing Geom^X /G(E,MV)/1 with Geom/G(E,MV)/1 queue, we show that the stablewaiting time of Geom^X /G(E,MV)/1 is distributed as the sum of two independent random variables, which help to illustrate the system size and waiting time of Geom^X /G/1 queue system with exhaustive service discipline and adaptive multistage vacations(denoted by Geom^X /G(E,AMV)/1 ) have decomposition properties.Secondly, Geom^X₁Geom^X₂ /G/1 queue with exhaustive service discipline is considered , the PGF of the stable system size is given as well. The stable system size of the Geom^X₁Geom^X₂ /G/1 queue with single vacation and multiple vacationsare discussed. Then Geom^X /G(E,AMV) /G/1 queue is discussed and in the steady state, the PGF of the system size and waiting time are obtained.In the end , adaptive multistage vacations are first introduced into Geom^X /G/1repairable queue system. We discussed the system under two different service disciplines, and some indexes such as system availability, failure frequency and reliability function are offered.