On Vacation During The Period To Reach The Customer Into The System With Probability P M/g/1 Multiple Vacation Queuing System

Queue system with vacations is an important model of queue theory . In this article we introduced the theoretical and practical situation about queue system with vacation and queue system with repairable service station all over the world. Base on the work, we study such problem: M/G/1queue system during vacations the arriver enter system with probability p. Using the method of imbedded Markov chain and renewal process , we do the following work:(1)Getting the expression of distributing generated functionofn1departure time queue length and the average customer number which stays in the system of departure time when the system is in equilibrium.(2)Getting the expression of L transformation of queue length at arbitrary time tand the limitation distribution when t?x.(3)Getting the expression of transformation 17(s)=:Ee^<sup>of delaying timeD^t and the distributing generated functionof waiting time...=1(4)Getting the expression of the distributing function D(t)of the servantbusy time and the expression of LS transformation of the distributing function QQ) of the system busy time.(5)Getting the expression of LS transformation a,(s) of probability A1(t) at arbitrary time t when the system is busy and the expression of LS transformation m0(s) of the severed customer number in (0, tl on the departure process. Besides,getting the distribution of the customer departure time interval when the system is in equilibrium.