The Down/up Crossing Properties Of Markov M~X/M/1 Queues Processes

This paper mainly studies the shuttle nature of the customers in a fixed range until any time t in the queuing process of MX/M/1.First of all,we study MX/M/l the domestic and foreign research progress of the queuing process and the preliminary knowledge involved in the article are introduced.Next,in order to study the nature of the(N-1)shuttle number of the MX/M/1 queuing process,we define a type of Q-matrix,and use the forward equation to calculate the explicit expression of the occurrence function of the transition probability of(X(t),Y(t)),and perform Laplace transform to get ?i,0*(?,v),then perform Laplace inverse transformation to get(?)P(1,0)(0,l)(t-?)vl.Finally,get the joint probability occurrence function of Y(t)when X(t)starts from any state,and the probability occurrence function of the number of customers who complete the service from 0 state,under the condition?<? the joint probability occurrence function of the number of shuttles Y(t)in the range of(N-1).