The Approximation Of GI/G/1 Queuing System

GI/G/1 queueing systems are important queue model in queue theory. Hou zhen ting and his colleagues prove that GI/G/1 queueing systems are Markov skeleton pro-cesses, and apply backward equations theory of Markov skeleton process to prove the stationary distributions and ergodic theorem,and give the explicit equation of the tran-sition function of the queue length of GI/G/1 queueing system.This paper investigates the approximation problem of the queue length of GI/G/1 queueing system,i.e.:If the distribution of inpnt{A(m) (x)} and the service time{B(m) (x)}of a list of GI/G/1 queue-ing systems{Qum,m∈N} respectively convergence to A(x)and B(x),here A(x)and B(x) respectively indicates the distribution of input and the service time of GI/G/1 queueing system Qu,then the transition probability of the queue length of{Qum,m∈N}convergence to the transition probability of the queue length of Qu.