With A Second Multi-select Services N Policy M / G / 1 Queuing System Performance Analysis

An M/G/1type queue with the second multi-optional services and N-policy is studied in this paper, which belongs to M/G/1exhaustive service queue systems with vacations. Up to the present, various M/G/1exhaustive service queue systems with vacations have been extensively studied, and among them the M/G/1type queue with the second multi-optional services and N-policy has important research value, and no special work focused on the model seems to have appeared in open literatures.First, the general service time is introduced and the queue length’s recursion formula at the epoch just after the departure of the n-th customer is obtained with embedded Markov chain method. Then the distribution of the queue length of the system in the steady state and its probability generating function are given. Meanwhile, the status transfer equation is offered to get the average queue length, the stochastic decomposition of the queue length and the LST (Laplace-Stieltjes transform) of waiting time in steady state.