An approximation for the system size of M/G/c queueing systems

In this paper, we propose an approximation analysis for the system size distribution of the M/G/c system which is transform-free. At first, we borrow the system size distribution from the Markovian service models and then introduce a newly defined parameter in place of traffic intensity. In this step, we find the distribution of the number of customers up to c. Next, we concentrate on each waiting space of the queue separately, rather than consider the entire queue as a whole. Then, according to the system state of the arrival epoch, we induce the probability distribution of the system size recursively. We discuss the effectiveness of this approximation method by comparing with simulation for the mean system size.