Abstract
An approximation method based on the diffusion theory is proposed for solving multi-server finite queueing problems having general independent inter-arrival time and general service time distributions. The discrete customer flow through the system is approximated by a continuous one, and a diffusion equation for the process of the number of customers in the system is constructed by using means and variances of the inter-arrival time and service time distributions. Two reflecting boundaries are imposed at the origin and m, the maximum number of customers being allowed in the system. Later, the boundary conditions are modified to improve the approximation. Approximate formulas for P_n. Probability of finding n customers in the system, and for N, mean number of lost customers from the system per mean service time, are given for steady state. Numerical examples for mean number of customers in the system are presented for some E_l/E_k/s(m) systems to show the effectiveness of the proposed method.
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