Refining the Diffusion Approximation for the M/G/m Queue

Despite its many and varied applications, the M/G/m queue has yet to be solved exactly. Consequently, researchers have developed many methods for approximating its solution. We refine a diffusion approximation model developed by Kimura for the M/G/m queue, using an alternative approach to characterize and solve the diffusion equations and incorporating some known results of the queue into the model. Numerical studies indicate that the refined model provides significantly improved performance. Moreover, the model is consistent with some known heavy-traffic limit results.