AnM/M/s-consistent diffusion model for theGI/G/s queue

This paper develops a diffusion-approximation model for a stableGI/G/s queue: The queue-length process in theGI/G/s queue is approximated by a diffusion process on the nonnegative real line. Some heuristics on the state space and the infinitesimal parameters of the approximating diffusion process are introduced to obtain an approximation formula for the steady-state queue-length distribution. It is shown that the formula is consistent with the exact results for theM/M/s andM/G/ queues. The accuracy of the approximations for principal congestion measures are numerically examined for some particular cases.