Refined mean‐field approximation for discrete‐time queueing networks with blocking

We study a discrete‐time queueing network with blocking that is primarily motivated by outpatient network management. To tackle the curse of dimensionality in performance analysis, we develop a refined mean‐field approximation that deals with changing population size, a nonconventional feature that makes the analysis challenging within the existing literature. We explicitly quantify the convergence rate for this approximation as O(1/N)$$ O\left(1/N\right) $$ with N$$ N $$ being the system size. Not only is this convergence better than the O(1/N)$$ O\left(1/\sqrt{N}\right) $$ convergence proven in prior work, but our approximation shows a significant improvement in performance prediction accuracy when the system size is small, compared to the conventional (unrefined) mean‐field approximation. This accuracy makes our approximation appealing to support decision‐making in practice.