Accuracy of fluid approximations for queueing systems with congestion‐sensitive demand and implications for capacity sizing

We study the accuracy of fluid approximations in single‐ and many‐server queueing systems in which the arrival rate depends on the congestion in the system. If the potential demand rate exceeds the system’s capacity, then the fluid approximations are found to exhibit $O\left(1\right)$ ‐accuracy–their error does not increase with system size. These fluid approximations are used to solve two capacity sizing problems: minimizing total system cost and maximizing social welfare. We find that the solutions to both these problems exhibit interesting differences, and further that under some conditions, the fluid prescriptions exhibit $o\left(1\right)$ ‐optimality, that is, their optimality gap is asymptotically zero.