Balancing Admission Control, Speedup, and Waiting in Service Systems

In a number of service settings, customer waiting, admission control, and speedup of service rates can occur during periods of congestion. For example, in a healthcare setting, this means that patients who require care may be sent to other, less ideal service outlets or hospital units. As expected, this comes at a cost to patient outcomes. In this work, we examine a multi-server queueing system which allows for admission control and speedup. We use dynamic programming to characterize properties of the optimal control and find that in some instances, the optimal policy has a simple form of a threshold policy. Leveraging this insight, we examine a queueing system where speedup is used when the number in the system exceeds some threshold and admission control is used when the number in the system exceeds some (potentially different) threshold. Using fluid analysis and a loss model, we establish approximations for the probability of speedup, the probability of admission control, and the expected queue length. We use the approximation analysis to characterize the region of the optimal solution and develop a greedy heuristic to derive a near optimal solution to the original optimization problem. We use simulation to demonstrate the quality of these approximations and find they can be quite accurate and robust. This analysis can provide insight to system administrators as they evaluate how to balance admission and speedup control—deciding when and to what extent to use each.