When to Use Speedup: An Examination of Service Systems with Returns

In a number of service systems, there can be substantial latitude to vary service rates. However, although speeding up service rate during periods of congestion may address a present congestion issue, it may actually exacerbate the problem by increasing the need for rework. We introduce a state-dependent queuing network where service times and return probabilities depend on the "overloaded" and "underloaded" state of the system. We use a fluid model to examine how different definitions of "overload" affect the long-term behavior of the system and provide insight into the impact of using speedup. We identify scenarios where speedup can be helpful to temporarily alleviate congestion and increase access to service. For such scenarios, we provide approximations for the likelihood of speedup to service. We also identify scenarios where speedup should never be used; moreover, in such a situation, an interesting bi-stability arises, such that the system shifts randomly between two equilibria states. Hence, our analysis sheds light on the potential benefits and pitfalls of using speedup when the subsequent returns may be unavoidable.