Regulation of a single-server queue with customers who dynamically choose their service durations

In recent years, there is a growing attention towards queueing models with customers who choose their service durations. The model assumptions in the existing literature imply that every customer knows his service demand when he enters into the service position. Clearly, this property is not consistent with some real-life situations. Motivated by this issue, the current work includes a single-server queueing model with customers who dynamically choose their service durations. In this setup, the main result is existence of a quadratic price function which (1) implies an optimal resource allocation from a social point of view and (2) internalizes the externalities in the system. In addition, it is explained how to compute its parameters efficiently.