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

In recent years, there is a growing research about queueing models with customers who choose their service durations. In general, 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. Thus, motivated by this issue, this work includes a single-server queueing model with customers who dynamically choose their service durations. In this setup, it is shown how to derive a price-regulation (Pigouvian tax) which implies an optimal resource allocation from a social point of view. In particular, this work includes an efficient procedure for computation of the parameters of this price function.