Pricing a threshold-queue with hysteresis

In this paper, we consider pricing schemes at an M/M/1 queue with infinite potential demand but where the number of customers in the queue depends on both the price and the offered quality of service (QoS). Our model aims at comparing the optimal revenue for three different strategies: first the case of a fixed price; second the case where there is a threshold on the queue occupancy such that a larger charge is imposed for an occupancy above the threshold (in order to maintain a given QoS); third the case of a threshold-queue with hysteresis in order to avoid costly oscillations around the aforementioned threshold. In all those three situations, we determine the equilibrium number of customers, and the parameters (price(s), threshold(s)) optimizing the revenue. We can therefore find the optimal strategy from the provider’s point of view. In this paper, we use a static demand because session lengths are assumed large with respect to the queue dynamics and therefore consider the system in steady-state. We then show that, contrary to what could be expected, a policy without threshold is recommended.