Pricing and Queuing - Borgs, Christian; Chayes, Jennifer; Doroudi, Sherwin; Harchol-Balter, Mor; Xu, Kuang (ACM SIGMETRICS Performance Evaluation Review, 2012)
We consider a pricing in a single observable queue, where customers all have the same valuation, V, and the same waiting cost, v. It is known that earning rate is maximized in such a model when state-dependent pricing is used and an admissions threshold is deployed whereby arriving customers may not join the queue if the total number of customers exceeds this threshold. This paper is the first to explicitly derive the optimal threshold. We use our explicit formulation to obtain asymptotic results on how the threshold grows with V.