2013/12/13 by Christian Borgs, Jennifer Chayes, Jennifer T. Chayes +4 · 1 citation
Business, Management and Accounting · Social Sciences · #Advanced Queuing Theory Analysis #Supply Chain and Inventory Management #Transportation Planning and Optimization
paper · doi:10.1017/s0269964813000351
openalex publication_date 2013/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
We consider the social welfare model of Naor [20] and revenue-maximization model of Chen and Frank [7], where a single class of delay-sensitive customers seek service from a server with an observable queue, under state dependent pricing. It is known that in this setting both revenue and social welfare can be maximized by a threshold policy, whereby customers are barred from entry once the queue length reaches a certain threshold. However, no explicit expression for this threshold has been found. This paper presents the first derivation of the optimal threshold in closed form, and a surprisingly simple formula for the (maximum) revenue under this optimal threshold. Utilizing properties of the Lambert W function, we also provide explicit scaling results of the optimal threshold as the customer valuation grows. Finally, we present a generalization of our results, allowing for settings with multiple servers.