Two pricing mechanisms for a service provider when customers’ delay costs are value-related

• Customers’ delay sensitivity is increasing in their own value for the service.
• We study the uniform pricing and priority auction for a service provider.
• Auction always performs better in revenue and social welfare making.
• Auction also renders more consumer surplus in most instances.

In this paper, we study two pricing mechanisms for a provider that serves delay-sensitive customers, one is the uniform pricing and the other is the priority auction. The expected delay cost of a customer is assumed to depend on his value for the service (i.e. the unit delay cost is a strictly increasing function of his value) and the expected sojourn time caused by the number of customers in the system (and his payment-based position in the queue if auction is adopted). Hence, each customer reacts to the service provider’s pricing mechanism by deciding whether or not to enter the service system and how much he pays. This resulting problem is a Stackelberg game. When auction is adopted, by using of adverse selection, we derive a feasible scheme in which customers with higher value would like to pay more. We further compare the performance of these two pricing mechanisms. Our numerical examples show that auction performs better not only in terms of revenue making but also in terms of social welfare improvement. Interestingly, auction can also render more customer surplus in most instances, which differs from the common techniques in revenue management field.