Optimal Pricing and Capacity in Service Systems With Delay-Sensitive Mixed-Risk Customers

In service systems with delay-sensitive customers, the decision of customers to join the queue or balk shapes the demand function, impacting the service provider's profits. Although risk aversion is a common assumption regarding customers' attitudes toward delay, in practice, customers may exhibit mixed-risk behavior. They may be risk-seekers if the waiting time is below a critical threshold and risk-averse if it is above it. To explore the impact of customers' mixed-risk behavior on the join/balk equilibrium strategy and the provider's pricing and service capacity policy, we study the problem of a profit-maximizing firm with an unobservable queue serving customers with mixed-risk behavior. The customers decide whether to join the queue or balk based on their expected utility. The firm must decide the entrance fee (price) and service rate (capacity) to maximize its expected profit given the customers' arrival rate at equilibrium. We identify the customers’ symmetric aggregate Nash equilibrium strategy, derive the firm's optimal price and capacity policy under a concave/convex service capacity cost, and perform a sensitivity analysis of the firm's performance with respect to the customers’ critical threshold