Optimal Price and Delay Differentiation in Large-Scale Queueing Systems
研究一个收益最大化的企业如何为异质性顾客设计不同价格和延迟的服务等级，通过确定性松弛方法近似随机问题，发现大规模系统中差异化策略的最优条件和战略延迟的作用。
We study a multiserver queueing model of a revenue-maximizing firm providing a service to a market of heterogeneous price- and delay-sensitive customers with private individual preferences. The firm may offer a selection of service classes that are differentiated in prices and delays. Using a deterministic relaxation, which simplifies the problem by preserving the economic aspects of price-and-delay differentiation while ignoring queueing delays, we construct a solution to the fully stochastic problem that is incentive compatible and near optimal in systems with large capacity and market potential. Our approach provides several new insights for large-scale systems: (i) the deterministic analysis captures all pricing, differentiation, and delay characteristics of the stochastic solution that are nonnegligible at large scale; (ii) service differentiation is optimal when the less delay-sensitive market segment is sufficiently elastic; (iii) the use of “strategic delay” depends on system capacity and market heterogeneity—and it contributes significant delay when the system capacity is underutilized or when the firm offers three or more service classes; and (iv) connecting economic optimization to queueing theory, the revenue-optimized system has the premium class operating in a “quality-driven” regime and the lower-tier service classes operating with noticeable delays that arise either endogenously (“efficiency-driven” regime) or with the addition of strategic delay by the service provider. This paper was accepted by Gérard Cachon, stochastic models and simulation.