Optimal Price and Delay Differentiation in Queueing Systems

We study a multi-server 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 highlights the first-order economic structure of the problem, we construct a solution 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 tractable first-order analysis characterizes essentially all salient features of the optimal solution; ii) service differentiation is optimal when the less delay-sensitive market segment is sufficiently elastic; iii) depending on system capacity and market heterogeneity, "intentional delay" (whereby delay is artificially added) in cheaper service classes may be used to justify price premiums in the more expensive service classes, akin to the role of "damaged goods" in the economics literature; 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 in an "efficiency-driven" regime (i.e., with noticeable delays that arise either endogenously or due to the injection of intentional delay by the service provider)