Optimal price and delay differentiation in large-scale queueing systems

Costis Maglaras, John Yao, Assaf Zeevi

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)2427-2444
Number of pages18
JournalManagement Science
Issue number5
StatePublished - May 2018
Externally publishedYes


  • Damaged goods
  • Many-server limits
  • Pricing
  • Queueing games
  • Revenue management
  • Service differentiation


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