Differentiated Quality of Service: Joint Pricing and Scheduling in Queuing Systems

Jan A. Van Mieghem
Associate Professor
Kellogg Graduate School of Business
Northwestern University

This article considers a service provider offering multiple service grades that are differentiated by price and quality. Quality of service is measured by the delay distributions that customers experience in receiving service and is incorporated through general delay cost functions that describe customer delay sensitivities. The firm directly controls the number of grades, their prices and scheduling. We study the optimal mix of service levels and prices that a profit maximizing firm will provide to heterogeneous, utility-maximizing customers.

The analysis highlights the impact of customer information and price regulation and clearly differentiates among customer types, service grades and queuing classes. Type information allows type-dependent scheduling resulting in perfect service discrimination while type-specific prices allow perfect price discrimination. The unknown optimal scheduling policy is approximated by the generalized $c\mu $ rule, which yields an analytic specification of scheduling, delay distributions and prices under realistic convex delay costs. A comprehensive benchmarking example is used to investigate the value of differentiated service. The economic queuing model is also analyzed in the absence of type information and type-specific prices. This shows how dynamic scheduling and multi-plan, non-linear, time-dependent pricing can reinforce each other to imperfectly discriminate on price and service. In special cases, incentive-compatible prices can be coordinating so that imperfect information is costless. Negative feedback inherent in the dynamic G$c\mu $ rule may help system coordination.