Price and Service Discrimination in Queuing Systems: Incentive Compatibility of <i>Gc</i>μ Scheduling

Abstract

This article studies the optimal prices and service quality grades that a queuing system—the “firm”—provides to heterogeneous, utility-maximizing customers who measure quality by their experienced delay distributions. Results are threefold: First, delay cost curves are introduced that allow for a flexible description of a customer's quality sensitivity. Second, a comprehensive executable approach is proposed that analytically specifies scheduling, delay distributions and prices for arbitrary delay sensitivity curves. The tractability of this approach derives from porting heavy-traffic Brownian results into the economic analysis. The generalized cμ (Gcμ) scheduling rule that emerges is dynamic so that, in general, service grades need not correspond to a static priority ranking. A benchmarking example investigates the value of differentiated service. Third, the notions of grade and rate incentive compatibility (IC) are introduced to study this system under asymmetric information and are established for Gcμ scheduling when service times are homogeneous and customers atomistic. Grade IC induces correct grade choice resulting in perfect service discrimination; rate IC additionally induces centralized-optimal rates. Dynamic Gcμ scheduling exhibits negative feedback that, together with time-dependent pricing, can also yield rate incentive compatibility with heterogeneous service times. Finally, multiplan pricing, which offers all customers a menu with a choice of multiple rate plans, is analyzed.