Pricing and Capacity Sizing for Systems with Shared Resources: Approximate Solutions and Scaling Relations

This paper considers pricing and capacity sizing decisions, in a single-class Markovian model motivated by communication and information services. The service provider is assumed to operate a finite set of processing resources that can be shared among users; however, this shared mode of operation results in a service-rate degradation. Users, in turn, are sensitive to the delay implied by the potential degradation in service rate, and to the usage fee charged for accessing the system. We study the equilibrium behavior of such systems in the specific context of pricing and capacity sizing under revenue and social optimization objectives. Exact solutions to these problems can only be obtained via exhaustive simulations. In contrast, we pursue approximate solutions that exploit large-capacity asymptotics. Economic considerations and natural scaling relations demonstrate that the optimal operational mode for the system is close to “heavy traffic.” This, in turn, supports the derivation of simple approximate solutions to economic optimization problems, via asymptotic methods that completely alleviate the need for simulation. These approximations seem to be extremely accurate. The main insights that are gleaned in the analysis follow: congestion costs are “small,” the optimal price admits a two-part decomposition, and the joint capacity sizing and pricing problem decouples and admits simple analytical solutions that are asymptotically optimal. All of the above phenomena are intimately related to statistical economies of scale that are an intrinsic part of these systems. (Shared Resources; Heavy Traffic; Equilibrium; Pricing; Many-Server Limits)