Pricing and capacity sizing for systems with shared resources:
approximate solutions and scaling relations
Costis Maglaras and Assaf Zeevi,
Management Science, Vol. 49, No. 8, pg.1018-1038,
2003.
Abstract:
This paper considers revenue management,
in particular, 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 are the following: Congestion costs are ``small'', the optimal price
admits an intuitive decomposition that is quite illuminating, 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 natural statistical economies of scale that are an
intrinsic part of these systems.
Keywords: shared resources, heavy traffic,
equilibrium, pricing, many-server limits
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