Pricing and design of differentiated services:
Approximate analysis and structural insights
Costis Maglaras and Assaf Zeevi, Submitted April
2003, revised November 2003, March 2004.
To appear in Operations Research
Abstract:
We consider a model of a service system that delivers
two non-substitutable services to a market of heterogenous users. The first
service is delivered subject to a ``guaranteed'' (G) processing rate, and the
second is a ``best-effort'' (BE) type service in which residual capacity not
allocated to the guaranteed class is {\it shared} among BE-users. Users, in
turn, are sensitive to both price and congestion-related effects. The service
provider's objective is to optimally design the system so as to extract maximum
revenues. The design variables in this problem consist of a pair of static
prices for the two services, a policy that controls admission of G-users into
the system, and the mechanism by which users are informed of the state of
congestion in the system. Since these objectives are difficult to address using
exact analysis, we pursue approximations that are tractable and lead to
structural insights. Specifically, we first solve a deterministic relaxation of
the original objective to obtain a ``fluid-optimal'' solution which is
subsequently evaluated and refined to account for stochastic fluctuations.
Using diffusion limits, we derive approximations that yield the following
structural results (i) pricing rules derived from the deterministic
analysis are ``almost'' optimal; (ii) the optimal operational regime
for the system is close to heavy-traffic, and; (iii) real-time congestion
notification results in increased revenues. Numerical results illustrate
the accuracy of the proposed approximations and validate the aforementioned
structural insights.
Keywords: congestion notification, diffusion
approximations, economics, Halfin-Whitt regime, many server limits, pricing,
queueing, revenue management, service differentiation
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