A practical trial-and-error implementation of marginal-cost pricing on networks

Deren Han; Hai Yang; Xiaoming Yuan

doi:10.3934/jimo.2010.6.299

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2010, Volume 6, Issue 2: 299-313. Doi: 10.3934/jimo.2010.6.299

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A practical trial-and-error implementation of marginal-cost pricing on networks

1.
School of Mathematics and Computer Sciences, Nanjing Normal University, Nanjing 210097
2.
Department of Civil Engineering, The Hong Kong University of Science and Technology, Hong Kong
3.
Department of Mathematics, Hong Kong Baptist University, Hong Kong

Received: November 30, 2008

Revised: October 31, 2009

Published: March 2010

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Abstract

This paper proposes a trial-and-error implementation of marginal-cost pricing on transportation networks in the absence of both demand functions and travel time functions. Assuming that the corresponding link flows for given trial tolls are observable and that the approximations of the exact travel time functions are provided, the new trial is obtained via solving a system of equations. The new trial-and-error implementation is proved to be convergent globally under mild assumptions, and its improvements over existing methods are verified by some numerical experiments.

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Mathematics Subject Classification: Primary: 90B20, 49J20, 90B50, 90C33.

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