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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 609729, 8 pages
http://dx.doi.org/10.1155/2015/609729
Research Article

Stability of Intelligent Transportation Network Dynamics: A Daily Path Flow Adjustment considering Travel Time Differentiation

1Microelectronics and Information Systems Research Center, National Chiao Tung University, 1001 University Road, Hsinchu 300, Taiwan
2Department of Transportation and Logistics Management, National Chiao Tung University, 1001 University Road, Hsinchu 300, Taiwan

Received 7 October 2014; Revised 13 February 2015; Accepted 15 February 2015

Academic Editor: Yan-Jun Liu

Copyright © 2015 Ming-Chorng Hwang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A theoretic formulation on how traffic time information distributed by ITS operations influences the trajectory of network flows is presented in this paper. The interactions between users and ITS operator are decomposed into three parts: (i) travel time induced path flow dynamics (PFDTT); (ii) demand induced path flow dynamics (PFDD); and (iii) predicted travel time dynamics for an origin-destination (OD) pair (PTTDOD). PFDTT describes the collective results of user’s daily route selection by pairwise comparison of path travel time provided by ITS services. The other two components, PTTDOD and PFDD, are concentrated on the evolutions of system variables which are predicted and observed, respectively, by ITS operators to act as a benchmark in guiding the target system towards an expected status faster. In addition to the delivered modelings, the stability theorem of the equilibrium solution in the sense of Lyapunov stability is also provided. A Lyapunov function is developed and employed to the proof of stability theorem to show the asymptotic behavior of the aimed system. The information of network flow dynamics plays a key role in traffic control policy-making. The evaluation of ITS-based strategies will not be reasonable without a well-established modeling of network flow evolutions.