Nonlinear Min-Cost-Pursued Route-Swapping Dynamic System | Zendy

Wenyi Zhang | Zendy; Wei Guan | Zendy; Jihui Ma | Zendy; Tao Wang | Zendy

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Nonlinear Min-Cost-Pursued Route-Swapping Dynamic System

Author(s) -

Wenyi Zhang,

Wei Guan,

Jihui Ma,

Tao Wang

Publication year - 2013

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2013/162128

Subject(s) - computer science , nonlinear system , pairwise comparison , swap (finance) , mathematical optimization , lyapunov function , stability (learning theory) , mathematics , artificial intelligence , physics , finance , quantum mechanics , machine learning , economics

This study proposes a nonlinear min-cost-pursued swapping dynamic (NMSD) system to model the evolution of selfish routing games on traffic network where travelers only swap from previous costly routes to the least costly ones. NMSD is a rational behavior adjustment process with stationary link flow pattern being the Wardrop user equilibrium. NMSD is able to prevent two behavioral deficiencies suffered by the existing min-cost-oriented models and keep solution invariance. NMSD relaxes the homogeneous user assumption, and the continuous-time NMSD (CNMSD) and discrete-time NMSD (DNMSD) share the same revision protocol. Moreover, CNMSD is Lyapunov-stable. Two numerical examples are conducted. The first one is designed to characterize the NMSD-conducted network traffic evolution and test the stability of day-to-day NMSD. The second one aims to explore the impacts of network scale on the stability of route-swaps conducted by pairwise and min-cost-pursed swapping behaviors

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