Networks and Spatial Economics

, Volume 19, Issue 3, pp 833–868 | Cite as

Tradable Credit Scheme for Control of Evolutionary Traffic Flows to System Optimum: Model and its Convergence

  • Ren-Yong GuoEmail author
  • Hai-Jun Huang
  • Hai Yang


We propose a dynamic tradable credit scheme for control of the day-to-day evolution process of traffic flows towards the system optimum (SO) state in a traffic network with elastic demand. In the scheme, the distribution and charge of travel credits are adjusted from period to period. The interacting dynamics among day-to-day traffic flows, period-to-period credit adjustment, and day-to-day credit price is formulated as an evolutionary game model. We mathematically prove two properties of the model, i.e., the consistence of the stationary state with the SO state and the convergence of the evolutionary trajectory. Finally, numerical results on a middle-size network are presented to validate the dynamic tradable credit scheme and to demonstrate the properties and application of the model.


Traffic dynamics Tradable mobility credits System optimum Convergence 



The work described in this paper was jointly supported by grants from the National Natural Science Foundation of China (71622005), the National Basic Research Program of China (2012CB725401), the Research Grants Council of the Hong Kong Special Administrative Region of China (HKUST16211114), and the Natural Science Foundation of Inner Mongolia of China (2014JQ03).


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Economics and ManagementBeihang UniversityBeijingPeople’s Republic of China
  2. 2.Key Lab of Complex System Analysis and Management DecisionMinistry of EducationBeijingPeople’s Republic of China
  3. 3.Department of Civil and Environmental EngineeringThe Hong Kong University of Science and TechnologyKowloonPeople’s Republic of China

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