Bounding the Inefficiency of the Reliability-Based Continuous Network Design Problem Under Cost Recovery

  • Anny B. Wang
  • W. Y. SzetoEmail author


This study defines the price of anarchy for general reliability-based transport network design problems, which is an indicator of inefficiency that reveals how much the design objective value exceeds its theoretical minimum value due to the risk averse and selfish routing behavior of travelers. This study examines a new problem, which is a reliability-based continuous network design problem under cost recovery. In this problem, the variations of system travel time and path travel times, the risk attitudes of the system manager and travelers, congestion toll charges, capacity expansions, and cost recovery constraint are explicitly considered. The design problem is formulated as a min-max problem with the reliability-based user equilibrium constraint. It is proved that the price of anarchy for this problem is bounded above, and the upper bound is independent of travel time functions, demands, and network topology. The upper bound is related to the travel time variations, the value of reliability, and the value of time.


Inefficiency Price of anarchy Transport network design problem Reliability-based user equilibrium 



This work was jointly supported by a grant [No. 201711159034] from the University Research Committee of the University of Hong Kong, a grant from the National Natural Science Foundation of China [No. 71771194], and a grant from the Guangzhou Science Technology and Innovation Commission [No. 201707010292]. The authors are grateful to the Editor-in-Chief and two reviewers for their constructive comments.


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Authors and Affiliations

  1. 1.Guangzhou Municipal Engineering Design & Research Institute Co., LtdGuangzhouPeople’s Republic of China
  2. 2.Department of Civil EngineeringThe University of Hong KongHong KongPeople’s Republic of China
  3. 3.The University of Hong Kong Shenzhen Institute of Research and InnovationShenzhenPeople’s Republic of China

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