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A Comparison of Dynamic User Optimal States with Zero, Fixed and Variable Tolerances

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Abstract

The notion of dynamic user equilibrium (DUE) and dynamic user optimum (DUO) were still treated interchangeably in the dynamic traffic assignment (DTA) literature until tolerance-based DUO was recently proposed as alternative definitions of DUO. The latter distinguishes DUO from DUE, and the tolerances can be prescribed a priori (i.e. DUO with fixed tolerance) or endogenously (i.e. DUO with variable tolerance). These tolerances reflect the differences in travel costs between used paths of an origin–destination (OD) pair. Since DUE requires zero difference in travel costs between used paths of an OD pair, it can be regarded as DUO with zero tolerance. This paper first compares the three alternative definitions of DUO and discusses their relationships. Secondly, the existence conditions of these DUO solutions are discussed. A key conclusion is that DUO with variable tolerance always exists even when the other two types of DUO solutions may not. The second conclusion is that, when the tolerances are equal to zero, the solution must be a DUE solution. Furthermore, DUE is a special case of DUO with variable tolerance; since the tolerance in the concept of DUO with variable tolerance is an endogenous variable, if a DUE solution exists, an efficient method for solving for DUO with variable tolerance should directly find such a DUE solution. All these are illustrated by means of three examples. Finally, it is acknowledged that the analysis of DUO with variable tolerance in the same rigor as that of DUE is a challenging problem and worthy of further research.

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Acknowledgments

This research is mainly supported by the National Natural Science Foundation of China (Grant No.: 71171026). It is also partly supported by the “Doctoral Fund of Ministry of Education of China” grant (No.: 20110041120009), a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU 716312E) and a grant (201211159009) from the University Research Committee of the University of Hong Kong. The support of all these agencies/organizations is gratefully acknowledged. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of these funding bodies.

This paper was first presented at the Fourth International Symposium on Dynamic Traffic Assignment, which took place on 4–6 June 2012, Martha’s Vineyard, USA, and then at the University of Illinois at Chicago on 13 June 2012 and at University College London (UCL) on 20 June 2012. All comments and questions received at these places were appreciated. The authors also thank Professor Terry Friesz and two anonymous referees for their insightful comments on the earlier versions of this paper.

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Authors and Affiliations

  1. College of Transport and Communications, Shanghai Maritime University, Pudong, Shanghai, 201306, China

    Y. E. Ge

  2. School of Transportation & Logistics, Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, Liaoning Province, China

    Y. E. Ge & B. R. Sun

  3. Department of Civil and Environmental Engineering, University of California, Davis, CA, USA

    H. M. Zhang

  4. School of Transportation Engineering, Tongji University, 4800 Cao’an Road, Shanghai, 201804, China

    H. M. Zhang

  5. Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China

    W. Y. Szeto

  6. School of Economics & Management, Shanghai Maritime University, Pudong, Shanghai, 200135, China

    Xizhao Zhou

  7. College of Transport & Communications, Shanghai Maritime University, 1550 Haigang Avenue, Pudong New District, Shanghai, 201306, China

    Y. E. Ge

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  1. Y. E. Ge
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  2. B. R. Sun
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  3. H. M. Zhang
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  4. W. Y. Szeto
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  5. Xizhao Zhou
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Correspondence to Y. E. Ge.

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Ge, Y.E., Sun, B.R., Zhang, H.M. et al. A Comparison of Dynamic User Optimal States with Zero, Fixed and Variable Tolerances. Netw Spat Econ 15, 583–598 (2015). https://doi.org/10.1007/s11067-014-9243-9

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