Abstract
This paper studies stability of user-equilibrium (UE) route flow solutions with respect to inputs to a traffic assignment problem, namely the travel demand and parameters in the link cost function. It shows, under certain continuity and strict monotonicity assumptions on the link cost function, that the UE link flow is a continuous function of the inputs, that the set of UE route flows is a continuous multifunction of the inputs, and that the UE route flow selected to maximize an objective function with certain properties is a continuous function of the inputs. The maximum entropy UE route flow is an example of the last. On the other hand, a UE route flow arbitrarily generated in a standard traffic assignment procedure may not bear such continuity property, as demonstrated by an example in this paper.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 609-617 |
| Number of pages | 9 |
| Journal | Transportation Research Part B: Methodological |
| Volume | 44 |
| Issue number | 4 |
| DOIs | |
| State | Published - May 2010 |
Funding
The comments of two anonymous reviewers are appreciated. The authors would like to thank Professors David Boyce and Hillel Bar-Gera for the exchange of ideas that has inspired the work. The need to give a formal proof for the stability of MEUE route flow sparkled from a conversation between the second author and Professor Michael Florian and Dr. Howard Slavin at the annual meeting of Transportation Research Board in 2009. The work is partially funded by the National Science Foundation under Grant DMS-0807893 , and partially funded by Federal Highway Administration under the award number DTFH61-08-H-00032. The views expressed in the paper are those of the authors’ alone.
Keywords
- Maximum entropy
- Stability
- Traffic assignment
- User equilibrium
ASJC Scopus subject areas
- Civil and Structural Engineering
- Transportation