Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/75916
Title: On the uniqueness of user equilibrium flow with speed limit
Authors: Liu, ZY
Yi, W 
Wang, SA 
Chen, J
Keywords: Speed limits
User equilibrium
Link flow
Solution uniqueness
Network-based analysis
Polyhedron
Issue Date: 2017
Publisher: Springer
Source: Networks and spatial economics, 2017, v. 17, no. 3, p. 763-775 How to cite?
Journal: Networks and spatial economics 
Abstract: This technical note focuses on the link flow uniqueness of user equilibrium (UE) with speed limits. Under a mild assumption on the monotonicity of link travel time function, the UE link flow solutions are well recognized to be unique. However, the incorporation of speed limits in the network has undermined the strict monotonicity of link travel time functions, thus the UE flows on the links with speed limits may not be unique. This note addresses the uniqueness problem with two major contributions. First, a polyhedron defined on links is provided, and it is proven that the UE link flow is unique if and only if the polyhedron only contains one value. Second, two concise methods are proposed to mathematically check whether the polyhedron is a singleton, which can be easily solved and convenient for practical use.
URI: http://hdl.handle.net/10397/75916
ISSN: 1566-113X
EISSN: 1572-9427
DOI: 10.1007/s11067-017-9343-4
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