Boundedly Rational User Equilibria (BRUE): Mathematical Formulation and Solution Sets

By Xuan Di, Henry X. Liu, Jong-Shi Pang, Xuegang Ban. 2013

111 citations recorded by the source corpus.

Abstract Boundedly rational user equilibria (BRUE) represent traffic flow distribution patterns where travellers can take any route whose travel cost is within an ‘indifference band’ of the shortest path cost. Those traffic flow patterns satisfying the above condition constitute a set, named the BRUE solution set. It is important to obtain all the BRUE flow patterns, because it can help predict the variation of the link flow pattern in a traffic network under the boundedly rational behavior assumption. However, the methodology of constructing the BRUE set has been lacking in the established literature. This paper fills the gap by constructing the BRUE solution set on traffic networks with fixed demands connecting multiple OD pairs. According to the definition of the ɛ-BRUE, where ɛ is the indifference band for the perceived travel cost, we formulate the ɛ-BRUE problem as a nonlinear complementarity problem (NCP), so that a BRUE solution can be obtained by solving a BRUE-NCP formulation. To obtain the whole BRUE solution set encompassing all BRUE flow patterns, we firstly propose a methodology of generating various path combinations which may be utilized under the boundedly rational behavior assumption. We find out that with the increase of the indifference band, the path set that contains boundedly rational equilibrium flows will be augmented, and the critical values of indifference bands to augment these path sets can be identified by solving a family of mathematical programs with equilibrium constraints (MPEC) sequentially. After these utilized path sets are attained, the BRUE solution set can be obtained when we assign all traffic demands to these utilized paths. Various numerical examples are given to illustrate our findings.

Subfields: Automotive Engineering, Transportation

View Paper: https://www.semanticscholar.org/paper/819b89769b3003387aeea66b1c5ff3a4cf2c6144

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Automotive Engineering

1. Xuan Di
2. Henry X. Liu

In Transportation

1. Xuan Di
2. Henry X. Liu
3. Xuegang Ban

Citations in the corpus

• Boundedly rational route choice behavior: A review of models and methodologies (2016, methodology): “According to Di et al. (2013) , the BRUE set can be represented as: F ε BRUE = { f ∈ F : f 1 + f 2 + f 3 = 4 , f 1 , f 2 , f 3 0 , | f 1 − f 2 | ε 11 ; | 12 f 1 + f 2 − 4 | ε; | f 1 + 12 f 2 − 4 | ε} . f SUE (α) ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ f 1 = 4 e −α(C 1 ) e −α(C 1 ) + e −α(C 2 ) + e −α(C 3 ) , f 2 = 4…”
• Second best toll pricing within the framework of bounded rationality (2016, methodology): “This set has been proven to be non-convex (Di et al., 2013; Lou et al., 2010).”