User Equilibrium Analysis Considering Travelers’ Context-Dependent Route Choice Behavior on the Risky Traffic Network
Abstract
:1. Introduction
- We study travelers’ context-dependent route choice behavior in a risky traffic network. Particularly, we extend the salience theory to propose a flow-dependent salience theory for this study, where the flow denotes the traffic flows on the risky route. Three significant properties of the flow-dependent salience theory are ordering, diminishing sensitivity, and symmetry.
- Following the convention in [35], we propose a salient travel utility model with a discrete salience ranking, and further propose the salient user equilibrium based on this model. An analysis procedure is proposed to prove the existence and uniqueness of the salient user equilibrium, which consists of two parts, the flow-dependent salience ranking analysis and flow-dependent route preference analysis. The sufficient conditions for the existence and uniqueness of the salient user equilibrium are identified based on this analysis procedure.
- Finally, numerical studies demonstrate our theoretical findings. The equilibrium results show non-intuitive insights into travelers’ route choice behavior. (a) Travelers can be risk-seeking (the travel utility of a risky route is small with a relatively high probability), risk-neutral (in special situations), or risk-averse (the travel utility of a risky route is large with a relatively high probability), which depends on the salient state. (b) The extent of travelers’ risk-seeking or risk-averse behavior depends on their extent of salience bias, while the risk-neutral behavior is irrelative to this salience bias. Our findings here can provide some new evidence about travelers’ risk attitudes to a risky traffic network (e.g., [7,11]).
2. Development of a General Salient Travel Utility Model
2.1. Review of Original Salience Theory
- Ordering. If for states, , we have thatis a subset of. Then:
- Diminishing sensitivity. Iffor, then for any:
- Reflection. For any two states, , such that. For, we have:
2.2. Salient Travel Utility Model
- Ordering. If for states, , we have thatis a subset of, then:
- Diminishing sensitivity. If, , then for any:
3. User Equilibrium Analysis with Salient Travel Utility Model
3.1. Definitions and Notations
3.2. Trivial Equilibrium Analysis
- The case where or :
- (1)
- . In this case, one corner equilibrium solution can be obtained by solving —i.e., ;
- (2)
- . In this case, one equilibrium solution can be obtained by solving —i.e., .
- 2.
- The case where :
- (1)
- When , the salient travelers become the rational travelers as discussed before, and they make the route choice decision based on the expected utility theory. In this case, one equilibrium solution, termed the expected flow, can be obtained by solving:
- (2)
- When , we analyze the salient user equilibrium based on the salient travel utility model, which will be studied in the next section.
3.3. Salient User Equilibrium Analysis
3.3.1. Salience Ranking Analysis
- (1)
- Examination of monotonicity
- (2)
- Examination of salience ranking for special points
- When , we have that , , and . Furthermore, and . By ordering the property, we obtain .
- When , we have , and . By ordering the property, we obtain .
- When , we have , , and . Furthermore, and . By ordering the property, we obtain .
- (3)
- Examination of salience equivalence:
- Considering the interval , let , and we obtain:
- 2.
- Considering the interval , let , and we obtain:
3.3.2. Equilibrium Analysis
- (1)
- When , we obtain —i.e., the salient travelers prefer the risky route to the non-risky route. Therefore, is not a salient user equilibrium.
- (2)
- Considering the interval , we have when . Besides this,. Therefore, we obtain —i.e., the salient travelers prefer the risky route to the non-risky route, and thus there is no salient user equilibrium in the considered interval. □
4. More Discussions on the Salient User Equilibrium
4.1. Diminishing Sensitivity
4.2. Relationship between and
5. Numerical Experiments
6. Conclusions and Future Directions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
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Xu, Q.; Ji, X. User Equilibrium Analysis Considering Travelers’ Context-Dependent Route Choice Behavior on the Risky Traffic Network. Sustainability 2020, 12, 6706. https://doi.org/10.3390/su12176706
Xu Q, Ji X. User Equilibrium Analysis Considering Travelers’ Context-Dependent Route Choice Behavior on the Risky Traffic Network. Sustainability. 2020; 12(17):6706. https://doi.org/10.3390/su12176706
Chicago/Turabian StyleXu, Qinghui, and Xiangfeng Ji. 2020. "User Equilibrium Analysis Considering Travelers’ Context-Dependent Route Choice Behavior on the Risky Traffic Network" Sustainability 12, no. 17: 6706. https://doi.org/10.3390/su12176706