Transportation Network Optimization Problems with Stochastic User Equilibrium Constraints

2004 ◽  
Vol 1882 (1) ◽  
pp. 113-119 ◽  
Author(s):  
Qiang Meng ◽  
Der-Horng Lee ◽  
Hai Yang ◽  
Hai-Jun Huang
Keyword(s):  
Network Optimization ◽  
Optimization Problems ◽  
Transportation Network ◽  
User Equilibrium ◽  
Equilibrium Constraints ◽  
Stochastic User Equilibrium

scholarly journals Bounding the Inefficiency of the Multiclass, Multicriteria C-Logit Stochastic User Equilibrium in a Transportation Network

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Lekai Yuan ◽  
Xi Zhang ◽  
Chaofeng Shi
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Stochastic System ◽  
Traffic Congestion ◽  
Transportation Network ◽  
User Equilibrium ◽  
Upper Bounds ◽  
Choice Probability ◽  
Stochastic User Equilibrium ◽  
System Optimum

We derive the exact inefficiency upper bounds of the multiclass C-Logit stochastic user equilibrium (CL-SUE) in a transportation network. All travelers are classified on the basis of different values of time (VOT) into M classes. The multiclass CL-SUE model gives a more realistic path choice probability in comparison with the logit-based stochastic user equilibrium model by considering the overlapping effects between paths. To find efficiency loss upper bounds of the multiclass CL-SUE, two equivalent variational inequalities for the multiclass CL-SUE model, i.e., time-based variational inequality (VI) and monetary-based VI, are formulated. We give four different methods to define the inefficiency of the multiclass CL-SUE, i.e., to compare multiclass CL-SUE with multiclass system optimum, or to compare multiclass CL-SUE with multiclass C-Logit stochastic system optimum (CL-SSO), under the time-based criterion and the monetary-based criterion, respectively. We further investigate the effects of various parameters which include the degree of path overlapping (the commonality factor), the network complexity, degree of traffic congestion, the VOT of user classes, the network familiarity, and the total demand on the inefficiency bounds.

scholarly journals Stochastic Electric Vehicle Network with Elastic Demand and Environmental Costs

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Jie Ma ◽  
Hua Wang ◽  
Tianpei Tang
Keyword(s):  
Large Scale ◽  
Transportation Network ◽  
Urban Transportation ◽  
User Equilibrium ◽  
Environmental Costs ◽  
Elastic Demand ◽  
Stochastic User Equilibrium ◽  
Travel Costs ◽  
Large Scale Network ◽  
Scale Network

Along with the increasing number of the electric vehicles (EVs), an urban transportation network with a large number of EVs will come true in the near future. Since many countries encourage EVs due to their environmental-friendly benefits, the environmental costs of vehicles have attracted much attention in recent years. In this paper, besides the environmental costs, we take into account the issues of the stochastic user equilibrium (SUE), the elastic demand (ED), and the driving range of EVs in the network. We propose an SUE with ED (SUEED) problem to consider these issues in the urban transportation network with EVs. An SUEED model is developed. We also propose a method of successive average (MSA) to solve the SUEED problem. The computational feasibility of the algorithm is tested in a large-scale network. Through a comparison analysis, we show the benefits of introducing EVs into the urban transportation network in the SUEED circumstance. Moreover, a sensitivity analysis is conducted to reveal the potential values of EVs against the development of EVs. The results suggest that EVs may help to reduce both the travelers’ travel costs and the environmental costs of the entire network.

A Generalized Single-Level Formulation for Origin–Destination Estimation under Stochastic User Equilibrium

2018 ◽  
Vol 2672 (48) ◽  
pp. 58-68 ◽  
Author(s):  
Wei Ma ◽  
Zhen (Sean) Qian
Keyword(s):  
Large Scale ◽  
User Equilibrium ◽  
Estimation Methods ◽  
Optimization Approach ◽  
Large Network ◽  
Equilibrium Constraints ◽  
Stochastic User Equilibrium ◽  
Single Level ◽  
Solution Algorithms ◽  
Large Scale Networks

Origin–destination (OD) demand is an indispensable component for modeling transportation networks, and the prevailing approach to estimating OD demand using traffic data is through bi-level optimization. A bi-level optimization approach considering equilibrium constraints is computationally challenging for large-scale networks, which prevents the OD estimation (ODE) being scalable. To solve for ODE in large-scale networks, this paper develops a generalized single-level formulation for ODE incorporating stochastic user equilibrium (SUE) constraints. Two single-level ODE models are specifically discussed and tested. One employs a SUE based on the satisfaction function, and the other is based on the Logit model. Analytical properties of the new formulation are analyzed. The estimation methods are proven to be unbiased. Gradient-based algorithms are proposed to solve for this formulation. Numerical experiments are conducted on a small network and a large network, along with sensitivity analysis on sensor locations, historical OD information and measurement error. Results indicate that the new single-level formulation, in conjunction with the proposed solution algorithms, can achieve accuracy comparable with the bi-level formulation, while being much more computationally efficient for large networks.

Stochastic user equilibrium with combined mode in a degradable multi-modal transportation network

2012 ◽  
Vol 7 (12) ◽  
Author(s):  
Meng Meng ◽  
Chun-fu Shao ◽  
Cheng-xiang Zhuge ◽  
Jing-jing Zeng ◽  
Chun-jiao Dong
Keyword(s):  
Transportation Network ◽  
User Equilibrium ◽  
Stochastic User Equilibrium ◽  
Combined Mode

scholarly journals Stochastic Transportation Network Considering ATIS with the Information of Environmental Cost

2018 ◽  
Vol 10 (11) ◽  
pp. 3861 ◽  
Author(s):  
Qiang Tu ◽  
Lin Cheng ◽  
Dawei Li ◽  
Jie Ma ◽  
Chao Sun
Keyword(s):  
Motor Vehicle ◽  
Transportation Network ◽  
User Equilibrium ◽  
Environmental Cost ◽  
Stochastic User Equilibrium ◽  
Environment Friendly ◽  
Traveler Information ◽  
Environment Problem ◽  
Transportation Research ◽  
The Impact

The environment problem is a sustainable hot topic in the field of transportation research. With higher awareness of the environment problem, travelers tend to choose more environment friendly traffic modes and travel routes. However, for motor vehicle drivers, the environmental cost is an implicit cost, which is not easily perceived. With the help of the advanced traveler information system (ATIS), a fresh scheme was proposed to reduce the environmental cost of the transportation network, which incorporates the information of environmental cost into ATIS to guide drivers to choose more environment-friendly routes. To test the validity of the scheme, we adopted the theory of stochastic network user equilibrium to assign two classes of drivers on the transportation network and analyzed the impact on environmental cost after applying this scheme. Mathematically, a mixed stochastic user equilibrium (SUE) model was proposed to analyze this scheme. The corresponding algorithm was also proposed. Both the model and algorithm were tested in the numerical examples. Through the examples, the validity and feasibility of our proposed scheme were also identified. Our research provided some new ideas for traffic planners and managers to reduce environmental costs caused by traffic.

scholarly journals Traffic Paradox Under Different Equilibrium Conditions Considering Elastic Demand

2019 ◽  
Vol 31 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Qiang Tu ◽  
Lin Cheng ◽  
Dawei Li ◽  
Jie Ma ◽  
Chao Sun
Keyword(s):  
Traffic Management ◽  
Network Performance ◽  
Transportation Network ◽  
Travel Cost ◽  
User Equilibrium ◽  
Stochastic User Equilibrium ◽  
Equilibrium Conditions ◽  
Traffic Demand ◽  
Travel Costs ◽  
Cost Sensitivity

Traffic paradox is an important phenomenon which needs attention in transportation network design and traffic management. Previous studies on traffic paradox always examined user equilibrium (UE) or stochastic user equilibrium (SUE) conditions with a fixed traffic demand (FD) and set the travel costs of links as constants under the SUE condition. However, traffic demand is elastic, especially when there are new links added to the network that may induce new traffic demand, and the travel costs of links actually depend on the traffic flows on them. This paper comprehensively investigates the traffic paradox under different equilibrium conditions including the user equilibrium and the stochastic user equilibrium with a fixed and elastic traffic demand. Origin-destination (OD) mean unit travel cost (MUTC) has been chosen as the main index to characterize whether the traffic paradox occurs. The impacts of travelers’ perception errors and travel cost sensitivity on the occurrence of the traffic paradox are also analyzed. The conclusions show that the occurrence of the traffic paradox depends on the traffic demand and equilibrium conditions; higher perception errors of travelers may lead to a better network performance, and a higher travel cost sensitivity will create a reversed traffic paradox. Finally, several appropriate traffic management measures are proposed to avoid the traffic paradox and improve the network performance.

scholarly journals Stochastic Congestion Pricing among Multiple Regions: Competition and Cooperation

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Hua Wang ◽  
Wei Mao ◽  
Hu Shao
Keyword(s):  
Social Welfare ◽  
Travel Time ◽  
Demand Uncertainty ◽  
Transportation Network ◽  
Congestion Pricing ◽  
User Equilibrium ◽  
Travel Time Reliability ◽  
Stochastic User Equilibrium ◽  
Multiple Regions ◽  
The Impact

Previous studies of road congestion pricing problem assume that transportation networks are managed by a central administrative authority with an objective of improving the performance of the whole network. In practice, a transportation network may be comprised of multiple independent local regions with relative independent objectives. In this paper, we investigate the cooperative and competitive behaviors among multiple regions in congestion pricing considering stochastic conditions; especially demand uncertainty is taken into account in transportation modelling. The corresponding congestion pricing models are formulated as a bilevel programming problem. In the upper level, congestion pricing model either aims to maximize the regional social welfare in competitive schemes or attempts to maximize the total social welfare of multiple regions in cooperative schemes. In the lower level, travellers are assumed to follow a reliability-based stochastic user equilibrium principle considering risks of late arrival under uncertain conditions. Numerical examples are carried out to compare the effects of different pricing schemes and to analyze the impact of travel time reliability. It is found that cooperative pricing strategy performs better than competitive strategy in improving network performance, and the pricing effects of both schemes are quite sensitive to travel time reliability.

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