Inefficiency of Stackelberg Stochastic Traffic Network with Tax Scheme

2013 ◽  
Vol 779-780 ◽  
pp. 1044-1051
Author(s):  
Ming Hua Zeng ◽  
Xi Yan Huang ◽  
Ni Dong ◽  
Xiao Guang Yang
Keyword(s):  
Variational Inequality ◽  
Flow Pattern ◽  
User Equilibrium ◽  
Upper Bounds ◽  
Time Function ◽  
Network Equilibrium ◽  
Traffic Network ◽  
Equilibrium Flow ◽  
Stochastic User Equilibrium ◽  
Stackelberg Strategy

Inefficiency upper bounds are explored in stochastic traffic network. Equilibrium flow pattern therein is deduced by a central Stackelberg strategy and tax schemes imposed on each link.. The equivalent variational inequality (VI) for Logit-based stochastic user equilibrium (SUE) model is established and first used to obtain upper bounds on Stackelberg network inefficiency under the assumption of separable, nondecreasing, and convex link time function and of fixed network origin-destination (OD) demand. For typical Bureau of Public Roads (BPR) functions and its affine forms, the upper bounds of their inefficiency are investigated with some meaningful results.

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.

Congestion, Stochastic, and Similarity Effects in Stochastic: User-Equilibrium Models

2000 ◽  
Vol 1733 (1) ◽  
pp. 80-87 ◽  
Author(s):  
Joseph N. Prashker ◽  
Shlomo Bekhor
Keyword(s):  
Flow Pattern ◽  
User Equilibrium ◽  
Physical Parameters ◽  
Stochastic User Equilibrium ◽  
Similarity Coefficients ◽  
Starting Point ◽  
Congestion Effect ◽  
Stochastic Assignment ◽  
Similarity Effect ◽  
Assignment Models

Different effects in stochastic user-equilibrium formulations are compared. The starting point is the logit assignment formulation for the stochastic user-equilibrium model. Recently, extended logit-based models were developed as solutions of equivalent stochastic user-equilibrium problems. These extended logit models are theoretically superior to the simple logit model, because they take into account the similarity among routes. The similarity indexes were defined based on physical parameters of the network, such as link lengths, and therefore did not depend on congestion. The assumption that similarity coefficients are independent of congestion means that the similarity effect and the congestion effect are treated separately. However, both similarity and congestion effects are taken into account in the equilibrium formulations. Simple network examples are presented to illustrate the sensitivity of the link flow pattern (and path flow pattern) to the three different effects in stochastic assignment models: the congestion effect, the stochastic effect, and the similarity effect. The relative influence of those effects on the flow patterns is discussed.

Action of Traffic Measures on Supply Chain Network Equilibrium

2014 ◽  
Vol 641-642 ◽  
pp. 866-870
Author(s):  
Wei Cao ◽  
Xi Zhang ◽  
Shou Wen Ji
Keyword(s):  
Supply Chain ◽  
Variational Inequality ◽  
Iterative Algorithm ◽  
Freight Transport ◽  
Network Equilibrium ◽  
Traffic Network ◽  
Supply Chain Network ◽  
Link Capacity ◽  
Numerical Example

The decision of freight transport are typically made for SCNE(Supply Chain Network Equilibrium),and its behavior is known to be influenced by regional conditions of traffic network,but little is known about role of traffic measures which have efficiency on SCNE.Unlike other studies in the extent literature,we aimed to cover the interaction between traffic measures and SCNE. We formulated variational inequality in terms of strategies and strategic flows as SCNE conditions.We employed an iterative algorithm of MSA to this variational inequality by solving a dynamic program.A numerical example proves the validity of our model and algorithm,and we show that our algorithm has faster convergence ability than existing algorithms.Moreover,results show that the amount of products and surpluses of SCN increase as traffic link capacity increases.We conclude that improvement of traffic network could enhance the efficiency of SCN.

scholarly journals Traffic Network Equilibrium Problems with Capacity Constraints of Arcs and Linear Scalarization Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
X. Q. Tian ◽  
Y. D. Xu
Keyword(s):  
Equilibrium Problems ◽  
Sufficient Conditions ◽  
Capacity Constraints ◽  
Network Equilibrium ◽  
Traffic Network ◽  
Equilibrium Flow ◽  
Traffic Network Equilibrium ◽  
Vector Equilibrium ◽  
Network Equilibrium Problems ◽  
Weak Vector

Traffic network equilibrium problems with capacity constraints of arcs are studied. A (weak) vector equilibrium principle with vector-valued cost functions, which are different from the ones in the work of Lin (2010), and three kinds of parametric equilibrium flows are introduced. Some necessary and sufficient conditions for a (weak) vector equilibrium flow to be a parametric equilibrium flow are derived. Relationships between a parametric equilibrium flow and a solution of a scalar variational inequality problem are also discussed. Some examples are given to illustrate our results.

scholarly journals Dynamic Traffic Network Model and Time-Dependent Braess’ Paradox

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Chunxue Zhao
Keyword(s):  
Variational Inequality ◽  
Dynamic System ◽  
Network Model ◽  
Equilibrium Condition ◽  
Dynamic Change ◽  
User Equilibrium ◽  
Traffic Network ◽  
Dynamic Traffic ◽  
Braess Paradox ◽  
System Optimal

We propose a dynamic traffic network model and give the equilibrium condition and the equivalent variational inequality of the network. In this model, instead of the influence of inflow rate and output rate on the link congestion, the influence of the adjacent links at the same paths is considered; in this case, the equivalence between the equilibrium condition and the variational inequality is proved. Then we take an example about the paradox using the variational inequality and find that the probability and the severity that Braess’ paradox occurs change with the influence of other links changing. Subsequently, we discuss the influence of other links on whether the adding link works under the dynamic system optimal. At last, we give the relationship between the total congestion under dynamic user equilibrium and that under dynamic system optimal. The results imply that we should take some methods and adjust the interaction between links rationally with the dynamic change of traffic situations.

scholarly journals Inefficiency of Logit-Based Stochastic User Equilibrium in a Traffic Network Under ATIS

2009 ◽  
Vol 11 (2) ◽  
pp. 255-269 ◽  
Author(s):  
Hai-Jun Huang ◽  
Tian-Liang Liu ◽  
Xiaolei Guo ◽  
Hai Yang
Keyword(s):  
User Equilibrium ◽  
Traffic Network ◽  
Stochastic User Equilibrium
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