Stochastic social optimum traffic assignment

European Journal of Operational Research

2010

Abstract. Bounding the inefficiency of selfish routing has become an emerging research subject. A central result obtained in the literature is that the inefficiency of deterministic User Equilibrium (UE) is bounded and the bound is independent of network topology. This paper makes a contribution to the literature by bounding the inefficiency of the logit-based Stochastic User Equilibrium (SUE). In a stochastic environment there are two different definitions of system optimization: one is the traditional System Optimum (SO) which minimizes the total actual system travel time, and the other is the Stochastic System Optimum (SSO) which minimizes the total perceived travel time of all users. Thus there are two ways to define the inefficiency of SUE, i.e. to compare SUE with SO in terms of total actual system travel time, or to compare SUE with SSO in terms of total perceived travel time.We establish upper bounds on the inefficiency of SUE in both situations.

Section: Bounding the Inefficiency Of Logit-based Stochastic User Equmentioning

confidence: 99%

“…For the logit-based stochastic traffic assignment model, the total perceived travel time of all users can be given in a closed-form expression as (Maher et al 2005)…”

Section: Bounding the Inefficiency Of Sue Compared With Ssomentioning

confidence: 99%

Bounding the inefficiency of logit-based stochastic user equilibrium

Guo

Yang

European Journal of Operational Research

2010

“…The validity of marginal cost pricing for general transportation networks has been proven by many studies under different assumptions, for example, with elastic demand (Huang and Yang, 1996), with logit-based SUE constraints (Yang and Huang, 1998), with general SUE constraints (Maher et al, 2005), and with stochastic demand (Sumalee and Xu, 2011), to name a few. The optimal marginal cost pricing scheme can easily be obtained by solving a traffic assignment problem.…”

Section: Relevant Studiesmentioning

confidence: 99%

Speed-based toll design for cordon-based congestion pricing scheme

Transportation Research Part C: Emerging Technologies

Meng

Wang

2013

113

The cordon-based Electronic Road Pricing (ERP) system in Singapore adopts the average travel speed as an index for evaluating the traffic congestion within a cordon area, and the maintenance of the average travel speed within a satisfactory range is taken as the objective of the toll adjustment. To formulate this practical speed-based toll design problem, this paper proposes a mathematical programming with equilibrium constraint (MPEC) model with the objective of maintaining the traffic condition in the cordon area. In the model, the network users' route choice behavior is assumed to follow probit-based stochastic user equilibrium with elastic demand, asymmetric link travel time functions and continuous value-of-time. A distributed revised genetic algorithm is designed for solving the MPEC model. Finally, a network example based on the ERP system is adopted to numerically validate the proposed models and algorithms, and further indicates that the computation speed can be improved greatly by using a distributed computing system. indicates that the computation speed can be improved greatly by using a distributed computing system.

“…In this paper, we will first proposes a linearly constrained minimization model in terms of path flows, inspired by Maher et al (2005), for the generalized SUE conditions. We will next rigorously show that the model possesses three important the properties: (i) any local minimum is a SUE path flow pattern with link capacity constraints; (ii) the optimal Lagrangian multipliers associated with the link capacity constraints are the SUE link queuing delays; (iii) a SUE link flow pattern with link capacity is unique.…”

Section: Q Meng Whk Lam L Yang 430mentioning

confidence: 99%

“…Remark 2. Maher et al (2005) have derived the analytical expressions of the path-specific delay functions,…”

Section: A Linearly Constrained Minimization Modelmentioning

confidence: 99%

General stochastic user equilibrium traffic assignment problem with link capacity constraints

Meng

Lam

J of Advced Transportation

2008

This paper addresses a general stochastic user equilibrium (SUE) traffic assignment problem with link capacity constraints. It first proposes a novel linearly constrained minimization model in terms of path flows and then shows that any of its local minimums satisfies the generalized SUE conditions. As the objective function of the proposed model involves path-specific delay functions without explicit mathematical expressions, its Lagrangian dual formulation is analyzed. On the basis of the Lagrangian dual model, a convergent Lagrangian dual method with a predetermined step size sequence is developed. This solution method merely invokes a subroutine at each iteration to perform a conventional SUE traffic assignment excluding link capacity constraints. Finally, two numerical examples are used to illustrate the proposed model and solution method.