Sensitivity Analysis for Equilibrium Network Flow

Tobin, Roger L.; Friesz, Terry L.

doi:10.1287/trsc.22.4.242

Cited by 300 publications

(151 citation statements)

References 16 publications

Supporting

Mentioning

141

Contrasting

Unclassified

Order By: Relevance

“…Generally, the solution of a bilevel programming model is also referred to as a Stackelberg equilibrium solution. To address the problem in which partial derivatives cannot be obtained directly from the implicit functional relationship between the decision variables of the upper and lower levels, Tobin [2] and Tobin and Friesz [3] proposed sensitivity analysis methods to derive the descent direction of the objective function in the upper level and obtain the local optimum solution of the model. We also adopted this approach to solve the model in this study.…”

Section: Sensitivity Analysis and Generalized Inverse Matrix Methodsmentioning

confidence: 99%

See 1 more Smart Citation

A Network Signal Timing Design Bilevel Optimization Model with Traveler Trip-Chain Route Choice Behavior Consideration

Wang¹,

Yen²,

Hu³

et al. 2017

JTTE

View full text Add to dashboard Cite

This study proposed a bilevel optimization model for the network signal timing design problem by considering the link flows reflected by the trip-chain route choice behaviors of road users. The bilevel programming model is formulated based on the interactions between signal timing control and trip-chain behavior, and a solution algorithm by combining variational inequality sensitivity analysis, the generalized inverse matrix method, and a gradient projection approach revised for trip-chain user equilibrium is developed for the transportation design problem. The performance of the developed model framework was verified through numerical analysis under different test scenarios.

show abstract

Section: Sensitivity Analysis and Generalized Inverse Matrix Methodsmentioning

confidence: 99%

“…In order to take the trip chain behavior of road users into account, we integrated the variational inequality sensitivity analysis approaches proposed by Tobin [2] and Tobin and Friesz [3] …”

Section: Introductionmentioning

confidence: 99%

A Network Signal Timing Design Bilevel Optimization Model with Traveler Trip-Chain Route Choice Behavior Consideration

Wang¹,

Yen²,

Hu³

et al. 2017

JTTE

View full text Add to dashboard Cite

show abstract

“…An alternative approximation can be made using the sensitivity analysis suggested by Tobin and Friesz (1988), which gives the following analytical expression for the Jacobian:…”

Section: Alternative Approximations Of the Jacobianmentioning

confidence: 99%

“…Information from the lower level problem is transferred by so called influence factors, which can be defined by path proportions or explicit derivatives. The derivatives are computed based on the sensitivity analysis by Tobin and Friesz (1988). Assuming complementary conditions to hold and disregarding any topological dependencies, they get approximate values of the derivatives, which are acceptable for small to medium sized networks.…”

mentioning

confidence: 99%

A heuristic for the bilevel origin–destination-matrix estimation problem

Lundgren

Peterson

2008

Transportation Research Part B: Methodological

View full text Add to dashboard Cite

In this paper we consider the estimation of an origin-destination (OD) matrix, given a target OD-matrix and traffic counts on a subset of the links in the network. We use a general nonlinear bilevel minimization formulation of the problem, where the lower level problem is to assign a given OD-matrix onto the network according to the user equilibrium principle. After reformulating the problem to a single level problem, the objective function includes implicitly given link flow variables, corresponding to the given OD-matrix. We propose a descent heuristic to solve the problem, which is an adaptation of the wellknown projected gradient method. In order to compute a search direction we have to approximate the Jacobian matrix representing the derivatives of the link flows with respect to a change in the OD-flows, and we propose to do this by solving a set of quadratic programs with linear constraints only. If the objective function is differentiable at the current point, the Jacobian is exact and we obtain a gradient. Numerical experiments are presented which indicate that the solution approach can be applied in practice to medium to large size networks.

show abstract

“…(1980) mentioned above, though the algorithm is developed for solving the more general problem. The second algorithm involves calculating the gradient using a sensitivity analysis method (Tobin and Friesz, 1988) to obtain the partial derivatives of UE link flows with respect to O-D flows. It has been shown ) that, at least in a two-link network, the first algorithm converges to the mutually consistent solution while the second algorithm to the bi-level solution.…”

Section: Previous Solution Algorithms For the Combined Problemmentioning

confidence: 99%

A bi-level programming approach for trip matrix estimation and traffic control problems with stochastic user equilibrium link flows

Maher

Zhang

Vliet

2001

Transportation Research Part B: Methodological

116

View full text Add to dashboard Cite

Article:Maher, M.J., Zhang, X. and van Vliet, D. (2001) Abstract ⎯ This paper deals with two mathematically similar problems in transport network analysis: trip matrix estimation and traffic signal optimisation on congested road networks.These two problems are formulated as bi-level programming problems with stochastic user equilibrium assignment as the second-level programming problem. We differentiate two types of solutions in the combined matrix estimation and stochastic user equilibrium assignment problem (or, the combined signal optimisation and stochastic user equilibrium assignment problem): one is the solution to the bi-level programming problem and the other the mutually consistent solution where the two sub-problems in the combined problem are solved simultaneously. In this paper, we shall concentrate on the bi-level programming approach although we shall also consider mutually consistent solutions so as to contrast the two types of solutions. The purpose of the paper is to present a solution algorithm for the two bi-level programming problems and to test the algorithm on several networks.

show abstract

Sensitivity Analysis for Equilibrium Network Flow

Cited by 300 publications

References 16 publications

A Network Signal Timing Design Bilevel Optimization Model with Traveler Trip-Chain Route Choice Behavior Consideration

A Network Signal Timing Design Bilevel Optimization Model with Traveler Trip-Chain Route Choice Behavior Consideration

A heuristic for the bilevel origin–destination-matrix estimation problem

A bi-level programming approach for trip matrix estimation and traffic control problems with stochastic user equilibrium link flows

Contact Info

Product

Resources

About