01099530

Component

https://doi.org/10.3141/2085-02

http://scholar.google.com...zbay&publication_year=2008

Stochastic optimization has become one of the important modeling approaches in transportation network analysis. For example, for traffic assignment problems based on stochastic simulation, it is necessary to use a mathematical algorithm that iteratively seeks out the optimal, the suboptimal solution, or both, because an analytical (closed-form) objective function is not available. Therefore, efficient stochastic approximation algorithms that can find optimal or suboptimal solutions to these problems are needed. The method of successive averages (MSA), a well-known algorithm, is used to solve both deterministic and stochastic equilibrium assignment problems. As found in previous studies, the MSA has questionable convergence characteristics, especially when the number of iterations is not sufficiently large. In fact, the stochastic approximation algorithm is of little practical use if the number of iterations to reduce the errors to within reasonable bounds is arbitrarily large. An efficient method to solve stochastic approximation problems is the simultaneous perturbation stochastic approximation (SPSA), which can be a viable alternative to the MSA because of its proven power to converge to suboptimal solutions in the presence of stochasticities and its ease of implementation. The performance of MSA and SPSA algorithms is compared for solving traffic assignment problems with varying levels of stochasticities on a small network. The utmost importance is given to comparison of the convergence characteristics of the two algorithms as well as to the computational times. A worst-case scenario is also studied to check the efficiency and practicality of both algorithms in terms of computational times and accuracy of results.

01120896

English

pp 12-20

2008

Transportation Research Record: Journal of the Transportation Research Board

9780309125963

Print

Figures (2) ; References (51) ; Tables (4)

Accuracy; Algorithms; Approximation (Mathematics); Mathematical analysis; Network analysis (Planning); Perturbations; Stochastic processes; Traffic assignment

Computational time; Method of successive averages; Transportation networks

Highways; Planning and Forecasting; I72: Traffic and Transport Planning

TRIS, TRB

Jan 29 2008 4:32PM

• Adaptive Route Choice Models in Stochastic Time-Dependent Networks
• Dynamic Network Loading Model with Explicit Traffic Wave Tracking
• Dynamic Origin–Destination Demand Estimation Using Turning Movement Counts
• Effectiveness of Origin–Destination Matrix Correction Procedure Using Traffic Counts
• Enhanced Lagged Cell-Transmission Model for Dynamic Traffic Assignment
• Generalized Wardrop Principle and Its Application in Regional Transportation
• Incorporating Within-Day Transitions in Simultaneous Offline Estimation of Dynamic Origin–Destination Flows Without Assignment Matrices
• Lower-Bound Solution Algorithm for Equilibrium Signal-Setting Problem
• Measurement of Uncertainty Costs with Dynamic Traffic Simulations
• Modeling User Responses to Pricing: Simultaneous Route and Departure Time Network Equilibrium with Heterogeneous Users
• Probit-Based Time-Dependent Stochastic User Equilibrium Traffic Assignment Model
• Robust Pricing of Transportation Networks Under Uncertain Demand
• Stochastic Multiclass Traffic Assignment with Consideration of Risk-Taking Behaviors
• Stochastic User Equilibrium Model with Implicit Travel Time Budget Constraint