01127155

Component

Macroscopic models are used to describe traffic flow. In a simulation the model equations are discretized in both space and time. Time discretization, despite its importance to numerical stability and accuracy, has not received much attention. Most current implementations apply explicit time integration methods, which need to obey to strict stability conditions. These may result in large computing times and prevent the implementation of macroscopic traffic flow models to applications where computational efficiency is crucial, such as real time applications. The authors describe and study implicit time integration methods which have less strict stability conditions, can be used with larger time steps and reduce the computing time. Furthermore, we study the accuracy of the numerical methods. The widely used root mean square error does not take into account the nature of the error. We propose two accuracy measures which take into account errors that are important to applications in traffic flow. The phase error measures a shift of the solution over time. Numerical diffusion indicates that the solution is too 'smooth'. The authors compare explicit and implicit schemes with simple test problems for computing time and accuracy. The authors found that implicit schemes, in these cases, result in 9 to 15 times smaller computing times. However, the accuracy and the nature of the error depends on the time integration method, but can be kept at an acceptable level for computationally efficient schemes. This shows that implicit time integration methods can play a key role in applications where small computing times are crucial.

01120148

09-0350

English

15p

2009

Transportation Research Board 88th Annual Meeting

DVD

Figures (7) ; References (17) ; Tables (1)

Accuracy; Integrated systems; Macroscopic traffic flow; Numerical analysis; Operations; Real time information; Traffic flow; Traffic models; Traffic simulation

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

Transportation Research Board Annual Meeting 2009 Paper #09-0350

TRIS, TRB

Jan 30 2009 4:37PM