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ANALYSIS OF CELL TRANSMISSION MODEL FOR TRAFFIC FLOW SIMULATION WITH APPLICATION TO NETWORK TRAFFIC

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Hyperbolic equations and systems

Published online by Cambridge University Press:  18 May 2021

A. S. MAULANA Open the ORCID record for A. S. MAULANA [Opens in a new window]  and
S. R. PUDJAPRASETYA Open the ORCID record for S. R. PUDJAPRASETYA [Opens in a new window]
A. S. MAULANA*
Affiliation:
Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung40132, Indonesia; [email protected]
S. R. PUDJAPRASETYA
Affiliation:
Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung40132, Indonesia; [email protected]
*
Email: [email protected]
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Abstract

The cell transmission model (CTM) is a macroscopic model that describes the dynamics of traffic flow over time and space. The effectiveness and accuracy of the CTM are discussed in this paper. First, the CTM formula is recognized as a finite-volume discretization of the kinematic traffic model with a trapezoidal flux function. To validate the constructed scheme, the simulation of shock waves and rarefaction waves as two important elements of traffic dynamics was performed. Adaptation of the CTM for intersecting and splitting cells is discussed. Its implementation on the road segment with traffic influx produces results that are consistent with the analytical solution of the kinematic model. Furthermore, a simulation on a simple road network shows the back and forth propagation of shock waves and rarefaction waves. Our numerical result agrees well with the existing result of Godunov’s finite-volume scheme. In addition, from this accurately proven scheme, we can extract information for the average travel time on a certain route, which is the most important information a traveller needs. It appears from simulations of different scenarios that, depending on the circumstances, a longer route may have a shorter travel time. Finally, there is a discussion on the possible application for traffic management in Indonesia during the Eid al-Fitr exodus.

Keywords

cell transmission modelkinematic wave modelmethod of characteristicsjunction

MSC classification

Primary: 35L67: Shocks and singularities
Secondary: 65M06: Finite difference methods
Type
Research Article
Information
The ANZIAM Journal , Volume 63 , Issue 1 , January 2021 , pp. 84 - 99
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Copyright
© Australian Mathematical Society 2021

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