Source code for javascript simulation of website
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Source code for javascript simulation of

Running the Simulation

This simulation uses JavaScript/html5.

The master html file, for example onramp.html, starts the actual simulation by the canvas tag:

<canvas id="canvas_onramp" width="800" height="600">some text for old browsers </canvas>

What to do with this canvas is specified in the init() procedure of onramp.js which starts the simulation and is assocoated with this canvas by the first command of the init procedure,

 canvas = document.getElementById("canvas_onramp");

(for ring.html, the init procedure of ring.js would be associated with the canvas of that file, and so on). At the end of the initialization, init() starts the actual simulation thread by the command

return setInterval(main_loop, 1000/fps);

In future versions, an additional control file canvasresize.js will implement a responsive design.

Programm Files and Structure

The javascript code uses pseudo objects in appropriately named files, particularly

<scenario>.js (ring.js, onramp.js etc)

the top-level simulation code for the corresponding scenario called in ring.html, onramp.html etc. Initializes the road network elements needed for the corresponding scenario (e.g. mainroad and onramp for the onramp scenario), starts/stops the simulation, controls the simulation updates in each time step depending on the scenario, draws everything, and implements the user controls defined in ring_gui.js, onramp_gui.js etc.

<scenario_gui>.js (ring_gui.js, etc.)

Defines the user control. Each simulation scenario (such as ring, onramp, roadworks) has both a top-level simulation javascript file <scenario>.js, and an associated gui <scenario>_gui.js (and of course an html file <scenario>.html).


represents a road network element (road link) and organizes the vehicles on it. Contains an array of vehicles and methods to get the neighboring vehicles for a given vehicle, to update all vehicles for one time step, to interact with/get information of neighboring road network elements.

It also provides methods to draw this network element and the vehicles on it. These drawing methods depend on the road geometry functions traj_x and traj_y to be provided by the calling pseudoclasses <scenario>.js


each vehicle has (i) properties such as length, width, type, (ii) dynamic variables such as position and speed, and (iii) instances of the acceleration/lane changing methods from models.js.


a collection of pseudo-classes for the longitudinal models (presently, the IDM), and lane-changing decision models (presently, MOBIL).


Helper-class providing some speed and type-dependent color maps to draw the vehicles.


external open library to implement sliders. Has some drawbacks (no docu of how to change sliders programmatically, initialize them to arbitrary values). In future versions, I plan to replace them with generic html5 sliders (range element).


callback (implementation) of the buttons for the different scenarios on the <scenario>.html simulation pages

Numerical Integration

The underlying car-following model for the longitudinal dynamics providing the accelerations (Intelligent-Driver Model, IDM, or extensions thereof) is time-continuous, so a numerical update scheme is necessary to get the speeds and positions of the vehicles as approximate integrals over the accelerations. For our purposes, it turned out that following ballistic scheme is most efficient in terms of computation load for a given precision. Its pseudo-code for an update of the speeds speed and positions pos over a fixed time interval dt reads



where acc(t) is the acceleration calculated by the car-following model at the (old) time t.

Lane-changing is modelled by the discrete model MOBIL, so no integration is needed there. In order to reuse the accelerations needed by MOBIL (Minimizing Obstructions By Intelligent Lane-changes") for calculating the lane-changing decisions, lane changing is performed after evaluating all accelerations. Furthermore, since MOBIL anticipates the future situation, the actual speed and positional update is performed after the lane changing. Hence the central update sequence performed for all road instances of the simulated network is given by


in the main simulation file of the given scenario (ring.js, onramp.js etc). The main method is either updateRing() (ring road), or updateU() (the other scenarios).

  • Notice that the update is in parallel, i.e., updating all accelerations on a given road, then all lanes, all speeds, and all positions sequentially (if there are interdependencies between the road elements of the network, this sequentiality should also be traversed over all road instances which, presently, is not done).

  • The central update step is prepended by updating the model parameters as a response to user interaction, if vehicles reach special zones such as the uphill region, or if they reach mandatory lane-changing regions before lane closing and offramps.

  • For closed links (ring road), the central update step is prepended by changing the vehicle population (overall density, truck percentage) as a response to user interaction.

  • For open links, the central method is appended by applying the boundary conditions roadInstance.updateBCdown and roadInstance.updateBCup for all non-closed network links. For further information on boundary conditions, see the info link Boundary Conditions at

  • The implementation of the actual models is given in models.js. Presently (as of November 2016), an extension of the Intelligent-Driver Model ("ACC model") is used as acceleration model, and MOBIL as the lane-changing model. We use the ACC model rather than the "original" IDM since the former is less sensitive to too low gaps which makes lane changing easier. For the same reason, we have modified MOBIL somewhat by making its bSafe parameter depending on the speed. Thus, we make lane changes more aggressive in congested situations. For further information, see the scientific references below, or the info links below the heading Traffic Flow Models at


The drawing is essentially based on images:

  • The background is just a jpeg image.

  • Each road network element is composed of typically 50-100 small road segments. Each road segment (a small png file) represents typically 10m-20m of the road length with all the lanes. By transforming this image (translation, rotation,scaling) and drawing it multiple times, realistically looking roads can be drawn.

  • The vehicles are drawn first as b/w. images (again translated, rotated, and scaled accordingly) to which an (appropriately transformed) semi-transparent rectangle is added to display the color-coding of the speeds.


[1] M. Treiber, A. Hennecke, and D. Helbing. Congested traffic states in empirical observations and microscopic simulations. Physical review E 62 1805-1824 (2000). Link, Preprint

[2] M. Treiber and A. Kesting. Traffic Flow Dynamics, Data, Models and Simulation. Springer 2013. Link

[3] A. Kesting, M. Treiber, and D. Helbing. General lane-changing model MOBIL for car-following models. Transportation Research Record, 86-94 (2007). Paper

[4] A. Kesting, M. Treiber, and D. Helbing. Enhanced intelligent driver model to access the impact of driving strategies on traffic capacity. Philosophical Transactions of the Royal Society A, 4585-4605 (2010). Preprint

[5] M. Treiber, and A. Kesting. An open-source microscopic traffic simulator. IEEE Intelligent Transportation Systems Magazine, 6-13 (2010). Preprint

[6] M. Treiber and V. Kanagaraj. Comparing Numerical Integration Schemes for Time-Continuous Car-Following Models Physica A: Statistical Mechanics and its Applications 419C, 183-195 DOI 10.1016/j.physa.2014.09.061 (2015). Preprint