Back to the simulation

Sources from GitHub

Information on the
mixed traffic flow simulation

This is an interactive simulation of the fully two-dimensional model which is fully documented in following reference:
  At present, only landscape-like viewports are supported, so the width of the simulation screen should be greater than the height (3:2 works well).

The simulation starts with little traffic on a homogeneous road (the U-bend is only there in order to display a longer road segment) with a small downstream bottleneck realized by a road narrowing.

There are two insert diagrams: a speed-density box-whisker plot at the top, and a flow-density scatter plot at the bottom. After each aggregation interval (presently, set to 3 s), an additional box-whisker element and data point is added to each plot, respectively. The plots give the global picture over the whole simulation area, i.e., the flow-densitry data approximate a macroscopic fundamental diagram and the boxes of the speed-density plot are longest for phase-segregated traffic, i.e., jammed in one portion and free in another.

Furthermore, there are three possibilities for interaction: The sliders, the buttons to the right, and loading a custom initial configuration

The sliders

• Timewarp controls the time-lapse factor simulated time progression vs. real time progression
• Inflow controls the traffic demand
• MaxOutflow installs a bottleneck at the outflow and thus controls the maximum outflow. By controlling the Inflow and Max Outflow sliders, a complete simulated flow-density scatter plot can be created in the lower right insert diagram:
  • The free branch is controlled by the inflow with MaxOutflow set to 100%
  • The congested branch is controlled by MaxOutflow with the Inflow set to the maximum

• The sliders FracTruck and FracBike control the traffic composition of the respective vehicle types with the remaining percentage (if any) consisting of cars
• The last four sliders control selected model parameters, see the paper:
  • τ_lat,OVM is the time constant for the lateral Optimal Velocity Model (see Chapter 10 of Traffic Flow Dynamics for the normal OVM) controlling the lateral motion. The lower τ_lat,OVM, the faster lateral movements are adapted to the desired ones (which are often zero)
  • sens_dvy is a new experimental parameter introducing relative speeds to the OVM-like lateral dynamics. This avoids lateral crashes for larger τ_lat,OVM values (approx > 1 s). For simulating the original model in the paper, set sens_dvy=0.
  • The push_lat factor p determines to which extent back vehicles are taken into account when moving laterally. For push_lat=0, the followers are exclusively responsible for avoiding crashs and the leaders do not look behind (not yet in the paper). For push_lat=1, the followers "push" the leaders aside to the same amount as the leaders the followers (actio=reactio) For simulating the original model in the paper, set push_lat=0.
  • The push_long factor p acts similarly for the longitudinal dynamics. For push_long=0, we have car-following, and for push_long=1 pure actio=reactio. Notice that, as in the backwards longitudinal interaction from the leader, only the follower with the strongest forward interaction is selected. Notice that there is no longer a "normal" fundamental diagram for push_long=1 and, instead, the flow increases always with the density. Increasing push_long increases the capacity. For simulating the original model in the paper, set push_long=0.

The buttons/switch areas

• The Display Forces toggle indicates, if on, the actual acceleration vector for each vehicle by an arrow (the simulation needs to be running to see the effect of this button)
• The Var. Width Left and Var. Width Right toggles introduce bottlenecks as predefined road narrowings at the right and left sides, respectively. Activating both bottlenecks simultaneously takes the model to its limits
• If the Floor Field toggle is on, lane-based traffic is simulated. This is introduced into the mixed traffic flow model by adding a floor field producing lateral forces whenever a car or a truck is not at the center of one of the five lanes. The bike drivers, however, drive just between the lanes. Since they are sufficiently wide, bike drivers can overtake and be overtaken.
  • Notice how the vehicles spontaneously order when switching this toggle on
  • destroying the lanes by switching the floor field off may lead to more effective mixed flow in congested conditions, particularly in the presence of congestions/stronger bottlenecks (create congestion by increasing the inflow, switching on Var Width Left or Right, or reducing MaxOutflow)
  • Notice that the floor field a.k.a lanes is only sensible if there are no significant road narrowings. Otherwise, the vehicles may leave the road...

Custom initial conditions (micro ICs)

The simulation can be customized by prescribing arbitrary microscopic initial conditions and road-blocking bottlenecks as specified in text files prescribing the type, initial longitudinal and lateral position (u,v), and initial velocity (speedLong,speedLat) of any object. Pressing the button "IC from file" opens a file selector for user-supplied files. Once selecting one, the simulation is cleared and re-run with the user-supplied vehicle configuration (the geometric bottlenecks are retained from the previous setting). The file format is as follows:

 # type     length   width  u     v       speedLong  speedLat
 car        5.0      2.0    20    3       15         0
 truck      10.0     3.0    20    -3      15         0
 bike       2.0      1.0    40    -3      5          1
 obstacle   80       2      300   9.5     0          0
 ...        ...      ...    ...   ...     ...        ...

Examples can be downloaded at the GitHub link or from the links further below. Besides the three moving types car, truck, and bike, there is also a type obstacle which can be used to implement various road-blocking bottlenecks.
Micro ICs are useful when analyzing certain model aspects with reproducible scenarios. For this reason, I also seed the random number generator when a new IC file is loaded. This is necessary because a certain acceleration noise is added to resolve stalemates in the traffic flow (see file IC_resolveStalemate.txt below). When using micro ICs, it is best to set the inflow to zero because otherwise new incoming vehicles may disturb the analysis/experiments. With zero inflow, there are also no further stochastic elements in the simulation in addition to the acceleration noise. Notice that the simulation is cleared from all past vehicles and past obstacles and bottlenecks when a new IC file is loaded but the other slider settings are unchanged.
As examples and templates for further modification, you can download several template initial configurations.

Hint: The filename indicates that the configurations work as intended for a road width of 3.5 m times the given number of lanes. furthermore, you should deactivate the "Var width*" geometry settings and set the inflow to zero because, otherwise, the additional inflow vehicles will interfere. You can also try if a given configuration works better with lanes (floorfield on) or without)

• A car navigating through a big obstacle parcours. The obstacles are virtual standing vehicles
• A car and a bike overtaking some slower trucks in the middle. This is more effective with lanes since, otherwise, the space between the trucks is quite narrow. Without lanes, it is only possible if the lateral pushing factor is above about push_lat=0.3 since, otherwise, the trucks in front do not care and the initial space is too low. Also with lanes, lateral pushing helps. Can also be done with a width of 10.5 m (3 lanes)
• A very strong road narrowing down to one lane. Some cooperation is necessary so that everyone can pass the bottleneck. This brings the model to its limits since no explicit cooperation is built into the drivers, so quite a chaos occurs. Best (i.e., shortest time for all vehicles traversing the simulation) is with lanes and longitudinal and lateral pushing activated
• This visualizes the amount of stochasticity (in form of acceleration noise) that is built into the simulator because, without noise, the two pairs should drive exactly in parallel. Obviously, very little noise is needed to resolve stalemates
• Here, the pushing effect should resolve the stalemate, so, finally, the car can overtake. For some reason, this does not yet work
• Two cars symmetrically behind a symmetrical 3-to-1 lane drop
• An obstacle parcours. You can also add some external inflow and look what happens
• A car and a truck just touching each other while driving at the beginning. How will the situation be resolved? For this, it is useful to set the timewarp to very low values before loading the file.