Car trajectory

    Here we present simulations of a car travelling within a road network, being influenced by traffic but without
    influencing it significantly. Such simulations are based on a algorithm which, after computing evolution of
    density in the network, traces the trajectory of the car in it.
    We reproduce two situations: a car moving along a road where a car accident occurs and a car moving
    within a traffic circle following a fixed path. In both cases we are able to give the time for covering the path
    of the car.



Situation 1: Traffic Jam

    On a single road of length 2, with a density equal to 0.25 at the incoming boundary, a car is moving
    towards a congestion provoked by a car accident, see Figures below. The car enters the road at
    time t=0 and the time for accident removal is t=0.5 (animation 1) or t=2.0 (animation 2).

 

 

 Animation 1 (time of accident removal: t= 0.5)

Animation 2 (time of accident removal: t= 2.0)




Situation 2: Traffic Circle

    A car is moving within the traffic circle depicted below according to a fixed path: (1,1R,2R,3R,4), see Figure below,
    and each road has the same length (equal to 1). The network is loaded with initial data (indicated as ρ(0,x)):


        ρ1(0,x)=0.25, ρ2(0,x)=0.4, ρ3(0,x)=ρ4 =(0,x)=ρ1R(0,x)=ρ2R(0,x)=ρ3R(0,x)=ρ4R(0,x)=0.5,


    and the car enters the traffic circle at time t=0.8.
    We study the effects of traffic on car trajectory for different boundary conditions and setting differently right of way
    parameter p.





    Animations 1, 2 and 3 have been produced assuming constant boundary data on incoming road 1 and 2:
    ρ1(t,0)=0.25 and ρ2(t,0)=0.4.





    Animations 4 and 5 have been produced assuming periodic boundary data on incoming road 1 and 2:
    ρ1(t,0)=ρ2(t,0)= 0.25 + 0.15*sin(5t).