Code covered by the BSD License  

Highlights from
Nagel Schreckenberg model implementation

image thumbnail

Nagel Schreckenberg model implementation

by

 

06 Feb 2012 (Updated )

Simulation of the Nagel Schreckenberg single-lane traffic model, with visualization and plotting.

NaSchr.m
% Nagel Schreckenberg model simulation
%Written by Alexander Farley 
%Feb 6 2012
%alexander.farley at utoronto.ca
%This script implements the Nagel Schreckenberg cellular automata based
%traffic model. Flow vs density curves are displayed. 
%
%
%Update June 5 2012: Fixed problem in vehicle velocity updates
%Update Jan 13 2013: Fixed problem with vmax=1 showing no flow
%Update June 12 2013: Corrected calculation of flow rate for FD plot
%


%Parameters
vmax = 6;
p = 0.6;
road_length = 40;
simulation_steps = 400;
render_on = 0;
pause_on = 0;
delay_on = 0;
delay_length = 0.05; %10 FPS

road = zeros(1,road_length);       %Contains occupation state
road_next = road;
velocities = zeros(1,road_length); %Contains velocity state
velocities_next = velocities;

%Sampling
num_samples = 1000;
samples = zeros(2,num_samples); %Contains density and flow rate
density_step = 1/num_samples;

history = zeros(simulation_steps, road_length);
velocity_history = zeros(simulation_steps, road_length);

figure

for g=1:num_samples
    
    %Generate traffic
    road = zeros(1,road_length);       %Contains occupation state
    road_next = road;
    density = g/num_samples;
    
    %Generate traffic
    
for i=1:road_length
    if rand < density 
        road(i) = 1;
    end
end

    if render_on
    imshow(road);
    drawnow
    end
    
    %Run simulation
for i=1:simulation_steps
    history(i, :) = road;
    velocity_history(i,:) = velocities;
           %--------------------Velocity update ------------------------%
    for j=1:road_length
       if road(j) == 1
           distance = 0;
           %Seek vmax ahead
           bf = 0;
           for k=1:vmax
               distance = k;
              
               if j+k <= road_length %The index is the "cell under consideration" - is it safe to land here?
                   index = j+k;
               else
                   index = j+k-road_length; %Deal with wrapping
               end
               
               if road(index) == 1 
                   bf = 1;
               end
               
               if bf == 1, break, end
           end
            
           if velocities(j) < vmax %Acceleration
               velocities(j) = velocities(j) + 1;
           end
           
           if (velocities(j) > distance - 1) && bf == 1 %Collision avoidance
               velocities(j) = distance - 1;
           end
           
           if rand < p && velocities(j) > 0 %Random braking
               velocities(j) = velocities(j) - 1;
           end
           
           
       end
    end
    
    %--------------------Movement -------------------------------%
    for j=1:road_length
        if road(j) ==1
            if j+velocities(j) <= road_length
                index = j+velocities(j);
            else
                index = j+velocities(j) - road_length; %Deal with wrapping
            end
            %Collision detection
            if road_next(index) == 1
                disp('Collision detected')
            end
            road_next(index) = 1;
            velocities_next(index) = velocities(j);
        end
    end
    
    velocities = velocities_next;
    
    road = road_next;
    road_next = zeros(1,road_length);
    
    if render_on
    imshow(road);
    drawnow
    end
    
    if pause_on
        pause
    end
    
    if delay_on
        pause(delay_length)
    end
    
end

    %Record density and flow rate
    velocity_history = velocity_history.*history;
    samples(:,g) = [mean2(history) (sum(velocity_history(:))/sum(history(:)))*mean2(history)];
    
    disp('Sample step:')
    g
end
    
scatter(samples(1,:), samples(2,:));
axis([0 1 0 1]);
xlabel('Density')
ylabel('Flow (normalized)')
title('Nagel Schreckenberg Flow-density Curve')

%imshow(history)

Contact us