NLP.asv

% Student dependent variables
Da = [4 6 5];
Db = [1 8 8];
E1 = Da(1) + Db(1);
E2 = Da(2) + Db(2);
E3 = Da(3) + Db(3);

% Constants
global TAU MU Cr RHOm ALPHA K A Vf RHOc T L LAMBDA;
TAU = 10/3600; % [hr]
MU = 80; % [km^2/hr]
Cr = 2000; % [veh/hr]
RHOm = 120; % [veh/hr/lane]
ALPHA = 0.1; % []
K = 10; % [veh/lane
A = 2;
Vf = 110;
RHOc = 33.5 + E1/3;
T = 10/3600;
L = 1;
LAMBDA = 3;

% functions
function [qi, rhonext] = nextrho(rhoi, qprev, qr, vi)
    global LAMBDA T L RHOc;
    qi = LAMBDA*rhoi*vi;
    rhonext = min([rhoi + (T/(LAMBDA*L))*(qprev - qi + qr) RHOc]);
end


function vnext = nextv(vi, vprev, rhonext, rhoi, VSL)
    global ALPHA Vf A RHOc T TAU L MU K;
    Vi = min([(1+ALPHA)*VSL; Vf*exp((-1/A)*(rhoi/RHOc)^A)]);
    posterm = vi + (T/TAU)*(Vi - vi) + (T/L)*vi*(vprev - vi);
    negterm = ((MU * T * (rhonext - rhoi))/(TAU * L * (rhoi + K)));
    vnext = posterm - negterm;
end

% Simulation
rho = zeros(5, 120);
v = zeros(5, 120);
rho(:,1) = 30 * ones(5,1);
v(:,1) = 80 * ones(5,1);

for k=1:120
    if k < 60
        q0 = 7000 + 100*E2;
    else
        q0 = 2000 + 100*E3;
    end
    
    [qi, rho(1,k+1)] = nextrho(rho(1,k), q0, 0, v(1, k));
    v(1, k+1) = nextv(v(1, k), v(1,k), rho(1+1, k), rho(1, k), 120);

    for i=2:4
        [qi, rho(i,k+1)] = nextrho(rho(i,k), qi, 0, v(i, k));
        v(i, k+1) = nextv(v(i, k), v(i-1,k), rho(i+1, k), rho(i, k), 120);
    end

    [qi, rho(5,k+1)] = nextrho(rho(5,k), qi, 0, v(i, k));
    v(5, k+1) = nextv(v(5, k), v(5-1,k), rho(5, k), rho(5,k), 120);
end

%plotting
figure()
title('Velocity')
xlabel('Time')
ylabel('Velocity')
hold on
for i=1:5
    plot(v(i,:))
end
legend('Segment 1', 'Segment 2', 'Segment 3', 'Segment 4', 'Segment 5')


figure()
title('density')
xlabel('Time')
ylabel('density')
hold on
for i=1:5
    plot(rho(i,:))
end
legend('Segment 1', 'Segment 2', 'Segment 3', 'Segment 4', 'Segment 5')