%% A16: Car Rental Company Steady-State Distribution
disp('A16: Car Rental Company');
% Initial state vector
x0_a16 = [0.1; 0.6; 0.3];
% Transition matrix for A16 scenario
P_a16 = [0.8 0.3 0.3;
0.1 0.6 0.1;
0.1 0.1 0.6];
% Initialize vectors to track state evolution
vAirport = [x0_a16(1)];
vTrainStation = [x0_a16(2)];
vCityCenter = [x0_a16(3)];
% Iteratively apply transition matrix to find steady state for A16
for i = 1:500
x1_a16 = P_a16^i * x0_a16;
vAirport = [vAirport x1_a16(1)];
vTrainStation = [vTrainStation x1_a16(2)];
vCityCenter = [vCityCenter x1_a16(3)];
end
% Plotting for A16
subplot(2,1,1); % Subplot for A16
hold on
plot(vAirport, 'g+-');
plot(vTrainStation, 'ro--');
plot(vCityCenter, 'b*');
legend('Airport', 'Train Station', 'City Center');
xlabel('Days');
ylabel('Proportion of Cars');
title('A16: Car Distribution Evolution');
%% B15: Bicycle Pool Steady-State Distribution
disp('B15: Bicycle Pool');
% Transition matrix based on B15 problem description
P_b15 = [160/200, 40/200, 60/200;
20/200, 140/200, 40/200;
20/200, 20/200, 100/200];
% Initial state: equal number of bicycles at each location
x0_b15 = [1/3; 1/3; 1/3];
% Initialize vectors to track state evolution
vResidence = [x0_b15(1)];
vLibrary = [x0_b15(2)];
vAthleticCentre = [x0_b15(3)];
% Iteratively apply P to find steady state for B15
for i = 1:500
x1_b15 = P_b15 * x0_b15;
vResidence = [vResidence x1_b15(1)];
vLibrary = [vLibrary x1_b15(2)];
vAthleticCentre = [vAthleticCentre x1_b15(3)];
x0_b15 = x1_b15; % Prepare for the next iteration
end
% Plotting for B15
subplot(2,1,2); % Subplot for B15
hold on
plot(vResidence, 'g');
plot(vLibrary, 'r');
plot(vAthleticCentre, 'b');
legend('Residence', 'Library', 'Athletic Centre');
xlabel('Days');
ylabel('Proportion of Bicycles');
title('B15: Bicycle Distribution Evolution');p