% 
% Written by:
% -- 
% John L. Weatherwax                2007-09-10
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clc; 
close all; drawnow; 

% get code to simulate a sample path corresponding to a M/M/1 queue:
addpath( '../Chapter8' ); 

T       = 20; 
lambda  = 0.2; 
mean_at = 1/lambda; 
fprintf( 'mean arrival time (mean_at) = %10.6f\n', mean_at ); 

[t,Ni,Ei,Ai,Di] = chap_8_prob_13(T,mean_at,5,10);
figure; stairs(t,Ni,'-b'); axis( [ min(t), max(t), 0, max(Ni)+0.5 ] ); 
xlabel('time'); ylabel('number in system'); title( 'number of customers in the queue' ); 
%saveas( gcf, '../../WriteUp/Graphics/Chapter11/', 'epsc' ); 

figure; sh1=stairs(t,Ai,'-r'); hold on; sh2=stairs(t,Di,'-g'); axis( [ min(t), max(t), 0, max([Ai(:);Di(:)])+0.5 ] ); 
xlabel('time'); ylabel('number'); title( 'A(t) and D(t)' );
legend( [sh1,sh2], {'A(t) total number of arrivals by time t','D(t) total number of departures by time t'}, ...
        'location', 'northwest' ); 
saveas( gcf, '../../WriteUp/Graphics/Chapter11/chap_11_prob_1_At_N_Dt', 'epsc' ); 

Li = Ai-Di; 
figure; shL=stairs(t,Li,'-r'); axis( [ min(t), max(t), 0, max(Li(:))+0.5 ] ); 
xlabel('time'); ylabel('number'); title( 'L(t)' );
saveas( gcf, '../../WriteUp/Graphics/Chapter11/chap_11_prob_1_Lt', 'epsc' ); 

% compute some average queue statistics: 
tL   = trapz(t,Li);
L_20 = tL/T;
W_20 = tL/Ai(end);
l_20 = Ai(end)/T; 
fprintf('L(20) = %10.6f; W(20) = %10.6f; lambda_a(20) = %10.6f\n', L_20, W_20, l_20 ); 


clear functions;