% 
% This code simulates a single-server queuing system up to a time t.  
% That is it generates a single sample path of the number of customers 
% in the system as a function of time up to time "t".  
%
% The customers arrive according to a Poisson process with rate lambda.
%
% The service time for each customer is uniformly distributed between a range
% [ul,ur]
%
% Outputs:
%   t: the times when the number of people in the system changes
%   Ni: the number of people in the system at each of the times in the array t
%
% Written by:
% -- 
% John L. Weatherwax                2006-09-14
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the% above email
% address.
% 
%-----

clc; close all; drawnow; 

%addpath( '/home/wax/Programming/Matlab/Code/ExternalSources/Misc/util/graphutil' );

%
% some simple sanity checks that this code works: 
% 

% Simple Case #1: 
%   with very long service times ... customers in the queue just build up: 
for ii=1:10
  [t,Ni,Ei,Ai,Di] = chap_8_prob_13(20,2,20,40);
  figure; stairs(t,Ni,'-b'); axis( [ min(t), max(t), 0, max(Ni)+0.5 ] ); 
  xlabel('time'); ylabel('number of customers in system');
end
saveas( gcf, '../../WriteUp/Graphics/Chapter8/long_service_times', 'epsc' ); 

% Simple Case #2: 
%   same as case #1 but with faster arrival rate: 
for ii=1:10
  [t,Ni,Ei] = chap_8_prob_13(20,0.2,20,40);
  figure; stairs(t,Ni,'-b'); axis( [ min(t), max(t), 0, max(Ni)+0.5 ] ); 
  xlabel('time'); ylabel('number of customers in system');
end
saveas( gcf, '../../WriteUp/Graphics/Chapter8/long_service_times_w_fast_arrival', 'epsc' ); 

% Simple Case #3:
%   with very short service times and a slow arrival rate we are always empty: 
for ii=1:10
  [t,Ni,Ei] = chap_8_prob_13(20,2,0.1,0.5);
  figure; stairs(t,Ni,'-b'); axis( [ min(t), max(t), 0, max(Ni)+0.5 ] ); 
  xlabel('time'); ylabel('number of customers in system');
end
saveas( gcf, '../../WriteUp/Graphics/Chapter8/short_service_times_w_slow_arrival', 'epsc' ); 

% Simple Case #4:
%   same as #3 but with a faster arrival rate ... we can almost keep up ... like a resonance condition/case
for ii=1:10
  [t,Ni,Ei] = chap_8_prob_13(20,0.1,0.05,0.075);
  figure; stairs(t,Ni,'-b'); axis( [ min(t), max(t), 0, max(Ni)+0.5 ] ); 
  xlabel('time'); ylabel('number of customers in system');
end
saveas( gcf, '../../WriteUp/Graphics/Chapter8/short_service_times_w_fast_arrival', 'epsc' ); 

return