% 
% 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; 

lambda_n = 2*[ 3:-1:1  ]; % \lambda_0, \lambda_1, \lambda_2 
mu_n     =   [ 3, 3, 4 ]; %     \mu_1,     \mu_2,     \mu_3 

rho_tmp = lambda_n ./ mu_n;
rho_n   = [ 1, cumprod( rho_tmp ) ]; 

p_0 = 1/sum( rho_n );
fprintf('the normalization probability is %10.6f\n', p_0 );

p_n = p_0*rho_n;

abm = dot( 0:3, p_n ); 
fprintf('average number of machines that are broken is given by %10.6f\n', abm );

abdr = dot( [lambda_n,0], p_n );
fprintf('average rate at which machines break down is given by %10.6f\n', abdr );