function [p_n] = mm1_queue_cap_N(lambda,mu,N)
% MM1_QUEUE_CAP_N - Returns the M/M/1 queue steady state probability when we have a capacity of N
%   
% Input: 
%  lambda: arrival rate
%  mu: departure rate
%  N: the number of lines in the queue
% 
% Output: 
%   p_n: is the steady-state probabity we are in the state X(t)=n
% 
% References: 
% 
% Introduction to Probability Models: Chapter 10
% by Roe Goodman 
% 
% 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.
% 
%-----

rho = lambda/mu;
p_0 = ( ( 1-rho^(N+1) )/( 1-rho ) )^(-1); 
p_n = (rho.^(0:N))*p_0;