C=erlangc(n,rho)

%
% p=erlangc(n,rho)
%
% This function computes the Erlang C probability that a system with n
% servers, infinite waiting line, Poisson arrival rate lambda, service rate 
% (per server) mu, and intensity rho=lambda/mu will have all servers busy.  
%
% It uses the formula 
%
%  C(n,rho)=n*B(n,rho)/(n-rho*(1-B(n,rho)))
%
% See Cooper, Introduction to Queueing Theory, 2nd Ed.
%
function C=erlangc(n,rho)
%
% Sanity check- make sure that n is a positive integer.
%
  if ((floor(n) ~= n) || (n < 1))
    warning('n is not a positive integer');
    C=NaN;
    return;
  end;
%
% Sanity check- make sure that rho >= 0.0.
%
  if (rho < 0.0)
    warning('rho is negative!');
    C=NaN;
    return;
  end;
%
% Calculate the Erlang B probability and then convert to Erlang C.
%
B=erlangb(n,rho);
C=n*B/(n-rho*(1-B));