%% B=erlangb(n,rho)%% This function computes the Erlang B probability that a system with n% servers, no waiting line, Poisson arrival rate lambda, service rate % (per server) mu, and intensity rho=lambda/mu will have all servers busy.  %% The probability is %%  B=(rho^m/m!)/(sum(rho^k/k!),k=0..m)%% It uses a recurrence relation which is more accurate than direct evaluation % of the formula.  This recurrence relation is a "folk theorem".  The author% would appreciate a reference to its first publication.  The recurrence is%%  B(0,rho)=1%%  B(n,rho)=(rho*B(n-1,rho)/n)/(1+rho*B(n-1,rho)/n)%%function B=erlangb(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');    B=NaN;    return;  end;%% Sanity check- make sure that rho >= 0.0.%  if (rho < 0.0)    warning('rho is negative!');    B=NaN;    return;  end;%% Start the recursion with B=1.%B=1;%% Run the recursion.%for k=1:n,  B=((rho*B)/k)/(1+rho*B/k); end;