%% n=erlangcinv(p,rho)%% This function finds the smallest n such 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% a probability <=p of having all servers busy. %% The Erlang B probability is computed using the same recursion that the % erlangb() function uses.  The B probability is then used to compute% the Erlang C probability.  The Erlang C probability is given by %%  C(n,rho)=n*B(n,rho)/(n-rho*(1-B(n,rho)))%% See Cooper, Introduction to Queueing Theory, 2nd Ed.%% This routine simply loops through the recursion until C is <= p, and% then returns n.  %function n=erlangcinv(p,rho)%% Start the recursion with B=1.%B=1;%% Loop, iterating the recursion until the probability is <= p.%n=1;while (1 == 1),  B=((rho*B)/n)/(1+rho*B/n);  C=n*B/(n-rho*(1-B));  if (C <= p),    return;  end;   n=n+1;end;