%% n=erlangbinv(p,rho)%% This function finds the smallest n such 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% a probability <=p of having all servers busy. %% The Erlang B probability is given by %%  B=(rho^m/m!)/(sum(rho^k/k!),k=0..m)%% We use 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)%% This routine simply loops through the recursion until B is <= p, and% then returns n.  %function n=erlangbinv(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);  if (B <= p),    return;  end;   n=n+1;end;