pfqn_xzgsblow.m

%{
%{
 % @file pfqn_xzgsblow.m
 % @brief Lower asymptotic bound on throughput (Zahorjan-Gittelsohn-Schweitzer-Bryant).
%}
%}
 
%{
%{
 % @brief Lower asymptotic bound on throughput (Zahorjan-Gittelsohn-Schweitzer-Bryant).
 % @fn pfqn_xzgsblow(L, N, Z)
 % @param L Service demand vector.
 % @param N Population.
 % @param Z Think time.
 % @return X Lower bound on throughput.
%}
%}
function X=pfqn_xzgsblow(L,N,Z)
M=length(L);
Lmax = max(L);
R=Z+sum(L)+Lmax*(N-1);
for ist=1:M
    if L(ist) < Lmax
        R=R+(L(ist)-Lmax)*pfqn_qzgblow(L,N-1,Z,ist); 
    end
end
discriminant = R^2 - 4*Z*Lmax*(N-1);
if discriminant < 0
    discriminant = 0;
end
X=2*N*(1/(R+sqrt(discriminant)));
 
end