pfqn_qzgbup.m

%{
%{
 % @file pfqn_qzgbup.m
 % @brief Upper asymptotic bound on queue length (Zahorjan-Gittelsohn-Bryant).
%}
%}
 
%{
%{
 % @brief Upper asymptotic bound on queue length (Zahorjan-Gittelsohn-Bryant).
 % @fn pfqn_qzgbup(L, N, Z, i)
 % @param L Service demand vector.
 % @param N Population.
 % @param Z Think time.
 % @param i Station index.
 % @return Qgb Upper bound on mean queue length at station i.
%}
%}
function Qgb=pfqn_qzgbup(L,N,Z,i)
sigma=sum(L.^2)/sum(L);
Yi=L(i)*min([1/max(L),N/(Z+sum(L)+sigma*(N-1-Z*pfqn_xzabaup(L,N-1,Z)))]);
if Yi<1
    Qgb=Yi/(1-Yi) - (Yi^(N+1))/(1-Yi);
else
    Qgb=N;
end
end