Package jline.api.pfqn.mva

Class Pfqn_dmlin

java.lang.Object
jline.api.pfqn.mva.Pfqn_dmlin
public final class Pfqn_dmlin extends Object
de Souza e Silva-Muntz Improved Linearizer (IL).

E. de Souza e Silva, R. R. Muntz, "A note on the computational cost of the Linearizer algorithm for queueing networks", IEEE Trans. Computers 39(6), 1990. Linearizer evaluates the arrival-instant queue length as

A_k^(c)(n) = sum_i (n_i - delta_c^(i)) [Q_ik(n)/n_i + Delta^(i)_ck],

re-summing the C Delta-terms at every Core iteration, at every one of the C+1 populations: O(K C^3) per refresh pass. IL splits that sum into the part that moves with the Core iterate and the part that does not,

 A_k^(c)(n)     = sum_i (n_i - delta_c^(i)) Q_ik(n)/n_i + xi_ck(n),
 xi_ck(N)       = sum_i (N_i - delta_c^(i)) Delta^(i)_ck,
 xi_ck(N - 1_j) = xi_ck(N) - Delta^(j)_ck,

so the C K aggregates xi are computed ONCE per refresh pass and each Core iteration then costs O(K C) instead of O(K C^2). Time drops to O(K C^2) with the space unchanged at O(K C^2), and, because the split is an identity and not an approximation, the fixed point is the one Linearizer reaches: pfqn_dmlin and pfqn_linearizer agree to round-off.