Package jline.api.pfqn.mva

Class Pfqn_clust

java.lang.Object
jline.api.pfqn.mva.Pfqn_clust
public final class Pfqn_clust extends Object
de Souza e Silva-Lavenberg-Muntz Clustering Approximation (CA).

E. de Souza e Silva, S. S. Lavenberg, R. R. Muntz, "A clustering approximation technique for queueing network models with a large number of chains", IEEE Trans. Computers C-35(5), 1986. The network is covered by subnetworks whose union is the whole network but which need not be disjoint. Every class visiting a subnetwork S is either LOCAL to S, and is then solved inside it, or FOREIGN, and is then seen only through the utilization it leaves behind. Each subnetwork is solved by an ordinary approximate MVA algorithm with two replacements: the complement of S is collapsed into a per-class delay P_c and the foreign classes into a per-centre utilization U_k,

 X_c(N) = N_c / (sum_{k in S} R_ck(N) + Z_c + P_c),
 Q_k(N) = [sum_{c in LC(S)} R_ck(N) X_c(N) + U_k] / (1 - U_k).

Choosing the PE algorithm for every subnetwork reproduces global PE exactly, so the useful setting is Linearizer inside, PE outside: the cost then sits between Pfqn_bs and Pfqn_linearizer, which is the point of the method.

When no decomposition is supplied the criterion of the paper is applied automatically: the cheap PAMB estimate of the centre utilizations is taken, every class is attached to the centre where it loads the most, classes sharing that centre form one cluster, and the subnetwork of a cluster is the set of centres its classes visit.