Package jline.api.pfqn.nc

Class Pfqn_clw

java.lang.Object

jline.api.pfqn.nc.Pfqn_clw

public final class Pfqn_clw
extends Object

Computes g(K) of a multichain closed product-form network with single-server and (optionally) infinite-server queues by numerically inverting its p-dimensional generating function (Choudhury, Leung and Whitt, 1995, eq. 4.5) G(z) = exp(sum_j rho_{j0} z_j) / prod_i (1 - sum_j rho_{ji} z_j)^{m_i} where j=1..p indexes chains and i=1..q' the distinct single-server queues with multiplicity m_i. g(K) is recovered by p nested one-dimensional lattice-Poisson inversions (eq. 2.3) with restrictive static scaling (eqs. 5.41-5.46) and log-domain recovery (eq. 7.1). Exact nested inversion of cost prod_j 2 l_j K_j; practical for moderate populations and few chains. The paper's Euler summation and dimension reduction speed-ups are not applied here.

Method Summary

Modifier and Type	Method	Description
static Ret.pfqnNc	pfqn_clw(Matrix L, Matrix N)
static Ret.pfqnNc	pfqn_clw(Matrix L, Matrix N, Matrix Z)
static Ret.pfqnNc	pfqn_clw(Matrix L, Matrix N, Matrix Z, Matrix m)
static Ret.pfqnNc	pfqn_clw(Matrix L, Matrix N, Matrix Z, Matrix m, Matrix lpar, Matrix gampar)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

pfqn_clw

public static Ret.pfqnNc pfqn_clw(Matrix L,
 Matrix N)

pfqn_clw

public static Ret.pfqnNc pfqn_clw(Matrix L,
 Matrix N,
 Matrix Z)

pfqn_clw

public static Ret.pfqnNc pfqn_clw(Matrix L,
 Matrix N,
 Matrix Z,
 Matrix m)

pfqn_clw

public static Ret.pfqnNc pfqn_clw(Matrix L,
 Matrix N,
 Matrix Z,
 Matrix m,
 Matrix lpar,
 Matrix gampar)

Parameters:

L - (q' x p) single-server relative traffic intensities, L(i,j)=rho_{ji}.

N - (1 x p or p x 1) closed-chain population vector K.

Z - (1 x p) aggregate infinite-server relative intensities rho_{j0}; null = 0.

m - (q' x 1) queue multiplicities m_i; null = ones.

lpar - (1 x p) inner lattice parameters l_j; null = 1,2,2,3,3,...

gampar - (1 x p) aliasing parameters gamma_j; null = 11,13,13,15,15,...

Returns:

normalization constant g(K) (Inf on overflow) and its natural log.