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 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). Both of the paper's accelerations are applied. Dimension reduction by decomposition (Sec. 3, Sec. 5.4) reads the interdependence graph of the factors of (4.5), removes the subset D minimizing |D| + max_i |S_i(D)| (eq. 3.3), and inverts each connected component of the remainder separately, multiplying the results. Euler summation (Sec. 2.4, eq. 2.22) replaces the nearly alternating inner sum of (2.3) by the Euler sum of its first n+m+1 terms wherever K_j exceeds n+m, so prod_j K_j becomes prod_j min(n+m+1, K_j) in the cost (eq. 2.26).

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	Pfqn_clw.Options	Accelerations and their parameters; the defaults are the paper's.

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)
static Ret.pfqnNc	pfqn_clw(Matrix L, Matrix N, Matrix Z, Matrix m, Matrix lpar, Matrix gampar, Pfqn_clw.Options opt)

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)

pfqn_clw

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

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 indexed by chain; null = by inversion depth, 1 at depth 1, 2 at depths 2-3, 3 deeper.

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

opt - accelerations; null = defaults.

Returns:

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