Package jline.api.pfqn.mva

Class Pfqn_qsa

java.lang.Object

jline.api.pfqn.mva.Pfqn_qsa

public final class Pfqn_qsa
extends Object

Schweitzer, Serazzi and Broglia, "A Queue-Shift Approximation Technique for Product-Form Queueing Networks", Tools'98, LNCS 1469, pp. 267-279. QSA approximates the arrival-instant queue lengths through the absolute shift of the AGGREGATE queue length, Y_ri(K) = 1 + Q_i(K - e_r) - Q_i(K), in place of the fractional deviations of Linearizer, so the unknowns are one per station rather than one per station-class. The core equation (13a) is imposed at K, at every K - e_s and, in the three-level variant of eq. (16), at every K - e_s - e_t through the affine extrapolation of eq. (15). Port of matlab/src/api/pfqn/pfqn_qsa.m. The quintuple (16) is solved as ONE system by damped Newton, as Sect. 4 of the paper prescribes: the decomposed successive substitution that works for Linearizer drifts to the degenerate root in which the bottleneck absorbs the whole population.

Method Summary

Modifier and Type	Method	Description
static Ret.pfqnAMVA	pfqn_qsa(Matrix L, Matrix N)
static Ret.pfqnAMVA	pfqn_qsa(Matrix L, Matrix N, Matrix Z)
static Ret.pfqnAMVA	pfqn_qsa(Matrix L, Matrix N, Matrix Z, SchedStrategy[] type, double tol, int maxiter)
static Ret.pfqnAMVA	pfqn_qsa(Matrix L, Matrix N, Matrix Z, SchedStrategy[] type, double tol, int maxiter, int levels, Matrix QN0)

Methods inherited from class java.lang.Object

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

Method Details

pfqn_qsa

public static Ret.pfqnAMVA pfqn_qsa(Matrix L,
 Matrix N)

pfqn_qsa

public static Ret.pfqnAMVA pfqn_qsa(Matrix L,
 Matrix N,
 Matrix Z)

pfqn_qsa

public static Ret.pfqnAMVA pfqn_qsa(Matrix L,
 Matrix N,
 Matrix Z,
 SchedStrategy[] type,
 double tol,
 int maxiter)

pfqn_qsa

public static Ret.pfqnAMVA pfqn_qsa(Matrix L,
 Matrix N,
 Matrix Z,
 SchedStrategy[] type,
 double tol,
 int maxiter,
 int levels,
 Matrix QN0)

Parameters:

L - service demand matrix (M x R)

N - population vector (1 x R)

Z - think time vector (1 x R)

type - scheduling strategy per station; SchedStrategy.INF marks a delay centre

tol - residual tolerance of the Newton iteration

maxiter - maximum Newton iterations

levels - 2 for the two-level QSA of eq. (14), 3 for eq. (16)

QN0 - warm start for the Bard-Schweitzer initialization (M x R), may be null