Package jline.api.fj

Class FJ_closed

java.lang.Object

jline.api.fj.FJ_closed

public final class FJ_closed
extends Object

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	FJ_closed.FJAmvaResult	[R, Q, X, U] of fj_amva.
static final class	FJ_closed.FJQgbResult	[Q, y] of fj_qgb: the bounded queue lengths and the geometric ratios.
static final class	FJ_closed.FJResptClosedResult	[R, exact] of fj_respt_closed.

Method Summary

Modifier and Type	Method	Description
static FJ_closed.FJAmvaResult	fj_amva(double[] D, int[] P, int M)
static FJ_closed.FJAmvaResult	fj_amva(double[] D, int[] P, int M, double Z)	Population-by-population mean value analysis of a closed network of fork-join subnetworks.
static FJ_closed.FJQgbResult	fj_qgb(double[] D, int[] P, int M)
static FJ_closed.FJQgbResult	fj_qgb(double[] D, int[] P, int M, double Z)	Geometric bound on the queue length of each fork-join subnetwork.
static FJ_closed.FJResptClosedResult	fj_respt_closed(int K, double x, int M)	The isolated parallel subsystem of Theorem 4.1, where every other job is necessarily inside the subnetwork so A = M-1.
static FJ_closed.FJResptClosedResult	fj_respt_closed(int K, double x, int M, double A)	Varki bound on the residence time of a closed fork-join subnetwork, R_{P_K}(M) <= x [ H_K + A ], with A the mean number of jobs an arriving job finds at the subnetwork.

Methods inherited from class java.lang.Object

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

Method Details

fj_qgb

public static FJ_closed.FJQgbResult fj_qgb(double[] D,
 int[] P,
 int M,
 double Z)

Geometric bound on the queue length of each fork-join subnetwork. y_n(M) = D_n M / (Z + sum_j D_j H_{P_j} + Dmax M), Q_n(M) = H_{P_n} [ y_n/(1-y_n) - y_n^(M+1)/(1-y_n) ]. The harmonic weights are what distinguishes this from the ordinary geometric bound of Pfqn_qzgblow: a P-way fork-join subnetwork inflates its own demand by H_P in the denominator and its queue length by H_P in the numerator. Setting every fork degree to one recovers that bound exactly.

fj_qgb

public static FJ_closed.FJQgbResult fj_qgb(double[] D,
 int[] P,
 int M)

fj_amva

public static FJ_closed.FJAmvaResult fj_amva(double[] D,
 int[] P,
 int M,
 double Z)

Population-by-population mean value analysis of a closed network of fork-join subnetworks. R_n(m) = D_n [ H_{P_n} + Q_n(m-1) ], X(m) = m / (Z + sum_n R_n(m)), Q_n(m) = X(m) R_n(m), started from Q_n(0) = 0. With every fork degree equal to one this is the exact single-class mean value analysis, because H_1 = 1; above that it is an approximation whose per-subnetwork residence time is an upper bound in the sense of Varki.

fj_amva

public static FJ_closed.FJAmvaResult fj_amva(double[] D,
 int[] P,
 int M)

fj_respt_closed

public static FJ_closed.FJResptClosedResult fj_respt_closed(int K,
 double x,
 int M,
 double A)

Varki bound on the residence time of a closed fork-join subnetwork, R_{P_K}(M) <= x [ H_K + A ], with A the mean number of jobs an arriving job finds at the subnetwork.

fj_respt_closed

public static FJ_closed.FJResptClosedResult fj_respt_closed(int K,
 double x,
 int M)

The isolated parallel subsystem of Theorem 4.1, where every other job is necessarily inside the subnetwork so A = M-1. The bound holds with equality at K = 2.