Package jline.api.pfqn.mva

Class Pfqn_chow

java.lang.Object

jline.api.pfqn.mva.Pfqn_chow

public final class Pfqn_chow
extends Object

Chow Second Approximation (SA) approximate MVA.

W.-M. Chow, "Approximations for large scale closed queueing networks", Perform. Eval. 3(1), 1983. The arrival-instant queue length is written exactly as

 A_k^(c)(N) = Q_k(N - 1_c) = Q_k(N) (1 + theta_ck),
 theta_ck   = [Q_k(N - 1_c) - Q_k(N)] / Q_k(N),
 

and the theta-terms are estimated ONCE, off the Bard LCP solution, before the fixed point is run. Two estimators are given: the BACKWARD one uses Qhat(N - 1_c), the FORWARD one Qhat(N + 1_c). Chow reports the forward form to be the more accurate of the two, so it is the default here. Setting every theta to zero recovers Pfqn_lcp.

Field Summary

Fields

Modifier and Type	Field	Description
static final String	BACKWARD	Estimator of the theta-terms.
static final String	FORWARD	Estimator of the theta-terms.

Method Summary

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

Methods inherited from class java.lang.Object

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

Field Details

FORWARD

public static final String FORWARD

Estimator of the theta-terms.

See Also:

• Constant Field Values

BACKWARD

public static final String BACKWARD

Estimator of the theta-terms.

See Also:

• Constant Field Values

Method Details

pfqn_chow

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

pfqn_chow

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

pfqn_chow

public static Ret.pfqnAMVA pfqn_chow(Matrix L,
 Matrix N,
 Matrix Z,
 double tol,
 int maxiter,
 Matrix QN0)

pfqn_chow

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

pfqn_chow

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