Package jline.solvers.fluid.analyzers

Class MinNormalAnalyzer

java.lang.Object

jline.solvers.fluid.analyzers.ClosingAndStateDepMethodsAnalyzer

jline.solvers.fluid.analyzers.MinNormalAnalyzer

All Implemented Interfaces:

FluidAnalyzer

public class MinNormalAnalyzer
extends ClosingAndStateDepMethodsAnalyzer

Second-order moment-closure fluid analysis, backing options.method='minnormal'. Java twin of the MATLAB solver_fluid_moments.

The default fluid methods close the moment hierarchy at first order: the drift of the mean depends on E[min(X_i,c_i)], which they replace by min(E[X_i],c_i). No second moment ever enters, so no variance is produced and the mean itself is biased wherever min() is not locally linear. This analyzer reinstates the second moment with the min-normal closure of Guenther, Stefanek and Bradley: the drift uses E[min(X_i,c_i)] under a normal marginal whose variance is produced by the covariance (Lyapunov) equation, so mean and covariance are solved self-consistently by fixed-point iteration. This corrects the mean, most visibly near rho = 1 where the first-order closure is worst, and it is the only fluid method that can represent GPS at all.

All performance measures are read back from the same event representation that defines the drift, so throughputs balance flow at the fixed point under whichever closure was used. That is also why this analyzer does not reuse the closing metric reader, which accepts SIRO as FCFS and has no GPS branch.

See Also:

• FluidMomentTerms
• FluidLyapunov

Field Summary

Fields

Modifier and Type	Field	Description
int[][]	classBlock	State coordinates of each (station,class), flattened as i*K+k.
int	outerIters	Number of outer (mean, covariance) iterations performed.
Matrix	qVar	Per-(station,class) queue-length variance.
double[]	sigma2	Per-station population variance.
double[]	sigma2Drift	The same variance as it enters the DRIFT: zero at the delay stations, which have no min() to close.
Matrix	sigmaMatrix	State-level stationary covariance at the converged fixed point.
int[][]	stationBlock	State coordinates of each station, i.e.

Fields inherited from class jline.solvers.fluid.analyzers.ClosingAndStateDepMethodsAnalyzer

lastPassageOde, xvec_it, xvec_t

Constructor Summary

Constructors

Constructor	Description
MinNormalAnalyzer()

Method Summary

Modifier and Type	Method	Description
void	analyze(NetworkStruct sn, SolverOptions options, SolverResult result)

Methods inherited from class jline.solvers.fluid.analyzers.ClosingAndStateDepMethodsAnalyzer

getXVecIt, solver_fluid, solver_fluid_iteration

Methods inherited from class java.lang.Object

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

Field Details

sigmaMatrix

public Matrix sigmaMatrix

State-level stationary covariance at the converged fixed point.

qVar

public Matrix qVar

Per-(station,class) queue-length variance.

classBlock

public int[][] classBlock

State coordinates of each (station,class), flattened as i*K+k.

stationBlock

public int[][] stationBlock

State coordinates of each station, i.e. every class and phase it serves.

sigma2

public double[] sigma2

Per-station population variance.

sigma2Drift

public double[] sigma2Drift

The same variance as it enters the DRIFT: zero at the delay stations, which have no min() to close. This, not sigma2, is what any later solve on the same fixed point (the passage-time ODE) must close its capacity term at, or it evaluates a first-order drift at a second-order fixed point.

outerIters

public int outerIters

Number of outer (mean, covariance) iterations performed.

Constructor Details

MinNormalAnalyzer

public MinNormalAnalyzer()

Method Details

analyze

public void analyze(NetworkStruct sn,
 SolverOptions options,
 SolverResult result)

Specified by:

analyze in interface FluidAnalyzer

Overrides:

analyze in class ClosingAndStateDepMethodsAnalyzer