Package jline.api.qsys

Class Qsys_bmapm1

java.lang.Object

jline.api.qsys.Qsys_bmapm1

public final class Qsys_bmapm1
extends Object

Analyzes a BMAP/M/1 queue by the matrix-analytic (M/G/1-type) method.

Beyond the usual performance measures the result exposes the intermediate matrix-analytic quantities themselves (theta, lambda, rho, the uniformization constant q, the randomized blocks A0/A1/B0/Bk, A, alpha, the matrix G, the drift, the measured decay rate and the level probabilities), so that the algorithm can be inspected and taught rather than only its output.

Port of MATLAB qsys_bmapm1.m.

Field Summary

Fields

Modifier and Type	Field	Description
static final int	DEFAULT_MAX_ITER	Default maximum functional iterations for G.
static final double	DEFAULT_TAIL_TOLERANCE	Default relative truncation target for the level distribution.
static final double	DEFAULT_TOLERANCE	Default convergence tolerance for G.

Method Summary

Modifier and Type	Method	Description
static QsysBmapM1Result	qsys_bmapm1(Matrix[] D, double mu)	Analyzes a BMAP/M/1 queue with the default uniformization constant and adaptive level truncation.
static QsysBmapM1Result	qsys_bmapm1(Matrix[] D, double mu, double uniformization, int maxIter, double tolerance, int maxLevel, double tailTolerance)	Analyzes a BMAP/M/1 queue.

Methods inherited from class java.lang.Object

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

Field Details

DEFAULT_MAX_ITER

public static final int DEFAULT_MAX_ITER

Default maximum functional iterations for G.

See Also:

• Constant Field Values

DEFAULT_TOLERANCE

public static final double DEFAULT_TOLERANCE

Default convergence tolerance for G.

See Also:

• Constant Field Values

DEFAULT_TAIL_TOLERANCE

public static final double DEFAULT_TAIL_TOLERANCE

Default relative truncation target for the level distribution.

See Also:

• Constant Field Values

Method Details

qsys_bmapm1

public static QsysBmapM1Result qsys_bmapm1(Matrix[] D,
 double mu)

Analyzes a BMAP/M/1 queue with the default uniformization constant and adaptive level truncation.

Parameters:

D - BMAP matrices {D0, D1, ..., DK}; D0 carries the hidden transitions, Dk (k >= 1) the transitions that release a batch of k customers

mu - exponential service rate

Returns:

the matrix-analytic result

qsys_bmapm1

public static QsysBmapM1Result qsys_bmapm1(Matrix[] D,
 double mu,
 double uniformization,
 int maxIter,
 double tolerance,
 int maxLevel,
 double tailTolerance)

Analyzes a BMAP/M/1 queue.

Parameters:

D - BMAP matrices {D0, D1, ..., DK}

mu - exponential service rate

uniformization - uniformization constant q used to randomize the generator into a discrete-time M/G/1-type chain; it must dominate every total outflow rate. Pass NaN to use max_i(-D0(i,i)) + mu

maxIter - maximum functional iterations for G

tolerance - convergence tolerance for G

maxLevel - fixed level truncation for the queue-length distribution; non-positive selects the adaptive rule

tailTolerance - relative truncation target for the level distribution

Returns:

the matrix-analytic result