Package jline.lang.processes

Class BMAP

java.lang.Object

jline.lang.processes.Distribution

jline.lang.processes.ContinuousDistribution

jline.lang.processes.Markovian

jline.lang.processes.MarkovModulated

jline.lang.processes.Marked

jline.lang.processes.MarkedMAP

jline.lang.processes.BMAP

All Implemented Interfaces:

Serializable, Copyable

public class BMAP
extends MarkedMAP
implements Serializable

A Batch Markovian Arrival Process (BMAP) BMAP is a point process where arrivals occur in batches. Uses the standard BMAP representation: - D0: infinitesimal generator for transitions without arrivals - D1: rate matrix for transitions generating 1 arrival - D2: rate matrix for transitions generating 2 arrivals - ... - Dk: rate matrix for transitions generating k arrivals BMAP extends MarkedMAP where each "mark" k represents a batch size k.

See Also:

• Serialized Form

Field Summary

Fields inherited from class jline.lang.processes.Markovian

nPhases, process

Fields inherited from class jline.lang.processes.Distribution

immediate, mean, name, numParam, params, support

Constructor Summary

Constructors

Constructor	Description
BMAP()	Default constructor creating an empty BMAP
BMAP(MatrixCell bmap)	Construct a BMAP from a MatrixCell containing {D0, D1, D2, ..., Dk}
BMAP(Matrix D0, Matrix... Dk)	Construct a BMAP from D0 and variable number of Dk matrices

Method Summary

Modifier and Type	Method	Description
static BMAP	fromMAPWithBatchPMF(Matrix D0, Matrix D1, int[] batchSizes, double[] pmf)	Factory method to create BMAP from a base MAP and batch size distribution Given a base MAP (D0_base, D1_base) for inter-batch arrivals and a batch size distribution, constructs the BMAP by scaling: Dk = D1_base * pmf[k-1]
Matrix	getBatchMatrix(int batchSize)	Get the D_k matrix for batch size k
double[]	getBatchRates()	Get the arrival rates for each batch size
int	getMaxBatchSize()	Get the maximum batch size supported by this BMAP
double	getMeanBatchSize()	Get the mean batch size (expected number of arrivals per batch) Computed as weighted average of batch sizes by their rates: E[batch size] = sum(k * rate_k) / sum(rate_k)
String	getName()	Returns the name of this distribution type.
String	toString()

Methods inherited from class jline.lang.processes.MarkedMAP

normalize, sample, sample, toTimeReversed

Methods inherited from class jline.lang.processes.Marked

D, D, getD1k

Methods inherited from class jline.lang.processes.MarkovModulated

evalACFT, getACFDecay

Methods inherited from class jline.lang.processes.Markovian

acf, embedded, embeddedProb, evalCDF, evalCDF, evalLST, evalMeanT, evalVarT, getACF, getEmbedded, getEmbeddedProb, getIDC, getIDI, getInitProb, getMean, getMoments, getMu, getNumberOfPhases, getPhi, getProcess, getRate, getSCV, getSkewness, getSubgenerator, getVar, getVariance, idc, idi, initProb, mean, moments, mu, numberOfPhases, numPhases, phi, process, rate, scv, setMean, setProcess, setRate, skewness, subgenerator, var, variance

Methods inherited from class jline.lang.processes.Distribution

evalProbInterval, getNumParams, getParam, getSupport, isContinuous, isDisabled, isDiscrete, isImmediate, isMarkovian, name, numParams, param, setNumParams, setParam, support

Methods inherited from class java.lang.Object

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

Methods inherited from interface jline.lang.Copyable

copy

Constructor Details

BMAP

public BMAP()

Default constructor creating an empty BMAP

BMAP

public BMAP(MatrixCell bmap)

Construct a BMAP from a MatrixCell containing {D0, D1, D2, ..., Dk}

Parameters:

bmap - MatrixCell where: - bmap.get(0) = D0 (transitions without arrivals) - bmap.get(k) = Dk (transitions generating k arrivals) for k >= 1

BMAP

public BMAP(Matrix D0,
 Matrix... Dk)

Construct a BMAP from D0 and variable number of Dk matrices

Parameters:

D0 - the infinitesimal generator for transitions without arrivals

Dk - variable number of matrices where Dk[i-1] represents transitions generating i arrivals

Method Details

getName

public String getName()

Returns the name of this distribution type.

Overrides:

getName in class Distribution

Returns:

"BMAP" to identify this as a Batch Markovian Arrival Process

fromMAPWithBatchPMF

public static BMAP fromMAPWithBatchPMF(Matrix D0,
 Matrix D1,
 int[] batchSizes,
 double[] pmf)

Factory method to create BMAP from a base MAP and batch size distribution Given a base MAP (D0_base, D1_base) for inter-batch arrivals and a batch size distribution, constructs the BMAP by scaling: Dk = D1_base * pmf[k-1]

Parameters:

D0 - the base MAP's D0 matrix (transitions without batch arrivals)

D1 - the base MAP's D1 matrix (inter-batch arrival transitions)

batchSizes - array of batch sizes (e.g., [1, 2, 4, 8])

pmf - probability mass function for batch sizes (must sum to 1)

Returns:

a BMAP constructed from the base MAP and batch distribution

getMaxBatchSize

public int getMaxBatchSize()

Get the maximum batch size supported by this BMAP

Returns:

the maximum batch size k where Dk is defined

getMeanBatchSize

public double getMeanBatchSize()

Get the mean batch size (expected number of arrivals per batch) Computed as weighted average of batch sizes by their rates: E[batch size] = sum(k * rate_k) / sum(rate_k)

Returns:

the mean batch size

getBatchRates

public double[] getBatchRates()

Get the arrival rates for each batch size

Returns:

array where result[k-1] is the rate of batch size k arrivals

getBatchMatrix

public Matrix getBatchMatrix(int batchSize)

Get the D_k matrix for batch size k

Parameters:

batchSize - the batch size (1, 2, 3, ...)

Returns:

D_k matrix for the specified batch size, or null if out of range

toString

public String toString()

Overrides:

toString in class Object