Package jline.lang.processes

Class RAP

java.lang.Object

jline.lang.processes.Distribution

jline.lang.processes.ContinuousDistribution

jline.lang.processes.Markovian

jline.lang.processes.RAP

All Implemented Interfaces:

Serializable, Copyable

public class RAP
extends Markovian

A Rational Arrival Process (RAP) distribution. RAP is a generalization of the Markovian Arrival Process (MAP) where the matrices H0 and H1 represent hidden and visible transitions respectively, but with relaxed constraints compared to MAP. Representation: - H0: matrix of hidden transition rates (transitions without arrivals) - H1: matrix of visible transition rates (transitions with arrivals) - H0 + H1 must form a valid infinitesimal generator (row sums = 0) - All eigenvalues of H0 must have negative real parts - Dominant eigenvalue of H0 must be negative and real The marginal distribution of inter-arrival times is a Matrix Exponential (ME) distribution.

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
RAP(Matrix H0, Matrix H1)	Creates a Rational Arrival Process with specified H0 and H1 matrices.

Method Summary

Modifier and Type	Method	Description
static RAP	fitMeanAndSCV(double mean, double scv)	Creates a RAP by fitting the given mean and squared coefficient of variation (SCV).
static RAP	fitMoments(double[] moments)	Creates a RAP by fitting the given moments.
static RAP	fitMomentsAndCorrelations(double[] moments, double[] correlations)	Creates a RAP by fitting the given moments and correlations.
static RAP	fromErlang(int k, double rate)	Creates a RAP from an Erlang renewal process.
static RAP	fromHyperExp(double p, double lambda1, double lambda2)	Creates a RAP from a Hyper-exponential distribution.
static RAP	fromMAP(MAP map)	Creates a RAP from a Markovian Arrival Process (MAP).
static RAP	fromPoisson(double rate)	Creates a RAP from an exponential renewal process (Poisson process).
Matrix	getH0()	Gets the H0 matrix (hidden transition rates).
Matrix	getH1()	Gets the H1 matrix (visible transition rates).
long	getNumberOfPhases()	Gets the number of phases in this Markovian distribution.
MatrixCell	getProcess()	Gets the matrix representation of this Markovian process.

Methods inherited from class jline.lang.processes.Markovian

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

Methods inherited from class jline.lang.processes.Distribution

evalProbInterval, getName, 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, toString, wait, wait, wait

Methods inherited from interface jline.lang.Copyable

copy

Constructor Details

RAP

public RAP(Matrix H0,
 Matrix H1)

Creates a Rational Arrival Process with specified H0 and H1 matrices.

Parameters:

H0 - matrix of hidden transition rates (square matrix)

H1 - matrix of visible transition rates (square matrix, same size as H0)

Throws:

IllegalArgumentException - if the representation is invalid

Method Details

getH0

public Matrix getH0()

Gets the H0 matrix (hidden transition rates).

Returns:

the H0 matrix

getH1

public Matrix getH1()

Gets the H1 matrix (visible transition rates).

Returns:

the H1 matrix

getNumberOfPhases

public long getNumberOfPhases()

Description copied from class: Markovian

Gets the number of phases in this Markovian distribution.

Overrides:

getNumberOfPhases in class Markovian

Returns:

the number of phases

getProcess

public MatrixCell getProcess()

Description copied from class: Markovian

Gets the matrix representation of this Markovian process.

Overrides:

getProcess in class Markovian

Returns:

MatrixCell containing D0, D1, ... matrices

fitMomentsAndCorrelations

public static RAP fitMomentsAndCorrelations(double[] moments,
 double[] correlations)

Creates a RAP by fitting the given moments and correlations. Uses BuTools RAPFromMomentsAndCorrelations algorithm if available.

Parameters:

moments - array of moments

correlations - array of lag-k correlations

Returns:

a RAP matching the given moments and correlations

Throws:

UnsupportedOperationException - if fitting algorithm is not yet implemented

fitMoments

public static RAP fitMoments(double[] moments)

Creates a RAP by fitting the given moments. Uses BuTools RAPFromMoments algorithm if available.

Parameters:

moments - array of moments

Returns:

a RAP matching the given moments

Throws:

UnsupportedOperationException - if fitting algorithm is not yet implemented

fromMAP

public static RAP fromMAP(MAP map)

Creates a RAP from a Markovian Arrival Process (MAP). This shows that MAP is a special case of RAP.

Parameters:

map - the MAP to convert to RAP

Returns:

a RAP equivalent to the given MAP

fromPoisson

public static RAP fromPoisson(double rate)

Creates a RAP from an exponential renewal process (Poisson process).

Parameters:

rate - the arrival rate (lambda)

Returns:

a RAP representing a Poisson process

fromErlang

public static RAP fromErlang(int k,
 double rate)

Creates a RAP from an Erlang renewal process.

Parameters:

k - number of phases

rate - rate parameter for each phase

Returns:

a RAP representing an Erlang renewal process

fromHyperExp

public static RAP fromHyperExp(double p,
 double lambda1,
 double lambda2)

Creates a RAP from a Hyper-exponential distribution.

Parameters:

p - probability of using the first phase

lambda1 - rate parameter for the first phase

lambda2 - rate parameter for the second phase

Returns:

a RAP representing a Hyper-exponential renewal process

fitMeanAndSCV

public static RAP fitMeanAndSCV(double mean,
 double scv)

Creates a RAP by fitting the given mean and squared coefficient of variation (SCV). Uses Erlang fitting for SCV invalid input: '<' 1 and HyperExp fitting for SCV >= 1.

Parameters:

mean - target mean inter-arrival time

scv - target squared coefficient of variation

Returns:

a RAP matching the given mean and SCV