Package jline.lang.processes

Class MMDP2

java.lang.Object

jline.lang.processes.Distribution

jline.lang.processes.ContinuousDistribution

jline.lang.processes.Markovian

jline.lang.processes.MMDP

jline.lang.processes.MMDP2

All Implemented Interfaces:

Serializable, Copyable

public class MMDP2
extends MMDP
implements Serializable

A 2-state Markov-Modulated Deterministic Process. Specialized MMDP with exactly 2 phases, using a convenient parameterization analogous to MMPP2. Parameterization:

• r0, r1: Deterministic rates in states 0 and 1
• sigma0: Transition rate from state 0 to state 1
• sigma1: Transition rate from state 1 to state 0

The generator matrix is: Q = [-sigma0, sigma0; sigma1, -sigma1] The rate matrix is: R = diag([r0, r1])

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
MMDP2(double r0, double r1, double sigma0, double sigma1)	Creates a 2-state Markov-Modulated Deterministic Process.

Method Summary

Modifier and Type	Method	Description
double	getMeanRate()	Computes the stationary mean rate (closed-form).
long	getNumberOfPhases()	Gets the number of phases in this Markovian distribution.
double	getSCV()	Computes the squared coefficient of variation (closed-form).
Matrix	Q()	Returns the generator matrix Q (closed-form for 2 states).
Matrix	r()	Returns the rate vector (diagonal of R).
Matrix	R()	Returns the rate matrix R (diagonal, closed-form for 2 states).
String	toString()

Methods inherited from class jline.lang.processes.MMDP

fromMAP, fromMMPP2, getMean, getProcess, getRate, isFeasible

Methods inherited from class jline.lang.processes.Markovian

acf, D, embedded, embeddedProb, evalCDF, evalCDF, evalLST, evalMeanT, evalVarT, getACF, getEmbedded, getEmbeddedProb, getIDC, getIDI, getInitProb, getMoments, getMu, getPhi, 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, wait, wait, wait

Methods inherited from interface jline.lang.Copyable

copy

Constructor Details

MMDP2

public MMDP2(double r0,
 double r1,
 double sigma0,
 double sigma1)

Creates a 2-state Markov-Modulated Deterministic Process.

Parameters:

r0 - deterministic rate in state 0

r1 - deterministic rate in state 1

sigma0 - transition rate from state 0 to state 1

sigma1 - transition rate from state 1 to state 0

Method Details

Q

public Matrix Q()

Returns the generator matrix Q (closed-form for 2 states).

Overrides:

Q in class MMDP

Returns:

2x2 generator matrix

R

public Matrix R()

Returns the rate matrix R (diagonal, closed-form for 2 states).

Overrides:

R in class MMDP

Returns:

2x2 diagonal rate matrix

r

public Matrix r()

Returns the rate vector (diagonal of R).

Overrides:

r in class MMDP

Returns:

2-vector of rates [r0; r1]

getNumberOfPhases

public long getNumberOfPhases()

Description copied from class: Markovian

Gets the number of phases in this Markovian distribution.

Overrides:

getNumberOfPhases in class MMDP

Returns:

the number of phases

getMeanRate

public double getMeanRate()

Computes the stationary mean rate (closed-form). For a 2-state MMDP, the mean rate has the closed form: E[r] = (r0*sigma1 + r1*sigma0) / (sigma0 + sigma1)

Overrides:

getMeanRate in class MMDP

Returns:

stationary mean deterministic rate

getSCV

public double getSCV()

Computes the squared coefficient of variation (closed-form). For a 2-state MMDP, the SCV has a closed form based on the variance of rates over the stationary distribution.

Overrides:

getSCV in class MMDP

Returns:

squared coefficient of variation

toString

public String toString()

Overrides:

toString in class MMDP