Package jline.lang.processes

Class MMDP

  • All Implemented Interfaces:
    java.io.Serializable , jline.lang.Copyable 
    
public class MMDP
extends Markovian implements Serializable

    A Markov-Modulated Deterministic Process (MMDP) for fluid queue modeling. Models fluid flow with deterministic rates modulated by a background Markov chain. Suitable for arrival and service processes in Markovian fluid queues analyzed by the mfq method of SolverFLD. The (Q, R) parameterization follows BUTools conventions: - Q: Generator matrix of the modulating CTMC (row sums = 0) - R: Diagonal matrix of deterministic rates per state MMDP is the deterministic analogue of MMPP: - MMPP: Poisson arrival rates modulated by a Markov chain - MMDP: Deterministic rates modulated by a Markov chain

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description

    • Constructor Summary

      Constructors 
      Constructor Description
      MMDP() Creates an empty MMDP instance.
      MMDP(Matrix Q, Matrix R) Creates an MMDP with specified generator Q and rate matrix R.

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description

    • Method Summary

      Modifier and Type Method Description
      Matrix Q() Returns the generator matrix Q.
      Matrix R() Returns the rate matrix R (diagonal).
      Matrix r() Returns the rate vector (diagonal of R).
      long getNumberOfPhases() Gets the number of phases in this Markovian distribution.
      double getMeanRate() Computes the stationary mean rate.
      double getMean() Gets the mean of this Markovian distribution.
      double getRate() Gets the rate of this distribution (inverse of mean).
      double getSCV() Computes the squared coefficient of variation of rates.
      MatrixCell getProcess() Gets the matrix representation of this Markovian process.
      static MMDP fromMAP(MAP map) Converts a MAP to MMDP (deterministic representation).
      static MMDP fromMMPP2(double r0, double r1, double sigma0, double sigma1) Creates an MMDP from MMPP2 parameters.
      static boolean isFeasible(Matrix Q, Matrix R) Checks if the given (Q, R) matrices define a valid MMDP.
      String toString()

      • Methods inherited from class jline.lang.processes.Markovian

        D, acf, 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, numPhases, numberOfPhases, 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 jline.lang.Copyable

        copy

      • Methods inherited from class java.lang.Object

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

    • Constructor Detail

      • MMDP

        MMDP()
        Creates an empty MMDP instance.

      • MMDP

        MMDP(Matrix Q, Matrix R)
        Creates an MMDP with specified generator Q and rate matrix R.
        Parameters:
        Q - n×n generator matrix (row sums = 0)
        R - n×n diagonal matrix of deterministic rates, or n-vector

    • Method Detail

      • Q

         Matrix Q()

        Returns the generator matrix Q.

        Returns:

        n×n generator matrix of the modulating CTMC

      • R

         Matrix R()

        Returns the rate matrix R (diagonal).

        Returns:

        n×n diagonal matrix of deterministic rates

      • r

         Matrix r()

        Returns the rate vector (diagonal of R).

        Returns:

        n-vector of deterministic rates per phase

      • getNumberOfPhases

         long getNumberOfPhases()

        Gets the number of phases in this Markovian distribution.

        Returns:

        the number of phases

      • getMeanRate

         double getMeanRate()

        Computes the stationary mean rate. For MMDP: E[r] = π * diag(R), where π is the stationary distribution of the modulating CTMC with generator Q.

        Returns:

        stationary mean deterministic rate

      • getMean

         double getMean()

        Gets the mean of this Markovian distribution.

        Returns:

        the mean value, or NaN if the process contains NaN values

      • getRate

         double getRate()

        Gets the rate of this distribution (inverse of mean).

        Returns:

        the rate value (1/mean)

      • getSCV

         double getSCV()

        Computes the squared coefficient of variation of rates. Computes Var[r]/E[r]^2 where expectation is over the stationary distribution of the modulating CTMC.

        Returns:

        squared coefficient of variation

      • getProcess

         MatrixCell getProcess()

        Gets the matrix representation of this Markovian process.

        Returns:

        MatrixCell containing D0, D1, ... matrices

      • fromMAP

         static MMDP fromMAP(MAP map)

        Converts a MAP to MMDP (deterministic representation). Converts a Markovian Arrival Process to a Markov-Modulated Deterministic Process by extracting the full generator and using row sums of D1 as the deterministic rates.

        Parameters:
        map - MAP object to convert
        Returns:

        MMDP representation of the MAP

      • fromMMPP2

         static MMDP fromMMPP2(double r0, double r1, double sigma0, double sigma1)

        Creates an MMDP from MMPP2 parameters. Creates a 2-state MMDP using the same parameterization as MMPP2.

        Parameters:
        r0 - rate in state 0
        r1 - rate in state 1
        sigma0 - transition rate from state 0 to state 1
        sigma1 - transition rate from state 1 to state 0
        Returns:

        2-state MMDP

      • isFeasible

         static boolean isFeasible(Matrix Q, Matrix R)

        Checks if the given (Q, R) matrices define a valid MMDP. Requirements: - Q must be a valid generator (square, row sums = 0, proper signs) - R must be diagonal with non-negative entries - Q and R must have compatible dimensions

        Parameters:
        Q - generator matrix
        R - rate matrix
        Returns:

        true if valid MMDP, false otherwise