Package jline.lang.processes

Class MAP

java.lang.Object
jline.lang.processes.Distribution
jline.lang.processes.ContinuousDistribution
jline.lang.processes.Markovian
jline.lang.processes.MarkovModulated
jline.lang.processes.MAP
All Implemented Interfaces:
Serializable, Copyable
public class MAP extends MarkovModulated implements Serializable
A Markovian Arrival Process
See Also:

  • Constructor Details

  • Method Details

    • rand

      public static MAP rand()

    • rand

      public static MAP rand(int order)

    • randn

      public static MAP randn()

    • randn

      public static MAP randn(int order, double mu, double sigma)

    • D

      public Matrix D(int i)
      Description copied from class: Markovian
      Gets the i-th matrix of the Markovian arrival process representation.
      Overrides:
      D in class Markovian
      Parameters:
      i - the matrix index (0 for D0, 1 for D1, etc.)
      Returns:
      the matrix at index i

    • evalCDF

      public double evalCDF(double t)
      Evaluates the cumulative distribution function (CDF) at time t. For a MAP, this represents the probability that an inter-arrival time is less than or equal to t.
      Overrides:
      evalCDF in class Markovian
      Parameters:
      t - the time value
      Returns:
      the CDF value at time t

    • evalLST

      public double evalLST(double s)
      Evaluates the Laplace-Stieltjes Transform (LST) at parameter s. For a MAP, LST(s) = alpha * (-T + s*I)^(-1) * t where alpha is the initial probability vector, T is the subgenerator, and t is the exit rate vector.
      Overrides:
      evalLST in class Markovian
      Parameters:
      s - the transform parameter
      Returns:
      the LST value at parameter s

    • getMean

      public double getMean()
      Description copied from class: Markovian
      Gets the mean of this Markovian distribution.
      Overrides:
      getMean in class Markovian
      Returns:
      the mean value, or NaN if the process contains NaN values

    • 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

    • getRate

      public double getRate()
      Description copied from class: Distribution
      Gets the rate of this distribution (inverse of mean).
      Overrides:
      getRate in class Markovian
      Returns:
      the rate value (1/mean)

    • getRenewalProcess

      public MatrixCell getRenewalProcess()

    • getSCV

      public double getSCV()
      Description copied from class: Distribution
      Gets the squared coefficient of variation (SCV) of this distribution. SCV = Var(X) / E[X]^2.
      Overrides:
      getSCV in class Markovian
      Returns:
      the squared coefficient of variation

    • getSkewness

      public double getSkewness()
      Description copied from class: Distribution
      Gets the skewness of this distribution. Skewness measures the asymmetry of the probability distribution.
      Overrides:
      getSkewness in class Markovian
      Returns:
      the skewness value

    • getVar

      public double getVar()
      Description copied from class: Distribution
      Gets the variance of this distribution. Computed as SCV * mean^2.
      Overrides:
      getVar in class Markovian
      Returns:
      the variance

    • toTimeReversed

      public MAP toTimeReversed()

    • evalMeanT

      public double evalMeanT(double t)
      Evaluates the mean of the counting process at time t. For MAP, this gives the expected number of arrivals by time t.
      Overrides:
      evalMeanT in class Markovian
      Parameters:
      t - the time value
      Returns:
      the mean number of arrivals by time t

    • evalVarT

      public double evalVarT(double t)
      Evaluates the variance of the counting process at time t. For MAP, this provides the variance of the number of arrivals by time t.
      Overrides:
      evalVarT in class Markovian
      Parameters:
      t - the time value
      Returns:
      the variance of arrivals by time t

    • evalACFT

      public Matrix evalACFT(int[] lags, double timescale)
      Evaluates the autocorrelation function at given lags and timescale. For MAP, this measures the correlation between arrivals at different times.
      Overrides:
      evalACFT in class MarkovModulated
      Parameters:
      lags - array of lag values
      timescale - the timescale parameter
      Returns:
      matrix of autocorrelation values

    • evalPDF

      public double evalPDF(double t)
      Evaluates the probability density function (PDF) at time t. For MAP, this is the derivative of the CDF.
      Parameters:
      t - the time value
      Returns:
      the PDF value at time t

    • normalize

      public void normalize()
      Normalizes the MAP so that D0+D1 forms a proper infinitesimal generator. Each row sum of (D0+D1) should equal zero for a valid generator.

    • fitCentralAndACFDecay

      public static MAP fitCentralAndACFDecay(double mean, double var, double skew, double gamma2)
      Fit MAP from central moments and autocorrelation function decay. This creates a MAP that matches the given statistical properties.
      Parameters:
      mean - the mean inter-arrival time
      var - the variance of inter-arrival times
      skew - the skewness of inter-arrival times
      gamma2 - the autocorrelation function decay parameter
      Returns:
      fitted MAP process

    • fitRawMomentsAndACFDecay

      public static MAP fitRawMomentsAndACFDecay(double m1, double m2, double m3, double gamma2)
      Fit MAP from raw moments and autocorrelation function decay. This is a simplified version that creates a 2-phase MAP.
      Parameters:
      m1 - first raw moment
      m2 - second raw moment
      m3 - third raw moment
      gamma2 - autocorrelation function decay parameter
      Returns:
      fitted MAP process

    • toString

      public String toString()
      Returns a string representation of this MAP process.
      Overrides:
      toString in class Object
      Returns:
      string representation showing dimensions and basic properties

    • equals

      public boolean equals(Object obj)
      Checks if this MAP is equal to another object.
      Overrides:
      equals in class Object
      Parameters:
      obj - the object to compare with
      Returns:
      true if equal, false otherwise

    • hashCode

      public int hashCode()
      Returns the hash code for this MAP process.
      Overrides:
      hashCode in class Object
      Returns:
      hash code based on matrix contents