Constructor Detail

• MAP

  MAP(MatrixCell map)

• MAP

  MAP()

• MAP

  MAP(Matrix D0, Matrix D1)

Method Detail

• rand

   static MAP rand()

• rand

   static MAP rand(int order)

• randn

   static MAP randn()

• randn

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

• D

   Matrix D(int i)

  Gets the i-th matrix of the Markovian arrival process representation.

  Parameters:

  i - the matrix index (0 for D0, 1 for D1, etc.

  Returns:

  the matrix at index i

• evalCDF

   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.

  Parameters:

  t - the time value

  Returns:

  the CDF value at time t

• evalLST

   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.

  Parameters:

  s - the transform parameter

  Returns:

  the LST value at parameter s

• getMean

   double getMean()

  Gets the mean of this Markovian distribution.

  Returns:

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

• getNumberOfPhases

   long getNumberOfPhases()

  Gets the number of phases in this Markovian distribution.

  Returns:

  the number of phases

• getProcess

   MatrixCell getProcess()

  Gets the matrix representation of this Markovian process.

  Returns:

  MatrixCell containing D0, D1, ... matrices

• getRate

   double getRate()

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

  Returns:

  the rate value (1/mean)

• getRenewalProcess

   MatrixCell getRenewalProcess()

• getSCV

   double getSCV()

  Gets the squared coefficient of variation (SCV) of this distribution. SCV = Var(X) / E[X]^2.

  Returns:

  the squared coefficient of variation

• getSkewness

   double getSkewness()

  Gets the skewness of this distribution. Skewness measures the asymmetry of the probability distribution.

  Returns:

  the skewness value

• getVar

   double getVar()

  Gets the variance of this distribution. Computed as SCV * mean^2.

  Returns:

  the variance

• toTimeReversed

   MAP toTimeReversed()

• evalMeanT

   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.

  Parameters:

  t - the time value

  Returns:

  the mean number of arrivals by time t

• evalVarT

   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.

  Parameters:

  t - the time value

  Returns:

  the variance of arrivals by time t

• evalACFT

   Matrix evalACFT(Array<int> lags, double timescale)

  Evaluates the autocorrelation function at given lags and timescale. For MAP, this measures the correlation between arrivals at different times.

  Parameters:

  lags - array of lag values

  timescale - the timescale parameter

  Returns:

  matrix of autocorrelation values

• evalPDF

   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

   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

   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

   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

   String toString()

  Returns a string representation of this MAP process.

  Returns:

  string representation showing dimensions and basic properties

• equals

   boolean equals(Object obj)

  Checks if this MAP is equal to another object.

  Parameters:

  obj - the object to compare with

  Returns:

  true if equal, false otherwise

• hashCode

   int hashCode()

  Returns the hash code for this MAP process.

  Returns:

  hash code based on matrix contents