Package jline.api.qsys

Class QsysBmapM1Result

java.lang.Object
jline.api.qsys.QsysBmapM1Result
public class QsysBmapM1Result extends Object
Result of the matrix-analytic (M/G/1-type) analysis of a BMAP/M/1 queue.

Beyond the usual performance measures it exposes the intermediate matrix-analytic quantities themselves, so that the algorithm can be inspected and taught rather than only its output. Port of MATLAB qsys_bmapm1.m.

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    final Matrix
    A
    A = A0 + A1 + sum_k Bk[k], the phase process of the randomized chain.
    final Matrix
    A0
    Randomized block A0 = (mu/q)I: a service completion, level down by one.
    final Matrix
    A1
    Randomized block A1 = (1/q)(D0 - mu*I) + I: level unchanged.
    final Matrix
    alpha
    Stationary vector of A.
    final String
    analyzer
    Name of the analyzer.
    final Matrix
    B0
    Boundary local block B0 = (1/q)D0 + I, used at level 0 where no service can complete.
    final Matrix[]
    Bk
    Randomized blocks Bk[k] = (1/q)D_k, raising the level by k; index 1..K.
    final double
    decayRate
    Geometric decay rate of the level probabilities, measured as the limiting ratio pi_(n+1)/pi_n.
    final double
    drift
    alpha*(sum_k k*Bk[k])*e - alpha*A0*e; the queue is stable iff this is negative.
    final Matrix
    G
    Minimal non-negative solution of G = A0 + A1*G + sum_k Bk[k]*G^(k+1).
    final double
    lambda
    Mean arrival rate, theta * sum_k k*D_k * e.
    final Matrix
    levelProb
    Level probabilities pi_n as rows (level 0 first).
    final double
    meanQueueLength
    Mean number in system.
    final double
    pi0
    Probability the system is empty (equals 1-rho exactly).
    final double
    q
    Uniformization constant actually used.
    final double
    rho
    Offered load lambda/mu.
    final Matrix
    theta
    Stationary vector of the BMAP phase process, generator sum_k D_k.
    final double
    throughput
    Throughput, equal to lambda.
    final double
    truncError
    Relative truncation residual at truncLevel.
    final int
    truncLevel
    Level truncation used for the level distribution.
    final double
    utilization
    Server utilization, equal to rho.

  • Constructor Summary

    Constructors
    Constructor
    Description
    QsysBmapM1Result(Matrix theta, double lambda, double rho, double q, Matrix A0, Matrix A1, Matrix B0, Matrix[] Bk, Matrix A, Matrix alpha, Matrix G, double drift, double decayRate, Matrix levelProb, double pi0, double meanQueueLength, double utilization, double throughput, int truncLevel, double truncError, String analyzer)
     

  • Method Summary

    Methods inherited from class java.lang.Object

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

  • Field Details

    • theta

      public final Matrix theta
      Stationary vector of the BMAP phase process, generator sum_k D_k.

    • lambda

      public final double lambda
      Mean arrival rate, theta * sum_k k*D_k * e.

    • rho

      public final double rho
      Offered load lambda/mu.

    • q

      public final double q
      Uniformization constant actually used.

    • A0

      public final Matrix A0
      Randomized block A0 = (mu/q)I: a service completion, level down by one.

    • A1

      public final Matrix A1
      Randomized block A1 = (1/q)(D0 - mu*I) + I: level unchanged.

    • B0

      public final Matrix B0
      Boundary local block B0 = (1/q)D0 + I, used at level 0 where no service can complete.

    • Bk

      public final Matrix[] Bk
      Randomized blocks Bk[k] = (1/q)D_k, raising the level by k; index 1..K.

    • A

      public final Matrix A
      A = A0 + A1 + sum_k Bk[k], the phase process of the randomized chain.

    • alpha

      public final Matrix alpha
      Stationary vector of A.

    • G

      public final Matrix G
      Minimal non-negative solution of G = A0 + A1*G + sum_k Bk[k]*G^(k+1).

    • drift

      public final double drift
      alpha*(sum_k k*Bk[k])*e - alpha*A0*e; the queue is stable iff this is negative.

    • decayRate

      public final double decayRate
      Geometric decay rate of the level probabilities, measured as the limiting ratio pi_(n+1)/pi_n. Reported rather than derived from a spectral convention so that it is unambiguous.

    • levelProb

      public final Matrix levelProb
      Level probabilities pi_n as rows (level 0 first).

    • pi0

      public final double pi0
      Probability the system is empty (equals 1-rho exactly).

    • meanQueueLength

      public final double meanQueueLength
      Mean number in system.

    • utilization

      public final double utilization
      Server utilization, equal to rho.

    • throughput

      public final double throughput
      Throughput, equal to lambda.

    • truncLevel

      public final int truncLevel
      Level truncation used for the level distribution.

    • truncError

      public final double truncError
      Relative truncation residual at truncLevel.

    • analyzer

      public final String analyzer
      Name of the analyzer.

  • Constructor Details

    • QsysBmapM1Result

      public QsysBmapM1Result(Matrix theta, double lambda, double rho, double q, Matrix A0, Matrix A1, Matrix B0, Matrix[] Bk, Matrix A, Matrix alpha, Matrix G, double drift, double decayRate, Matrix levelProb, double pi0, double meanQueueLength, double utilization, double throughput, int truncLevel, double truncError, String analyzer)