Package jline.api.qsys

Class Qsys_mxg1

java.lang.Object
jline.api.qsys.Qsys_mxg1
public final class Qsys_mxg1 extends Object
M^X/G/1 FCFS queue with batch Poisson arrivals. Port of MATLAB qsys_mxg1.m.

With E[S] = 1/mu and E[S^2] = (1+cs^2)/mu^2 (Haverkort 1998, eq. 5.31): Wq = lambda E[S^2] / (2(1-rho)) + E[X(X-1)] E[S] / (2 E[X] (1-rho)), where lambda = lambdaBatch E[X] and rho = lambda E[S]. cs = 1 gives qsys_mxm1 and a batch size of 1 gives qsys_mg1.

  • Method Details

    • qsys_mxg1

      public static QsysMeanValueResult qsys_mxg1(double lambdaBatch, double mu, double cs, double EX, double EX2)
      M^X/G/1 from the first two raw moments of the batch size.
      Parameters:
      lambdaBatch - batch arrival rate
      mu - service rate of a job
      cs - coefficient of variation of the service time
      EX - mean batch size
      EX2 - second raw moment of the batch size
      Returns:
      W, Wq, U = rho, Q = lambda W

    • qsys_mxg1

      public static QsysMeanValueResult qsys_mxg1(double lambdaBatch, double mu, double cs, double[] batchSizes, double[] pmf)
      M^X/G/1 from a batch-size pmf (weights are renormalised).

    • qsys_mxg1_var

      public static QsysMeanValueResult qsys_mxg1_var(double lambdaBatch, double mu, double cs, double EX, double varX)
      M^X/G/1 from the mean and variance of the batch size.