Package jline.api.qsys

Class Qsys_mxm1Kt

  • All Implemented Interfaces:
    
public final class Qsys_mxm1Kt

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description

    • Field Summary

      Fields 
      Modifier and Type Field Description

    • Constructor Summary

      Constructors 
      Constructor Description

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description

    • Method Summary

      Modifier and Type Method Description
      final static Ret.qsys qsys_mxm1(Double lambdaBatch, Double mu, Double meanBatchSize, Double secondMomentBatchSize) Analyzes an MX/M/1 queueing system using batch arrival moments.
      final static Ret.qsys qsys_mxm1(Double lambdaBatch, Double mu, IntArray batchSizes, DoubleArray pmf) Analyzes an MX/M/1 queueing system using batch sizes and PMF.
      final static Ret.qsys qsys_mxm1_var(Double lambdaBatch, Double mu, Double meanBatchSize, Double varianceBatchSize) Analyzes an MX/M/1 queueing system using mean and variance of batch size.

      • Methods inherited from class java.lang.Object

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

    • Constructor Detail

    • Method Detail

      • qsys_mxm1

         final static Ret.qsys qsys_mxm1(Double lambdaBatch, Double mu, Double meanBatchSize, Double secondMomentBatchSize)

        Analyzes an MX/M/1 queueing system using batch arrival moments.

        Uses the correct MX/M/1 formula that accounts for both queueing delay and internal batch delay (jobs within the same batch wait for each other):

        • Effective arrival rate: λ = λ_b * EX

        • Utilization: ρ = λ / μ

        • Mean waiting time in queue: W_q = ρ/(μ(1-ρ)) + (EX² - EX)/(2μE1-ρ) \_________/ \__________________________/ M/M/1 term Internal batch delay

        • Mean time in system: W = W_q + 1/μ

        Parameters:
        lambdaBatch - Batch arrival rate (λ_b)
        mu - Service rate
        meanBatchSize - Mean batch size EX
        secondMomentBatchSize - Second moment of batch size EX²
        Returns:

        qsys containing average time in system (W) and utilization (rho)

      • qsys_mxm1

         final static Ret.qsys qsys_mxm1(Double lambdaBatch, Double mu, IntArray batchSizes, DoubleArray pmf)

        Analyzes an MX/M/1 queueing system using batch sizes and PMF.

        Parameters:
        lambdaBatch - Batch arrival rate (λ_b)
        mu - Service rate
        batchSizes - Array of possible batch sizes
        pmf - Probability mass function for batch sizes (will be normalized)
        Returns:

        qsys containing average time in system (W) and utilization (rho)

      • qsys_mxm1_var

         final static Ret.qsys qsys_mxm1_var(Double lambdaBatch, Double mu, Double meanBatchSize, Double varianceBatchSize)

        Analyzes an MX/M/1 queueing system using mean and variance of batch size.

        Parameters:
        lambdaBatch - Batch arrival rate (λ_b)
        mu - Service rate
        meanBatchSize - Mean batch size EX
        varianceBatchSize - Variance of batch size Var(X)
        Returns:

        qsys containing average time in system (W) and utilization (rho)