Package jline.api.fj

Class FJ_rmaxKt

  • All Implemented Interfaces:
    
public final class FJ_rmaxKt

    • 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 Double fj_rmax(Integer K, Double lambda, Double mu) Compute maximum response time R_K^max(rho) for K M/M/1 queues.
      final static Double fj_rmax_erlang(Integer K, Integer k, Double lambda, Double mu) Maximum response time R_K^max for Erlang service times.
      final static Double fj_rmax_evd(Integer K, Double R, Double sigmaR, Boolean calibrated) Maximum response time using Extreme Value Distribution (EVD) approximation.

      • Methods inherited from class java.lang.Object

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

    • Constructor Detail

    • Method Detail

      • fj_rmax

         final static Double fj_rmax(Integer K, Double lambda, Double mu)

        Compute maximum response time R_K^max(rho) for K M/M/1 queues.

        R_K^max(rho) = H_K * R(rho) = H_K / (mu - lambda)

        This serves as an upper bound to the K-way Fork-Join response time.

        Parameters:
        K - Number of parallel servers (positive integer)
        lambda - Arrival rate
        mu - Service rate (mu lambda for stability)
        Returns:

        Expected maximum response time R_K^max(rho)

      • fj_rmax_erlang

         final static Double fj_rmax_erlang(Integer K, Integer k, Double lambda, Double mu)

        Maximum response time R_K^max for Erlang service times.

        Computes the expected maximum response time for K M/E_k/1 queues. For K=2, uses a closed-form formula. For general K, uses numerical integration.

        Parameters:
        K - Number of parallel servers (positive integer)
        k - Number of Erlang stages (positive integer)
        lambda - Arrival rate
        mu - Service rate per Erlang stage (mean service = k/mu)
        Returns:

        Expected maximum response time

      • fj_rmax_evd

         final static Double fj_rmax_evd(Integer K, Double R, Double sigmaR, Boolean calibrated)

        Maximum response time using Extreme Value Distribution (EVD) approximation.

        R_K^max(rho) = R(rho) + (sqrt(6)*ln(K)/pi) * sigma_R(rho)

        Optionally uses a calibrated version from Thomasian et al. 2007 that divides the correction term by 1.27 for improved accuracy.

        Parameters:
        K - Number of parallel servers (positive integer)
        R - Mean response time
        sigmaR - Standard deviation of response time
        calibrated - Use calibrated formula (default: false)
        Returns:

        Approximate maximum response time