Package jline.api

Class QSYS

java.lang.Object
jline.api.QSYS
public class QSYS extends Object
APIs for evaluating queueing systems such as M/M/1, M/M/k, M/G/1, and others.

  • Constructor Summary

    Constructors
    Constructor
    Description
    QSYS()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    static double
    ErlangC(double nu, int C)
    Calculates the probability that an arriving customer is forced to join the queue (i.e., all servers are occupied) in an M/M/k system.
    static Ret.qsys
    qsys_gig1_approx_allencunneen(double lambda, double mu, double ca, double cs)
    Analyzes a G/G/1 queueing system using the Allen-Cunneen approximation.
    static Ret.qsys
    qsys_gig1_approx_heyman(double lambda, double mu, double ca, double cs)
    Analyzes a G/G/1 queueing system using Heyman's approximation.
    static Ret.qsys
    qsys_gig1_approx_klb(double lambda, double mu, double ca, double cs)
    Analyzes a G/G/1 queueing system using the Kramer-Langenbach-Belz (KLB) approximation.
    static Ret.qsys
    qsys_gig1_approx_kobayashi(double lambda, double mu, double ca, double cs)
    Analyzes a G/G/1 queueing system using Kobayashi's approximation.
    static Ret.qsys
    qsys_gig1_approx_marchal(double lambda, double mu, double ca, double cs)
    Analyzes a G/G/1 queueing system using Marchal's approximation.
    static Ret.qsys
    qsys_gig1_ubnd_kingman(double lambda, double mu, double ca, double cs)
    Calculates an upper bound on the waiting time for a G/G/1 system using Kingman's formula.
    static Ret.qsys
    qsys_gigk_approx(double lambda, double mu, double ca, double cs, int k)
    Analyzes a G/G/k queueing system using an approximation method.
    static Ret.qsys
    qsys_gigk_approx_kingman(double lambda, double mu, double ca, double cs, int k)
    Analyzes a G/G/k queueing system using Kingman's approximation.
    static Ret.qsys
    qsys_gm1(double sigma, double mu)
    Analyzes a G/M/1 queueing system.
    static Ret.qsys
    qsys_mg1(double lambda, double mu, double cs)
    Analyzes an M/G/1 queueing system.
    static Ret.qsys
    qsys_mm1(double lambda, double mu)
    Analyzes an M/M/1 queueing system.
    static Ret.qsys
    qsys_mmk(double lambda, double mu, int k)
    Analyzes an M/M/k queueing system.

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • QSYS

      public QSYS()

  • Method Details

    • qsys_mm1

      public static Ret.qsys qsys_mm1(double lambda, double mu)
      Analyzes an M/M/1 queueing system.
      Parameters:
      lambda - Arrival rate.
      mu - Service rate.
      Returns:
      qsysReturn containing average waiting time (W) and utilization (rho).

    • qsys_mmk

      public static Ret.qsys qsys_mmk(double lambda, double mu, int k)
      Analyzes an M/M/k queueing system.
      Parameters:
      lambda - Arrival rate.
      mu - Service rate.
      k - Number of servers.
      Returns:
      qsysReturn containing average waiting time (W) and utilization (rho).

    • qsys_mg1

      public static Ret.qsys qsys_mg1(double lambda, double mu, double cs)
      Analyzes an M/G/1 queueing system.
      Parameters:
      lambda - Arrival rate.
      mu - Service rate.
      cs - Coefficient of variation of the service time.
      Returns:
      qsysReturn containing average waiting time (W) and modified utilization (rhohat).

    • qsys_gigk_approx

      public static Ret.qsys qsys_gigk_approx(double lambda, double mu, double ca, double cs, int k)
      Analyzes a G/G/k queueing system using an approximation method.
      Parameters:
      lambda - Arrival rate.
      mu - Service rate.
      ca - Coefficient of variation of the arrival process.
      cs - Coefficient of variation of the service time.
      k - Number of servers.
      Returns:
      qsysReturn containing average waiting time (W) and modified utilization (rhohat).

    • qsys_gigk_approx_kingman

      public static Ret.qsys qsys_gigk_approx_kingman(double lambda, double mu, double ca, double cs, int k)
      Analyzes a G/G/k queueing system using Kingman's approximation.
      Parameters:
      lambda - Arrival rate.
      mu - Service rate.
      ca - Coefficient of variation of the arrival process.
      cs - Coefficient of variation of the service time.
      k - Number of servers.
      Returns:
      qsysReturn containing average waiting time (W) and modified utilization (rhohat).

    • qsys_gig1_ubnd_kingman

      public static Ret.qsys qsys_gig1_ubnd_kingman(double lambda, double mu, double ca, double cs)
      Calculates an upper bound on the waiting time for a G/G/1 system using Kingman's formula.
      Parameters:
      lambda - Arrival rate.
      mu - Service rate.
      ca - Coefficient of variation of the arrival process.
      cs - Coefficient of variation of the service time.
      Returns:
      qsysReturn containing upper bound on average waiting time (W) and modified utilization (rhohat).

    • qsys_gig1_approx_heyman

      public static Ret.qsys qsys_gig1_approx_heyman(double lambda, double mu, double ca, double cs)
      Analyzes a G/G/1 queueing system using Heyman's approximation.
      Parameters:
      lambda - Arrival rate.
      mu - Service rate.
      ca - Coefficient of variation of the arrival process.
      cs - Coefficient of variation of the service time.
      Returns:
      qsysReturn containing average waiting time (W) and modified utilization (rhohat).

    • qsys_gig1_approx_allencunneen

      public static Ret.qsys qsys_gig1_approx_allencunneen(double lambda, double mu, double ca, double cs)
      Analyzes a G/G/1 queueing system using the Allen-Cunneen approximation.
      Parameters:
      lambda - Arrival rate.
      mu - Service rate.
      ca - Coefficient of variation of the arrival process.
      cs - Coefficient of variation of the service time.
      Returns:
      qsysReturn containing average waiting time (W) and modified utilization (rhohat).

    • qsys_gig1_approx_kobayashi

      public static Ret.qsys qsys_gig1_approx_kobayashi(double lambda, double mu, double ca, double cs)
      Analyzes a G/G/1 queueing system using Kobayashi's approximation.
      Parameters:
      lambda - Arrival rate.
      mu - Service rate.
      ca - Coefficient of variation of the arrival process.
      cs - Coefficient of variation of the service time.
      Returns:
      qsysReturn containing average waiting time (W) and modified utilization (rhohat).

    • qsys_gig1_approx_klb

      public static Ret.qsys qsys_gig1_approx_klb(double lambda, double mu, double ca, double cs)
      Analyzes a G/G/1 queueing system using the Kramer-Langenbach-Belz (KLB) approximation.
      Parameters:
      lambda - Arrival rate.
      mu - Service rate.
      ca - Coefficient of variation of the arrival process.
      cs - Coefficient of variation of the service time.
      Returns:
      qsysReturn containing average waiting time (W) and modified utilization (rhohat).

    • qsys_gig1_approx_marchal

      public static Ret.qsys qsys_gig1_approx_marchal(double lambda, double mu, double ca, double cs)
      Analyzes a G/G/1 queueing system using Marchal's approximation.
      Parameters:
      lambda - Arrival rate.
      mu - Service rate.
      ca - Coefficient of variation of the arrival process.
      cs - Coefficient of variation of the service time.
      Returns:
      qsysReturn containing average waiting time (W) and modified utilization (rhohat).

    • qsys_gm1

      public static Ret.qsys qsys_gm1(double sigma, double mu)
      Analyzes a G/M/1 queueing system.
      Parameters:
      sigma - Traffic intensity.
      mu - Service rate.
      Returns:
      qsysReturn containing average waiting time (W) and utilization (rhohat).

    • ErlangC

      public static double ErlangC(double nu, int C)
      Calculates the probability that an arriving customer is forced to join the queue (i.e., all servers are occupied) in an M/M/k system.
      Parameters:
      nu - Utilization.
      C - The number of servers.
      Returns:
      Probability that an arriving customer is forced to join the queue.