Package jline.api.qsys

Class Qsys_gig1_ubnd_kingman

java.lang.Object

jline.api.qsys.Qsys_gig1_ubnd_kingman

public final class Qsys_gig1_ubnd_kingman
extends Object

Method Summary

Modifier and Type	Method	Description
static Ret.qsys	qsys_gig1_ubnd_kingman(double lambda, double mu, double ca, double cs)	Kingman's upper bound on the mean waiting time of a G/G/1 queue: Wq <= lambda*(sa^2+ss^2)/(2*(1-rho)), with sa^2=ca^2/lambda^2 and ss^2=cs^2/mu^2.

Methods inherited from class java.lang.Object

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

Method Details

qsys_gig1_ubnd_kingman

public static Ret.qsys qsys_gig1_ubnd_kingman(double lambda,
 double mu,
 double ca,
 double cs)

Kingman's upper bound on the mean waiting time of a G/G/1 queue: Wq <= lambda*(sa^2+ss^2)/(2*(1-rho)), with sa^2=ca^2/lambda^2 and ss^2=cs^2/mu^2. The returned W adds the mean service time, so it upper-bounds the mean response time (time in system).

Reference: Kingman, J.F.C. (1962). Some inequalities for the queue GI/G/1. Biometrika 49(3/4), 315-324.

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 response time (W) and modified utilization (rhohat).