Package jline.api.qsys

Class Qsys_mg1_vacation

java.lang.Object

jline.api.qsys.Qsys_mg1_vacation

public final class Qsys_mg1_vacation
extends Object

M/G/1 (and M^X/G/1) FCFS queue with exhaustive service and server vacations. Port of MATLAB qsys_mg1_vacation.m.

• "multiple" (Haverkort 1998, eq. 5.38 and 5.41): Wq = E[V^2]/(2E[V]) + Wq(M^X/G/1);
• "single" (Haverkort 1998, eq. 5.39): Wq = lambda E[V^2] / (2 (V*(lambda) + lambda E[V])) + Wq(M^X/G/1), with V*(lambda) the vacation LST at the batch arrival rate.

lambda is the batch rate and each batch brings X jobs with moments EX, EX2.

Method Summary

Modifier and Type	Method	Description
static QsysMeanValueResult	qsys_mg1_vacation(double lambda, double mu, double cs, double EV, double EV2)	Multiple vacations with single (unit-batch) Poisson arrivals.
static QsysMeanValueResult	qsys_mg1_vacation(double lambda, double mu, double cs, double EV, double EV2, String policy, double vlst, double EX, double EX2)	Full form.

Methods inherited from class java.lang.Object

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

Method Details

qsys_mg1_vacation

public static QsysMeanValueResult qsys_mg1_vacation(double lambda,
 double mu,
 double cs,
 double EV,
 double EV2)

Multiple vacations with single (unit-batch) Poisson arrivals.

qsys_mg1_vacation

public static QsysMeanValueResult qsys_mg1_vacation(double lambda,
 double mu,
 double cs,
 double EV,
 double EV2,
 String policy,
 double vlst,
 double EX,
 double EX2)

Full form.

Parameters:

lambda - (batch) arrival rate

mu - service rate of a job

cs - coefficient of variation of the service time

EV - mean vacation time (EV > 0)

EV2 - second raw moment of the vacation time

policy - "multiple" or "single"

vlst - vacation LST at lambda, V*(lambda); read only by "single"

EX - mean batch size (1 for single arrivals)

EX2 - second raw moment of the batch size (1 for single arrivals)

Returns:

W, Wq, U = lambda EX / mu, Q = lambda EX W