Package jline.api.qsys

Class Qsys_mg11_retrial

java.lang.Object

jline.api.qsys.Qsys_mg11_retrial

public final class Qsys_mg11_retrial
extends Object

Exact mean performance of the M/G/1/1 retrial queue.

Port of matlab/src/api/qsys/qsys_mg11_retrial.m. Poisson arrivals of rate lambda, one server with a general service time of rate mu and squared coefficient of variation cs^2, no waiting room, and blocked customers that join an orbit and retry after exponential delays.

LINEAR (default, classical): each orbiting customer retries at rate nu (Falin and Templeton 1997, Sec. 1.3): E[Norb] = lambda^2 b2/(2(1-rho)) + lambda rho/(nu(1-rho)), rho < 1.

CONSTANT: the orbit retries at rate nu whatever its size; with a = nu/(lambda+nu), E[N] = (rho(1-rho) + lambda^2 b2/2)/(a - rho), rho < a.

References: G. I. Falin and J. G. C. Templeton, Retrial Queues, Chapman and Hall, 1997; T. Phung-Duc, Retrial queueing models: a survey on theory and applications, arXiv:1906.09560, 2019, Sec. 3.1.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	Qsys_mg11_retrial.Result	Mean performance of the M/G/1/1 retrial queue.

Method Summary

Modifier and Type	Method	Description
static Qsys_mg11_retrial.Result	qsys_mg11_retrial(double lambda, double mu, double cs, double nu)	LINEAR policy.
static Qsys_mg11_retrial.Result	qsys_mg11_retrial(double lambda, double mu, double cs, double nu, int policy)

Methods inherited from class java.lang.Object

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

Method Details

qsys_mg11_retrial

public static Qsys_mg11_retrial.Result qsys_mg11_retrial(double lambda,
 double mu,
 double cs,
 double nu)

LINEAR policy.

qsys_mg11_retrial

public static Qsys_mg11_retrial.Result qsys_mg11_retrial(double lambda,
 double mu,
 double cs,
 double nu,
 int policy)

Parameters:

lambda - arrival rate

mu - service rate (mean service time 1/mu)

cs - coefficient of variation of the service time

nu - retrial rate (per customer under LINEAR, of the orbit under CONSTANT)

policy - RetrialPolicy.LINEAR or RetrialPolicy.CONSTANT