Package jline.api.qsys

Class Qsys_retrial_isstable

java.lang.Object

jline.api.qsys.Qsys_retrial_isstable

public final class Qsys_retrial_isstable
extends Object

Stability (positive recurrence) of the M/M/c/c retrial queue.

Port of matlab/src/api/qsys/qsys_retrial_isstable.m. Poisson arrivals of rate lambda, c exponential servers of rate mu and exponential retrials; lambda and mu may be vectors, one entry per class.

Conditions: a finite orbit, gamma > 0, or q < 1 under LINEAR always gives a stable chain. LINEAR with q = 1 and gamma = 0 is stable iff sum_k lambda_k p_k / mu_k < c (Falin and Templeton 1997, Sec. 2.1 for p = 1). CONSTANT, single class, gamma = 0: with x = B((lambda+alpha)/mu, c) the orbit drift is negative iff lambda p x < alpha (1-x) + alpha (1-q) x (Artalejo, Gomez-Corral and Neuts 2001 for p = q = 1). A multiclass queue under CONSTANT, or one mixing self-limiting and persistent classes, is refused (LINE:unsupported:Retrial).

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	Qsys_retrial_isstable.Result	Verdict, slack of the condition (positive iff stable) and the rule applied.

Method Summary

Modifier and Type	Method	Description
static Qsys_retrial_isstable.Result	qsys_retrial_isstable(double[] lambda, double[] mu, int c, double[] alpha, int policy, double[] p, double[] q, double[] gamma, double maxOrbit)	Multiclass form.
static Qsys_retrial_isstable.Result	qsys_retrial_isstable(double lambda, double mu, int c, double alpha)	Single-class form with LINEAR policy, p = q = 1, gamma = 0, unbounded orbit.
static Qsys_retrial_isstable.Result	qsys_retrial_isstable(double lambda, double mu, int c, double alpha, int policy, double p, double q, double gamma, double maxOrbit)	Single-class form.

Methods inherited from class java.lang.Object

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

Method Details

qsys_retrial_isstable

public static Qsys_retrial_isstable.Result qsys_retrial_isstable(double lambda,
 double mu,
 int c,
 double alpha)

Single-class form with LINEAR policy, p = q = 1, gamma = 0, unbounded orbit.

qsys_retrial_isstable

public static Qsys_retrial_isstable.Result qsys_retrial_isstable(double lambda,
 double mu,
 int c,
 double alpha,
 int policy,
 double p,
 double q,
 double gamma,
 double maxOrbit)

Single-class form.

qsys_retrial_isstable

public static Qsys_retrial_isstable.Result qsys_retrial_isstable(double[] lambda,
 double[] mu,
 int c,
 double[] alpha,
 int policy,
 double[] p,
 double[] q,
 double[] gamma,
 double maxOrbit)

Multiclass form. Any of mu, alpha, p, q, gamma may be a length-1 array (expanded to all classes); p, q, gamma and alpha may be null for their defaults (1, 1, 0, 0).

Parameters:

maxOrbit - orbit capacity, negative or infinite for unbounded