Package jline.api.snc

Class Snc_perc_backlog

java.lang.Object

jline.api.snc.Snc_perc_backlog

public final class Snc_perc_backlog
extends Object

Backlog quantile at a prescribed violation probability.

Inverts Snc_bound_backlog in b: at fixed theta the smallest level for which the bound certifies P{B > b} <= eps is

   b(theta) = sigmaA + sigmaS - log(eps*(1-exp(-theta*(rhoS-rhoA))))/theta,
 

and the reported quantile is its minimum over the feasible thetas. The minimizing theta differs from the one of the forward bound at a given level, which is why the inversion is done in closed form and re-optimized rather than by a search on the forward bound.

Port of matlab/src/api/snc/snc_perc_backlog.m.

Method Summary

Modifier and Type	Method	Description
static SncResult	snc_perc_backlog(SncEnvelope arv, SncEnvelope srv, double eps)
static SncResult	snc_perc_backlog(SncEnvelope arv, SncEnvelope srv, double eps, double thetamax)

Methods inherited from class java.lang.Object

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

Method Details

snc_perc_backlog

public static SncResult snc_perc_backlog(SncEnvelope arv,
 SncEnvelope srv,
 double eps)

Parameters:

arv - arrival envelope

srv - service envelope

eps - violation probability, 0 < eps < 1

Returns:

the quantile and the minimizing theta

snc_perc_backlog

public static SncResult snc_perc_backlog(SncEnvelope arv,
 SncEnvelope srv,
 double eps,
 double thetamax)

Parameters:

arv - arrival envelope

srv - service envelope

eps - violation probability, 0 < eps < 1

thetamax - upper end of the theta search

Returns:

the quantile and the minimizing theta