Package jline.api.snc

Class Snc_bound_backlog

java.lang.Object

jline.api.snc.Snc_bound_backlog

public final class Snc_bound_backlog
extends Object

Violation probability of a backlog level.

For a flow with arrival envelope (sigmaA,rhoA) served by an element with service envelope (sigmaS,rhoS), the backlog of the stable station obeys, for every theta > 0,

   P{B(t) > b} <= exp(-theta*(b-sigmaA-sigmaS)) / (1-exp(-theta*(rhoS-rhoA))),
 

the union bound over the start of the backlogged period summed as a geometric series on the unit-slot time axis. The returned value is the infimum over theta, clipped at 1, and is an UPPER BOUND on the tail, never an estimate of it: the decay rate is asymptotically exact and the prefactor is loose.

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

Method Summary

Modifier and Type	Method	Description
static SncResult	snc_bound_backlog(SncEnvelope arv, SncEnvelope srv, double b)
static SncResult	snc_bound_backlog(SncEnvelope arv, SncEnvelope srv, double b, double thetamax)

Methods inherited from class java.lang.Object

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

Method Details

snc_bound_backlog

public static SncResult snc_bound_backlog(SncEnvelope arv,
 SncEnvelope srv,
 double b)

Parameters:

arv - arrival envelope

srv - service envelope

b - backlog level, units of the envelopes

Returns:

the bound on P{B > b} in [0,1], and the minimizing theta

snc_bound_backlog

public static SncResult snc_bound_backlog(SncEnvelope arv,
 SncEnvelope srv,
 double b,
 double thetamax)

Parameters:

arv - arrival envelope

srv - service envelope

b - backlog level

thetamax - upper end of the theta search

Returns:

the bound on P{B > b} in [0,1], and the minimizing theta