Package jline.api.snc

Class Snc_mean_backlog

java.lang.Object

jline.api.snc.Snc_mean_backlog

public final class Snc_mean_backlog
extends Object

Upper bound on the mean backlog, from integrating the backlog tail bound.

The counterpart of Snc_mean_delay with a = theta: the clipped integral of K*exp(-theta*b) is (log(K)+1)/theta when K >= 1 and K/theta otherwise. The unit of the answer is the unit of the envelopes: jobs when the pair is Snc_env_poisson with Snc_srv_exp, units of work when it is Snc_env_cpoisson with Snc_srv_rate.

SolverBA does NOT use this for its queue-length column: it applies Little's law to the response-time bound instead, so that Q and R stay consistent with the exact open-network throughput. The two are close but not identical, since each optimizes its own theta.

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

Method Summary

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

Methods inherited from class java.lang.Object

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

Method Details

snc_mean_backlog

public static SncResult snc_mean_backlog(SncEnvelope arv,
 SncEnvelope srv)

Parameters:

arv - arrival envelope

srv - service envelope

Returns:

the bound on E[B] and the minimizing theta

snc_mean_backlog

public static SncResult snc_mean_backlog(SncEnvelope arv,
 SncEnvelope srv,
 double thetamax)

Parameters:

arv - arrival envelope

srv - service envelope

thetamax - upper end of the theta search

Returns:

the bound on E[B] and the minimizing theta