Package jline.api.snc

Class Snc_conv

java.lang.Object

jline.api.snc.Snc_conv

public final class Snc_conv
extends Object

Min-plus convolution of two service envelopes (tandem concatenation).

Two stations traversed in series offer the flow their min-plus convolution. For independent servers with exponential-form envelopes, summing the geometric series over the intermediate epoch gives

   rho   = min(rho1,rho2),
   sigma = sigma1 + sigma2 - log(1-exp(-theta*|rho1-rho2|))/theta.
 

This is the pay-bursts-only-once result: the end-to-end burst term grows additively rather than the delay bounds of the two stations being summed. The series diverges when the rates are equal, so equal rates are handled by shifting the slower server down by delta, the usual regularization; delta then trades rate against burst and can be optimized jointly with theta.

Port of matlab/src/api/snc/snc_conv.m. Original: F. Ciucu, A. Burchard, J. Liebeherr, "Scaling Properties of Statistical End-to-End Bounds in the Network Calculus", IEEE Trans. Inf. Theory 52(6), 2300-2312, 2006.

Method Summary

Modifier and Type	Method	Description
static SncEnvelope	of(SncEnvelope s1, SncEnvelope s2)
static double[]	snc_conv(double sigma1, double rho1, double sigma2, double rho2, double theta)
static double[]	snc_conv(double sigma1, double rho1, double sigma2, double rho2, double theta, double delta)

Methods inherited from class java.lang.Object

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

Method Details

snc_conv

public static double[] snc_conv(double sigma1,
 double rho1,
 double sigma2,
 double rho2,
 double theta)

Parameters:

sigma1 - burst term of the first station

rho1 - rate term of the first station

sigma2 - burst term of the second station

rho2 - rate term of the second station

theta - Chernoff parameter, theta > 0

Returns:

{sigma, rho} of the concatenated element

snc_conv

public static double[] snc_conv(double sigma1,
 double rho1,
 double sigma2,
 double rho2,
 double theta,
 double delta)

Parameters:

sigma1 - burst term of the first station

rho1 - rate term of the first station

sigma2 - burst term of the second station

rho2 - rate term of the second station

theta - Chernoff parameter, theta > 0

delta - rate separation used when the two rates coincide

Returns:

{sigma, rho} of the concatenated element

of

public static SncEnvelope of(SncEnvelope s1,
 SncEnvelope s2)

Parameters:

s1 - the first service element

s2 - the second service element

Returns:

the concatenated element as a function of theta