snc_env_cpoisson.h File Reference

MGF arrival envelope of a compound Poisson flow with Exp job sizes. More...

#include <cmath>
#include <limits>
#include "line/api/snc/snc_types.h"
#include "line/util/error.h"

Include dependency graph for snc_env_cpoisson.h:

Go to the source code of this file.

Namespaces
namespace	line
namespace	line::snc

Functions
Env	line::snc::snc_env_cpoisson (double lambda, double mu, double theta)
	MGF arrival envelope of a compound Poisson flow with Exp job sizes.
Envelope	line::snc::snc_env_cpoisson_fn (double lambda, double mu)
	The same envelope as a function of theta.

Detailed Description

MGF arrival envelope of a compound Poisson flow with Exp job sizes.

Jobs arrive Poisson at rate lambda and each carries an Exp(mu) amount of work, so rho(theta) = lambda/(mu-theta) for 0 < theta < mu and the burst is zero. Fed to a constant-rate server of rate mu (snc_srv_rate) this is the network calculus model of the M/M/1 queue in units of WORK, and the delay bound then decays at the exact rate mu-lambda.

INFEASIBILITY IS A VALUE, NOT AN ERROR: at theta >= mu the job-size MGF diverges and rho is returned as infinity, which the theta search discards.

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

Definition in file snc_env_cpoisson.h.