Classes
struct	Env
	The pair (sigma, rho) of an envelope evaluated at one theta. More...
struct	SncResult
	A bound together with the theta that attains it. More...

Typedefs
using	Envelope = std::function<Env(double)>
	An envelope as a function of the Chernoff parameter.

Functions
SncResult	snc_bound_backlog (const Envelope &arv, const Envelope &srv, double b, double thetamax=1e3)
	Violation probability of a backlog level.
SncResult	snc_bound_delay (const Envelope &arv, const Envelope &srv, double d, double thetamax=1e3)
	Violation probability of a delay target.
Env	snc_conv (const Env &s1, const Env &s2, double theta, double delta=-1.0)
	Min-plus convolution of two service envelopes (tandem concatenation).
Env	snc_env_cpoisson (double lambda, double mu, double theta)
	MGF arrival envelope of a compound Poisson flow with Exp job sizes.
Envelope	snc_env_cpoisson_fn (double lambda, double mu)
	The same envelope as a function of theta.
Env	snc_env_map (const Matrix< double > &D0, const Matrix< double > &D1, double theta)
	MGF arrival envelope of a MAP/MMPP flow with unit-size jobs.
Envelope	snc_env_map_fn (const Matrix< double > &D0, const Matrix< double > &D1)
	The same envelope as a function of theta.
Env	snc_env_poisson (double lambda, double theta)
	MGF arrival envelope of a Poisson flow with unit-size jobs.
Envelope	snc_env_poisson_fn (double lambda)
	The same envelope as a function of theta.
Env	snc_env_tokenbucket (double b, double r)
	Deterministic token-bucket arrival envelope.
Env	snc_env_tokenbucket (double b, double r, double theta)
	Deterministic token-bucket arrival envelope.
Envelope	snc_env_tokenbucket_fn (double b, double r)
	The same envelope as a function of theta.
Env	snc_leftover (const Env &srv, const Env &cross)
	Leftover service envelope under blind (arbitrary) multiplexing.
SncResult	snc_mean_backlog (const Envelope &arv, const Envelope &srv, double thetamax=1e3)
	Upper bound on the mean backlog, from integrating the backlog tail bound.
SncResult	snc_mean_delay (const Envelope &arv, const Envelope &srv, double thetamax=1e3)
	Upper bound on the mean delay, from integrating the delay tail bound.
Env	snc_output (const Env &arv, const Env &srv, double theta)
	Output (departure) arrival envelope of a flow leaving a server.
SncResult	snc_perc_backlog (const Envelope &arv, const Envelope &srv, double eps, double thetamax=1e3)
	Backlog quantile at a prescribed violation probability.
SncResult	snc_perc_delay (const Envelope &arv, const Envelope &srv, double eps, double thetamax=1e3)
	Delay quantile at a prescribed violation probability.
Env	snc_srv_exp (double mu, double theta)
	MGF service envelope of an exponential server, in JOB units.
Envelope	snc_srv_exp_fn (double mu)
	The same envelope as a function of theta.
Env	snc_srv_rate (double C)
	MGF service envelope of a constant-rate work-conserving server.
Env	snc_srv_rate (double C, double theta)
	MGF service envelope of a constant-rate work-conserving server.
Envelope	snc_srv_rate_fn (double C)
	The same envelope as a function of theta.
SncResult	snc_thetaopt (const std::function< double(double)> &fun, double thetamax=1e3)
	Minimizes a Chernoff bound over the free parameter theta.

Typedef Documentation

◆ Envelope

using line::snc::Envelope = std::function<Env(double)>

An envelope as a function of the Chernoff parameter.

Definition at line 48 of file snc_types.h.

Function Documentation

◆ snc_bound_backlog()

SncResult line::snc::snc_bound_backlog	(	const Envelope &	arv,
		const Envelope &	srv,
		double	b,
		double	thetamax = 1e3 )

inline

Violation probability of a backlog level.

Parameters

arv	arrival envelope
srv	service envelope
b	backlog level, units of the envelopes
thetamax	upper end of the theta search

Definition at line 44 of file snc_bound_backlog.h.

References snc_bound_backlog(), snc_thetaopt(), line::snc::SncResult::theta, line::UnsupportedError::UnsupportedError(), and line::snc::SncResult::value.

Referenced by snc_bound_backlog().

◆ snc_bound_delay()

SncResult line::snc::snc_bound_delay	(	const Envelope &	arv,
		const Envelope &	srv,
		double	d,
		double	thetamax = 1e3 )

inline

Violation probability of a delay target.

Parameters

arv	arrival envelope
srv	service envelope
d	delay target, slots
thetamax	upper end of the theta search

Definition at line 44 of file snc_bound_delay.h.

References snc_bound_delay(), snc_thetaopt(), line::snc::SncResult::theta, line::UnsupportedError::UnsupportedError(), and line::snc::SncResult::value.

Referenced by snc_bound_delay().

◆ snc_conv()

Env line::snc::snc_conv	(	const Env &	s1,
		const Env &	s2,
		double	theta,
		double	delta = -1.0 )

inline

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

Parameters

s1	envelope of the first station
s2	envelope of the second station
theta	Chernoff parameter, theta > 0
delta	rate separation used when the two rates coincide; a nonpositive value selects the default 1e-2*min(rho1,rho2)

Definition at line 49 of file snc_conv.h.

References line::snc::Env::rho, line::snc::Env::sigma, snc_conv(), and line::UnsupportedError::UnsupportedError().

Referenced by snc_conv().