snc_bound_backlog.h File Reference

Violation probability of a backlog level. More...

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

Include dependency graph for snc_bound_backlog.h:

Go to the source code of this file.

Namespaces
namespace	line
namespace	line::snc

Functions
SncResult	line::snc::snc_bound_backlog (const Envelope &arv, const Envelope &srv, double b, double thetamax=1e3)
	Violation probability of a backlog level.

Detailed Description

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.

Definition in file snc_bound_backlog.h.