snc_bound_delay.h File Reference

Violation probability of a delay target. 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_delay.h:

Go to the source code of this file.

Namespaces
namespace	line
namespace	line::snc

Functions
SncResult	line::snc::snc_bound_delay (const Envelope &arv, const Envelope &srv, double d, double thetamax=1e3)
	Violation probability of a delay target.

Detailed Description

Violation probability of a delay target.

For a flow with arrival envelope (sigmaA,rhoA) served by an element with service envelope (sigmaS,rhoS), the virtual delay of the stable station obeys, for every theta > 0,

P{D(t) > d} <= exp(-theta*(rhoS*d-sigmaA-sigmaS)) / (1-exp(-theta*(rhoS-rhoA))),

the horizontal rather than vertical deviation between the arrival and service envelopes. On the M/M/1 read in job units (snc_env_poisson with snc_srv_exp) the optimal theta tends to log(mu/lambda), so the bound reproduces the exact asymptotic decay rate exp(-(mu-lambda)*d).

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

Definition in file snc_bound_delay.h.