qsys_gig1_ubnd_kingman.h File Reference

Kingman upper bound on the mean waiting time of a G/G/1 queue. More...

#include "line/api/qsys/qsys_types.h"
#include "line/num/number.h"

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Namespaces
namespace	line
namespace	line::qsys

Functions
template<class T>
QsysResult< T >	line::qsys::qsys_gig1_ubnd_kingman (const T &lambda, const T &mu, const T &ca, const T &cs)
	Kingman upper bound on the mean waiting time of a G/G/1 queue.

Detailed Description

Kingman upper bound on the mean waiting time of a G/G/1 queue.

Templated port of matlab/src/api/qsys/qsys_gig1_ubnd_kingman.m, cross-checked against jar/src/main/java/jline/api/qsys/Qsys_gig1_ubnd_kingman.java (identical).

Wq <= lambda (sa^2 + ss^2)/(2(1-rho)), sa^2 = ca^2/lambda^2, ss^2 = cs^2/mu^2 W = Wq + 1/mu

Reference: Kingman, J.F.C. (1962). Some inequalities for the queue GI/G/1. Biometrika 49(3/4), 315-324.

Pure field arithmetic, exact for T = Rational.

Definition in file qsys_gig1_ubnd_kingman.h.