qsys_gig1_approx_marchal.h File Reference

Marchal approximation of the mean response time of a G/I/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_approx_marchal (const T &lambda, const T &mu, const T &ca, const T &cs)
	Marchal approximation of the mean response time of a G/I/G/1 queue.

Detailed Description

Marchal approximation of the mean response time of a G/I/G/1 queue.

Templated port of matlab/src/api/qsys/qsys_gig1_approx_marchal.m, cross-checked against jar/src/main/java/jline/api/qsys/Qsys_gig1_approx_marchal.java (identical).

W = rho/(1-rho) * (1+cs^2)/2/mu * (ca + rho^2 cs^2)/(1 + rho^2 cs^2) + 1/mu

The numerator carries ca and not ca^2. That is what both MATLAB and the JAR compute, so the port reproduces it verbatim rather than "correcting" it to the published form. Pure field arithmetic, exact for T = Rational; it still reduces to M/M/1 at ca = cs = 1 because the correction ratio becomes one.

Definition in file qsys_gig1_approx_marchal.h.