qsys_gigk_approx_kingman.h File Reference

Kingman (Lee-Longton) scaling of the exact M/M/k waiting time. More...

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

Include dependency graph for qsys_gigk_approx_kingman.h:

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Namespaces
namespace	line
namespace	line::qsys

Functions
template<class T>
QsysResult< T >	line::qsys::qsys_gigk_approx_kingman (const T &lambda, const T &mu, const T &ca, const T &cs, unsigned k)
	Kingman (Lee-Longton) scaling of the exact M/M/k waiting time.

Detailed Description

Kingman (Lee-Longton) scaling of the exact M/M/k waiting time.

Templated port of matlab/src/api/qsys/qsys_gigk_approx_kingman.m, cross-checked against jar/src/main/java/jline/api/qsys/Qsys_gigk_approx_kingman.java. The numbers agree; the JAR reads the M/M/k answer back out of the static fields of Ret.qsys, which this port replaces by a plain return value (the port has no global mutable state).

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

The M/M/k baseline is Erlang-C, all integer powers, so the whole function is pure field arithmetic and exact for T = Rational. At k = 1 it reduces exactly to the Allen-Cunneen / Heyman G/I/G/1 formula.

Definition in file qsys_gigk_approx_kingman.h.