qsys_gm1.h File Reference

Exact mean response time of the G/M/1 queue. More...

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

Include dependency graph for qsys_gm1.h:

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Namespaces
namespace	line
namespace	line::qsys

Functions
template<class T>
T	line::qsys::qsys_gm1 (const T &sigma, const T &mu)
	Exact mean response time of the G/M/1 queue.

Detailed Description

Exact mean response time of the G/M/1 queue.

Templated port of matlab/src/api/qsys/qsys_gm1.m, cross-checked against jar/src/main/java/jline/api/qsys/Qsys_gm1.java. The two agree on W; the JAR additionally reports rhohat = 0, whereas MATLAB returns W alone. The port follows MATLAB and returns the single value.

W = 1/(1-sigma)/mu

sigma is the load seen at arrival instants, i.e. the root in (0,1) of sigma = A*(mu(1-sigma)) with A* the Laplace transform of the interarrival time. It is an input here, so the function itself is pure field arithmetic and exact for T = Rational.

Definition in file qsys_gm1.h.