qsys_gig1_approx_myskja2.h File Reference

Myskja's enhanced third-moment approximation of the mean response time of a G/I/G/1 queue. More...

#include "line/api/qsys/qsys_mg1.h"
#include "line/api/qsys/qsys_types.h"
#include "line/num/number.h"

Include dependency graph for qsys_gig1_approx_myskja2.h:

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Namespaces
namespace	line
namespace	line::qsys

Functions
template<class T>
QsysResult< T >	line::qsys::qsys_gig1_approx_myskja2 (const T &lambda, const T &mu, const T &ca, const T &cs, const T &q0, const T &qa)
	Myskja's enhanced third-moment approximation of the mean response time of a G/I/G/1 queue.

Detailed Description

Myskja's enhanced third-moment approximation of the mean response time of a G/I/G/1 queue.

Templated port of matlab/src/api/qsys/qsys_gig1_approx_myskja2.m.

ra = (1+ca^2)/2, rs = (1+cs^2)/2, rho = lambda/mu theta = [ rho(qa-ra) - (qa-ra^2) ] / [ 2 rho (ra-1) ] d = (1+1/ra)(1-rs)(1-(q0/qa)^3)(1-rho^3) D = (rs-theta)^2 + (2 rs - 1 + d)(ra-1), clamped at 0 W = (rho/(1-rho))/lambda [ rs + (1/rho)( sqrt(D) - (rs-theta) ) ]

At ca = 1 the interpolation parameter theta is a 0/0 form, so the exact M/G/1 answer is returned instead; that is also the anchor the method interpolates from.

ARITHMETIC. sqrt(D) and the cube of q0/qa make this transcendental (the cube alone would not, but the square root does), so the function is gated.

MATLAB-vs-JAR. jline.api.qsys.Qsys_gig1_approx_myskja2 sets ra = (1+ca)/2, rs = (1+cs)/2 and branches on |ca-1| < 1e-8, i.e. it reads ca/cs as squared coefficients of variation, and in the M/G/1 branch it calls qsys_mg1 with sqrt(cs) rather than cs. MATLAB reads them as coefficients of variation throughout. The two disagree on every non-Markovian input; this port follows MATLAB.

Definition in file qsys_gig1_approx_myskja2.h.