fj_respt_varki.h File Reference

Varki approximation to the mean response time of a K-way fork-join system of M/M/1 branches. More...

#include "line/api/fj/fj_harmonic.h"
#include "line/api/fj/fj_types.h"
#include "line/num/number.h"
#include "line/util/error.h"

Include dependency graph for fj_respt_varki.h:

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Namespaces
namespace	line
namespace	line::fj

Functions
template<class T>
T	line::fj::fj_respt_varki (unsigned K, const T &lambda, const T &mu)
	Varki approximation to the mean response time of a K-way fork-join system of M/M/1 branches.

Detailed Description

Varki approximation to the mean response time of a K-way fork-join system of M/M/1 branches.

Templated port of matlab/src/api/fj/fj_respt_varki.m, cross-checked against FJ_respt.fj_respt_varki in jar/src/main/java/jline/api/fj/FJ_respt.java (identical).

R_K = (1/mu) [ H_K + rho/(2(1-rho)) ( S1 + (1-2 rho) S2 ) ] S1 = sum_{i=1..K} 1/(i - rho), S2 = sum_{i=1..K} 1/(i (i - rho))

Rational in rho, hence exact in the field. Note that the denominators i - rho are positive for every i >= 1 whenever rho < 1, so the only pole is at rho = 1.

Definition in file fj_respt_varki.h.