fj_respt_nt.h File Reference

Nelson-Tantawi 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_nt.h:

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Namespaces
namespace	line
namespace	line::fj

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

Detailed Description

Nelson-Tantawi 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_nt.m, cross-checked against FJ_respt.fj_respt_nt in jar/src/main/java/jline/api/fj/FJ_respt.java (identical apart from the K > 32 accuracy warning, which MATLAB emits and neither the JAR nor this port does).

R_K = [ H_K/H_2 + (1 - H_K/H_2) 4 rho/11 ] (3/2 - rho/8) / (mu - lambda)

Rational in rho, hence exact in the field. At K = 2 it reduces exactly to fj_respt_2way, an identity that only holds bit-for-bit in exact arithmetic.

Definition in file fj_respt_nt.h.