pfqn_pff_delay.h File Reference

Product-form factor of a delay station. More...

#include <cmath>
#include <cstddef>
#include <vector>
#include "line/api/pfqn/pfqn_asympt_common.h"
#include "line/num/number.h"
#include "line/util/error.h"

Include dependency graph for pfqn_pff_delay.h:

Go to the source code of this file.

Namespaces
namespace	line
namespace	line::pfqn

Functions
template<class T>
T	line::pfqn::pfqn_pff_delay (const std::vector< T > &Z, const std::vector< int > &n)
	Product-form factor of a delay station.

Detailed Description

Product-form factor of a delay station.

Templated port of jar/src/main/java/jline/api/pfqn/nc/Pfqn_pff_delay.java. MATLAB has no standalone counterpart: the same expression is inlined wherever a normalizing-constant recursion folds in the delay term.

F_Z(n) = prod_r Z_r^{n_r} / n_r!

the contribution of the delay stations to the normalizing constant of a closed product-form network. The empty population gives 1, and a class with a positive population but no think time gives 0, the delay being unreachable for it.

The product is accumulated in the LOG DOMAIN and exponentiated once, so a large population does not overflow through the intermediate powers even where the value itself is representable.

Arithmetic: TRANSCENDENTAL, because of that log-domain accumulation. The same quantity in exact arithmetic is available from the delay balance function inside pfqn_ca, which forms it as a ratio of exact rationals.

Definition in file pfqn_pff_delay.h.