qsys_mgc_ps.h File Reference

Exact analysis of the M/G/c processor-sharing queue. More...

#include <algorithm>
#include <cmath>
#include <string>
#include <vector>
#include "line/api/qsys/qsys_res.h"
#include "line/util/error.h"

Include dependency graph for qsys_mgc_ps.h:

Go to the source code of this file.

Namespaces
namespace	line
	Conservation laws of a layered queueing network, enumerated from its structure.
namespace	line::qsys

Functions
QsysRes	line::qsys::qsys_mgc_ps (double lambda, double mu, unsigned c)
	Exact M/G/c-PS queue.

Detailed Description

Exact analysis of the M/G/c processor-sharing queue.

Port of matlab/src/api/qsys/qsys_mgc_ps.m. The queue-length law is insensitive and equals that of M/M/c: with A = lambda/mu, a = A/c and the Erlang C probability C,

E[N] = C a/(1 - a) + A, Var[N] = a C (1 + a - a C)/(1 - a)^2 + A (1 + C),

and E[T] = E[N]/lambda by Little's law. The distribution is the M/M/c law, normalized in log space and truncated where its geometric tail falls below 1e-14.

ARITHMETIC: double, as the reference.

Definition in file qsys_mgc_ps.h.