qsys_mg1_setup.h File Reference

M/G/1 with setup times: the server switches off when empty and needs a setup time U before serving the job that finds it off. More...

#include <string>
#include "line/api/qsys/qsys_res.h"
#include "line/lang/distribution.h"
#include "line/num/number.h"
#include "line/util/error.h"

Include dependency graph for qsys_mg1_setup.h:

Go to the source code of this file.

Classes
struct	line::qsys::Mg1SetupResult< T >
	MATLAB's [W, Wq, U, Q, res] outputs. More...

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

Functions
template<class T>
Mg1SetupResult< T >	line::qsys::qsys_mg1_setup (const T &lambda, const T &mu, const T &cs, const T &EU, const T &EU2)
	M/G/1 with setup times, setup given by its first two moments.
template<class T>
Mg1SetupResult< T >	line::qsys::qsys_mg1_setup (const T &lambda, const T &mu, const T &cs, const lang::Distrib< T > &U)
	M/G/1 with setup times, setup given as a Distribution (MATLAB passes it in place of EU and reads its mean and variance).

Detailed Description

M/G/1 with setup times: the server switches off when empty and needs a setup time U before serving the job that finds it off.

Port of matlab/src/api/qsys/qsys_mg1_setup.m. By the decomposition of Fuhrmann and Cooper, the waiting time is the M/G/1 waiting time plus the equilibrium excess of the setup period,

Wq = lambda E[S^2] / (2 (1 - rho)) + (2 E[U] + lambda E[U^2]) / (2 (1 + lambda E[U])).

ARITHMETIC: field. Only the squared coefficient of variation appears, so the computation is exact for T = Rational.

Definition in file qsys_mg1_setup.h.