qsys_mg1_exceptional.h File Reference

M/G/1 with exceptional first service: the job that starts a busy period has service law Bf, every other job law B (Welch, 1964). More...

#include "line/api/qsys/qsys_res.h"
#include "line/num/number.h"
#include "line/util/error.h"

Include dependency graph for qsys_mg1_exceptional.h:

Go to the source code of this file.

Classes
struct	line::qsys::Mg1ExceptionalResult< 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>
Mg1ExceptionalResult< T >	line::qsys::qsys_mg1_exceptional (const T &lambda, const T &mu, const T &cs, const T &muf, const T &csf)
	M/G/1 with exceptional first service.

Detailed Description

M/G/1 with exceptional first service: the job that starts a busy period has service law Bf, every other job law B (Welch, 1964).

Port of matlab/src/api/qsys/qsys_mg1_exceptional.m. With x = P(empty) = (1 - lambda E[B]) / (1 + lambda E[Bf] - lambda E[B]), the fraction of time serving first jobs is rhof = lambda x E[Bf] and other jobs rho = lambda (1-x) E[B];

Wq = (rhof E[Bf^2]/(2E[Bf]) + rho E[B^2]/(2E[B])) / (1 - lambda E[B]), W = Wq + x E[Bf] + (1 - x) E[B].

ARITHMETIC: field; exact for T = Rational.

Definition in file qsys_mg1_exceptional.h.