qsys_mg1_busy.h File Reference

Busy-period measures of the M/G/1 queue. More...

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

Include dependency graph for qsys_mg1_busy.h:

Go to the source code of this file.

Classes
struct	line::qsys::Mg1BusyOptions
	MATLAB's name-value options of qsys_mg1_busy; a negative ES3 means not given. More...

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

Functions
QsysRes	line::qsys::qsys_mg1_busy (double lambda, double mu, double cs, const Mg1BusyOptions &o=Mg1BusyOptions())
	Busy-period measures of the M/G/1 queue.

Detailed Description

Busy-period measures of the M/G/1 queue.

Port of matlab/src/api/qsys/qsys_mg1_busy.m. The busy period BP has

E[BP] = E[S]/(1-rho), E[BP^2] = E[S^2]/(1-rho)^3, E[BP^3] = E[S^3]/(1-rho)^4 + 3 lambda E[S^2]^2/(1-rho)^5,

the number served in it has mean 1/(1-rho) and variance (rho(1-rho) + lambda^2 E[S^2])/(1-rho)^3, and given the service LST its own LST solves Takacs' equation b(s) = B(s + lambda - lambda b(s)), here by the reference's fixed-point iteration from b = 0.

ARITHMETIC: double, as the reference.

Definition in file qsys_mg1_busy.h.