qsys_mg1_psjf.h File Reference

M/G/1 under PSJF (preemptive shortest job first). More...

#include <algorithm>
#include <cstddef>
#include <numeric>
#include <vector>
#include "line/api/qsys/qsys_mg1_setf.h"
#include "line/api/qsys/qsys_quadrature.h"
#include "line/api/qsys/qsys_types.h"
#include "line/num/number.h"
#include "line/util/error.h"

Include dependency graph for qsys_mg1_psjf.h:

Go to the source code of this file.

Namespaces
namespace	line
namespace	line::qsys

Functions
template<class T>
Mg1DisciplineResult< T >	line::qsys::qsys_mg1_psjf (const std::vector< T > &lambda, const std::vector< T > &mu, const std::vector< T > &cs)
	M/G/1 under PSJF (preemptive shortest job first).

Detailed Description

M/G/1 under PSJF (preemptive shortest job first).

Templated port of matlab/src/api/qsys/qsys_mg1_psjf.m, cross-checked against jar/src/main/java/jline/api/qsys/Qsys_mg1_psjf.java.

Priority follows the original size, so a job of size x is delayed only by work of size at most x (Wierman and Harchol-Balter, SIGMETRICS 2003, Sec. 3.2):

rho(x) = lambda int_0^x t f(t) dt m2(x) = lambda int_0^x t^2 f(t) dt E[T(x)] = x/(1-rho(x)) + m2(x)/(2 (1-rho(x))^2)

As in qsys_mg1_fb, MATLAB has an exponential path – closed-form truncated moments of the mixture, class mean by quadrature over [0, 20/mu_k] – and a general path that sorts the classes by increasing mean size and evaluates the same expression at x = 1/mu_k with the truncated moments replaced by the per-class second moments of the classes at least as fast. Both are reproduced.

ARITHMETIC. exp and the adaptive quadrature make this transcendental.

Definition in file qsys_mg1_psjf.h.