pfqn_mmsample2.h File Reference

Sampled McKenna-Mitra integral form of the normalizing constant of a repairman (single-queue plus delay) model. More...

#include <algorithm>
#include <cmath>
#include <cstddef>
#include <limits>
#include <vector>
#include "line/api/pfqn/pfqn_ca.h"
#include "line/api/pfqn/pfqn_mc_common.h"
#include "line/num/number.h"
#include "line/util/error.h"
#include "line/util/matrix.h"

Include dependency graph for pfqn_mmsample2.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::pfqn

Functions
template<class T>
NcResult< T >	line::pfqn::pfqn_mmsample2 (const Matrix< T > &L, const std::vector< int > &N, const std::vector< T > &Z, std::size_t samples, McRng &rng)
	Sampled McKenna-Mitra integral form of the normalizing constant of a repairman (single-queue plus delay) model.
template<class T>
NcResult< T >	line::pfqn::pfqn_mmsample2 (const Matrix< T > &L, const std::vector< int > &N, const std::vector< T > &Z, McRng &rng)
	Reference call shape with an explicit grid size.

Detailed Description

Sampled McKenna-Mitra integral form of the normalizing constant of a repairman (single-queue plus delay) model.

Templated port of matlab/src/api/pfqn/pfqn_mmsample2.m, cross-checked against jar/src/main/java/jline/api/pfqn/nc/Pfqn_mmsample2.java.

For a single queue the McKenna-Mitra form collapses to the one-dimensional integral

G(N) = 1/prod_r N_r! int_0^inf e^{-u} prod_r (Z_r + L_r u)^{N_r} du,

whose log-integrand at the grid point u is

f(u) = -u + sum_r N_r log(Z_r + L_r u).

The reference lays a grid of ceil(samples/2) uniform points on [0,1) plus ceil(samples/2) points log-spaced over [1, 1e5], SORTS it, rescales the demands so that every coefficient is at least one, takes the panel widths du = [v(1), diff(v)] (the first panel covering [0, v(1)]) and reports the quadrature sum in the log domain,

lG = log sum_i du_i exp(f(v_i)) - sum_r log N_r! + sum(N) log(scaleFactor).

(An earlier reference took the maximum of the weighted log-integrand over an unsorted grid with the integrand (Z_r + L_r) u; MATLAB has since been corrected and this port follows the corrected estimator.)

Only the FIRST row of L is read, matching the reference: this is a single-queue model and additional rows are ignored.

Arithmetic: INEXACT BY CONSTRUCTION. The grid is random, the integrand is evaluated in the log domain, and the log-spaced block is generated by exponentiation.

RNG contract: see pfqn_mc_common.h. Comparable to MATLAB only in distribution, never stream for stream; reproducible within this port only when the generator is passed in the same state.

Definition in file pfqn_mmsample2.h.