infer_fmlps.h File Reference

Fluid response-time likelihood, and the FMLPS demand estimator built on it. More...

#include <algorithm>
#include <cmath>
#include <cstddef>
#include <limits>
#include <vector>
#include "line/api/infer/infer_mlps.h"
#include "line/lang/qn/network_struct.h"
#include "line/num/number.h"
#include "line/solvers/fluid/fluid_odes.h"
#include "line/util/error.h"
#include "line/util/matrix.h"
#include "line/solvers/fluid/fluid_stiff.h"
#include "line/util/lsoda.h"
#include "line/util/ode.h"

Include dependency graph for infer_fmlps.h:

Go to the source code of this file.

Classes
struct	line::api::FluidRtLikelihood
	What the fluid likelihood call reports. More...

Namespaces
namespace	line
namespace	line::api

Functions
template<class T>
FluidRtLikelihood	line::api::infer_fluid_ps_rt_likelihood (const qn::NetworkStruct< T > &sn, std::size_t ist, std::size_t cls, const std::vector< double > &levels, double rsampled, double marked=1.0)
	The fluid passage-time density at one observed response time.
template<class T>
std::vector< double >	line::api::infer_fmlps (const qn::NetworkStruct< T > &sn, std::size_t ist, const std::vector< MlpsSample > &samples)
	FMLPS: the fluid analogue of MLPS.

Detailed Description

Fluid response-time likelihood, and the FMLPS demand estimator built on it.

Port of matlab/src/api/infer/infer_fluid_ps_rt_likelihood.m and infer_fmlps.m. Both are MATLAB-ONLY: no JAR, no native-Python twin.

Reference: Casale et al., "Fluid Analysis of Queueing in Processor Sharing Systems".

WHAT THE LIKELIHOOD IS. MLPS builds an exact CTMC per observation and reads a phase-type density; that is exact and costs a state space. FMLPS replaces it with the FLUID limit: mark one unit of fluid at the reference station in the tagged class, let the deterministic drift carry it, and the passage-time density at the observed response time is -d/dt (marked mass) / mass0. The marked mass is nonincreasing, so that derivative is the density and the likelihood needs no separate normalization.

THE AUGMENTATION IS THE SAME ONE fluid_passage_time PERFORMS, and this file deliberately reuses it rather than re-deriving the drift. The reference expands sn.mu, sn.phi, sn.proc and the routing table from K to K+1 classes by hand and hands the loose arrays to solver_fluid_odes; the C++ fluid solver takes a NetworkStruct, and the marked-fluid construction it already carries is exactly the tagged class K+1 – a departure of the marked block UNMARKS the fluid and delivers it wherever the class routes, which is precisely the reference's "absorption at refIdx: the tagged class switches back to the original classes". Re-transcribing the routing expansion would duplicate the one part of the reference where the index arithmetic (l:Kc:end against l:K:end) is easiest to get wrong.

TWO DIFFERENCES FROM THE CTMC ESTIMATOR THAT A CALLER MUST KNOW:

• the fluid density is a LIMIT, so on a small population it is an approximation where MLPS is exact. It is what buys a model whose state space MLPS cannot enumerate;
• the reference returns a likelihood of exactly ZERO when the integration terminates before the observed time (the marked fluid is gone). That is kept: a zero likelihood is information, and replacing it with a floor would make an impossible observation look merely unlikely.

ARITHMETIC: double, following the ODE.

Definition in file infer_fmlps.h.