fluid_petri.h File Reference

Fluid analysis of a stochastic Petri net: one simultaneous algebraic solve per active set. More...

#include <algorithm>
#include <cmath>
#include <cstddef>
#include <limits>
#include <map>
#include <set>
#include <string>
#include <vector>
#include "line/solvers/fluid/fluid_moments.h"
#include "line/solvers/fluid/fluid_petri_system.h"
#include "line/solvers/fluid/fluid_petri_terms.h"
#include "line/util/error.h"
#include "line/util/linalg.h"
#include "line/util/matrix.h"
#include "line/util/ode.h"
#include "line/util/svd.h"

Include dependency graph for fluid_petri.h:

Go to the source code of this file.

Classes
struct	line::fluid::petri::PetriConservation
	The conserved quantities of a net, as equations. More...
struct	line::fluid::petri::PetriConstraints
	Every finite place capacity as a linear row A x <= b. More...
struct	line::fluid::petri::PetriImmediate
	The active set of the immediate modes and the equations pinning their flows. More...
struct	line::fluid::petri::PetriImmediate::Row
struct	line::fluid::petri::PetriVerdict
	Whether the fluid Petri route can answer this model, and why not. More...
struct	line::fluid::petri::PetriReport
	What the Petri route computes that the station table has no column for. More...
struct	line::fluid::petri::PetriSolution
	Everything solver_fluid_petri returns. More...
struct	line::fluid::petri::PetriOptions
	Tuning of the outer solve. More...

Namespaces
namespace	line
namespace	line::fluid
namespace	line::fluid::petri

Functions
PetriConservation	line::fluid::petri::petri_conservation (const PetriTerms &t)
	The conserved quantities, as equations: u'D = 0 implies u'x is constant.
template<class T>
PetriConstraints	line::fluid::petri::petri_constraints (const qn::NetworkStruct< T > &sn, const PetriTerms &t)
	THE GATE IS A LOSS ON THE DEPOSIT: LINE loses the tokens a firing would push past a place's capacity, so the fluid analogue scales the DEPOSIT leg of every event adding mass to the capped place and leaves the removal leg alone.
void	line::fluid::petri::petri_immediate (const PetriTerms &t, const std::vector< double > &x, PetriImmediate &imm)
	An immediate transition has no rate: its fluid limit is a FLOW, an algebraic unknown pinned by the constraint that its binding input place holds no mass,.
template<class T>
PetriVerdict	line::fluid::petri::petri_applicable (const qn::NetworkStruct< T > &sn)
	A QUEUEING STATION IS THE ONE STRUCTURAL EXCLUSION: a net whose tokens also visit a Queue or a Delay is two formalisms at once, and LINE has no reference semantics for the hand-off.
template<class T>
PetriSolution	line::fluid::petri::solver_fluid_petri (const qn::NetworkStruct< T > &sn, const PetriOptions &opt=PetriOptions())
	Fluid analysis of a stochastic Petri net.

Detailed Description

Fluid analysis of a stochastic Petri net: one simultaneous algebraic solve per active set.

Port of matlab/src/solvers/FLD/solver_fluid_petri.m, together with fluid_petri_conservation.m, fluid_petri_constraints.m, fluid_petri_immediate.m and fluid_petri_applicable.m. Cross-checked against jar/src/main/java/jline/solvers/fluid/petri/PetriSolver.java and the python solver_fld/methods/petri.py.

A net's fluid limit is NOT the queueing drift with places in place of stations. Its immediate transitions have no rate at all: their limit is a FLOW, an algebraic unknown pinned by the constraint that the input place they bind holds no mass. The marking, the diffusion covariance, those flows, the multi-server phase latches and the capacity gates therefore solve SIMULTANEOUSLY, as one algebraic system per active set, rather than by integrating an ODE to its fixed point.

THE ACTIVE SET IS WHAT ITERATES. A pass solves the system for a fixed choice of which immediate modes fire, which coordinate each pins, and which capacities bind; the answer says whether that choice was right (a negative flow, a negative marking, a violated or a released capacity), and the next pass makes ONE move. The moves are ordered so that a failure of each invalidates the next.

Definition in file fluid_petri.h.