solver_nc.h File Reference

Port of solver_nc.m: the load-INDEPENDENT normalizing-constant analyzer. More...

#include <algorithm>
#include <cmath>
#include <limits>
#include <string>
#include <vector>
#include "line/api/npfqn/npfqn_nonexp_approx.h"
#include "line/api/pfqn/pfqn_nc.h"
#include "line/lang/qn/network_struct.h"
#include "line/solvers/nc/solver_nc_lcfsqn.h"
#include "line/solvers/mva/mva_types.h"
#include "line/solvers/mva/sn_chain.h"
#include "line/solvers/nc/nc_types.h"
#include "line/solvers/nc/solver_nc_sdr.h"
#include "line/util/error.h"
#include "line/util/matrix.h"

Include dependency graph for solver_nc.h:

Go to the source code of this file.

Classes
struct	line::nc::GlobalConstants
	The MATLAB GlobalConstants, as reported by lineStart at its defaults. More...

Namespaces
namespace	line
namespace	line::nc

Enumerations
enum class	line::nc::SchedStrategy
	Scheduling disciplines, with the values of MATLAB SchedStrategy. More...

Functions
template<class T>
NcSolution< T >	line::nc::solver_nc (const qn::NetworkStruct< T > &sn, const NcSolverOptions &opt)
	Port of solver_nc.m.

Detailed Description

Port of solver_nc.m: the load-INDEPENDENT normalizing-constant analyzer.

WHAT IT COMPUTES. One evaluation of the normalizing constant G(N) settles the whole product-form network: the chain throughput is X_c = G(N - 1_c) / G(N), and the chain queue length at station i follows from a constant evaluated on the model with station i REPLICATED into a private class,

Q_ic = Zms_ic X_c + Lms_ic exp(lG_ar(i,c) - lG),

which is the arrival-theorem identity written in constants rather than in a recursion. That is why this file calls pfqn_nc once per chain and once per (station, chain) pair rather than solving anything itself: the algorithms live in api/pfqn, and choosing among them is pfqn_nc's job.

MULTISERVER IS SEIDMANN'S APPROXIMATION, NOT AN EXACT SOLVE. A station with c > 1 servers is split into a demand L/c at a single server plus a pure delay L (c-1)/c. It is exact only in the limit; the reference warns and continues, and @@SolverNC/runAnalyzer converts genuine multiservers to load-dependent rates BEFORE reaching here whenever the model is product-form, so this branch serves the models that have no exact load-dependent form.

WHY THERE IS AN OUTER LOOP AT ALL. SolverOptions('NC') sets config.highvar = 'interp', so a non-product-form FCFS station has its service time rescaled by npfqn_nonexp_approx after each pass and the analyzer re-solves until the decay rates eta stop moving. With no FCFS station the reference pins iter_max to 1 and the loop runs once.

ARITHMETIC. Every measure here is formed from differences of LOGARITHMS of normalizing constants, which is the only way the ratios stay representable; there is no exact-field formulation of exp(lG' - lG), so a non-transcendental backend is refused by name rather than narrowed.

Definition in file solver_nc.h.