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LINE Solver (C++)
Templated C++ port of the LINE queueing solver
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LINE Solver (C++)
Templated C++ port of the LINE queueing solver
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Port of @@SolverNC/getCdfRespT.m, and of its two aliases getSjrnT and sjrnT. More...
#include <algorithm>#include <cmath>#include <cstddef>#include <string>#include <vector>#include "line/api/mam/map_cdf.h"#include "line/api/pfqn/pfqn_stdf.h"#include "line/api/pfqn/pfqn_stdf_heur.h"#include "line/lang/distribution.h"#include "line/lang/qn/network_struct.h"#include "line/solvers/nc/nc_types.h"#include "line/solvers/nc/sn_pf_params.h"#include "line/util/error.h"#include "line/util/matrix.h"Go to the source code of this file.
Classes | |
| struct | line::nc::CdfRespTResult< T > |
| The response-time distributions, station by class. More... | |
Namespaces | |
| namespace | line |
| namespace | line::nc |
Functions | |
| template<class T> | |
| CdfRespTResult< T > | line::nc::solver_nc_cdf_respt (const qn::NetworkStruct< T > &sn, const NcSolverOptions &opt) |
| Port of @@SolverNC/getCdfRespT.m. | |
| template<class T> | |
| CdfRespTResult< T > | line::nc::solver_nc_sjrnt (const qn::NetworkStruct< T > &sn, const NcSolverOptions &opt) |
| Port of @@SolverNC/getSjrnT.m: an alias of getCdfRespT. | |
Port of @@SolverNC/getCdfRespT.m, and of its two aliases getSjrnT and sjrnT.
WHAT IT ADDS OVER THE AVERAGE TABLE. getAvg reports E[R]; this reports the whole law Pr[R <= t], which is what a percentile or a service-level target needs. The two are not interchangeable: a product-form response time is not exponential, so E[R] does not determine its tail.
TWO KINDS OF STATION, TWO DIFFERENT LAWS. At an FCFS queue the sojourn time is the tagged-job passage time through a closed network and comes from pfqn_stdf (exact) or pfqn_stdf_heur (the rd heuristic). At a delay station there is no queueing at all, so the sojourn time IS the service time and the law is the distribution's own CDF, taken through map_cdf. The reference computes both and returns them in one station-indexed table.
WHY THE TIME GRID IS WHAT IT IS. The reference builds logspace(0, 2 log10 T, 100) with T = max(sum(N) * mean(1/rates)) over the FCFS stations: the population times the mean service time is the scale on which the FCFS subsystem empties, and squaring it gives a grid that still resolves the tail. It is reproduced exactly, because the grid is part of the answer – the CDF is reported AT these points. Note which axis that mean runs along: sn.rates(fcfsNodeIds,:) is (stations x classes) and MATLAB's mean takes the FIRST NON-SINGLETON dimension, so it averages over STATIONS and max then runs over classes – except with a single FCFS station, where the row is 1xR and the same call averages over CLASSES instead. Both branches are reproduced below; see _kb/06-solver-catalog.md (NC, getCdfRespT).
TWO PROPERTIES OF THAT GRID TO KNOW BEFORE READING ITS OUTPUT, neither of them a porting artifact. It DESCENDS when T < 1, because 2 log10 T is then negative, and it COLLAPSES to a hundred identical points at T = 1 exactly. Delay(1)+FCFS(3) with two classes at N=3 hits the second case: T = 3 * 1/3. The law is still correct at whatever points the grid names.
REFUSED, as the reference refuses it: a model with no FCFS station. MATLAB warns and returns an empty cell array, which reads as a completed analysis with no data; this throws instead.
ARITHMETIC. pfqn_stdf and map_cdf are transcendental, and the grid itself is a logspace, so a non-transcendental backend is refused by name.
Definition in file solver_nc_cdf.h.
1.18.0