Port of solver_mam_basic_mmap.m, solver_mam_basic_mmap_inner.m and solver_mam_basic_mmap_closed.m: the MMAP fork-join decomposition, reached as the dec.source.mmap method and as branch 2b of the dispatch (every open fork-join model that is not in the homogeneous class solver_mam_fj serves). More...

#include <algorithm>
#include <cmath>
#include <limits>
#include <map>
#include <string>
#include <utility>
#include <vector>
#include "line/api/da/da_fpi.h"
#include "line/api/mam/map_moment.h"
#include "line/api/mam/map_transform.h"
#include "line/api/mam/mmap_compress.h"
#include "line/api/mam/mmap_lambda.h"
#include "line/api/mam/mmapph1fcfs.h"
#include "line/api/mam/qbd_depproc.h"
#include "line/api/mam/qbd_mapmap1.h"
#include "line/api/qsys/qsys_mmck.h"
#include "line/lang/distribution.h"
#include "line/lang/qn/network_struct.h"
#include "line/solvers/mam/mam_types.h"
#include "line/solvers/mam/solver_mam_basic.h"
#include "line/solvers/mam/solver_mam_bmap.h"
#include "line/solvers/mam/solver_mam_traffic.h"
#include "line/util/error.h"
#include "line/util/matrix.h"

Include dependency graph for solver_mam_basic_mmap.h:

Classes
struct	line::mam::MmapDecConfig
	The options.config fields the MMAP decomposition reads on top of MamOptions. More...

Namespaces
namespace	line
namespace	line::mam

Functions
template<class T>
mva::MvaSolution< T >	line::mam::solver_mam_basic_mmap_inner (const qn::NetworkStruct< T > &L, const MamOptions &opt, const MmapDecConfig &cfg, const std::vector< T > &lambda, std::size_t *totiter)
	Port of solver_mam_basic_mmap_inner.m.
template<class T>
mva::MvaSolution< T >	line::mam::solver_mam_basic_mmap_closed (const qn::NetworkStruct< T > &L, const MamOptions &opt, const MmapDecConfig &cfg, std::size_t *totiter)
	Port of solver_mam_basic_mmap_closed.m: the per-class bisection on the surrogate arrival rate that makes the inner analyzer's queue lengths match the closed population.
template<class T>
mva::MvaSolution< T >	line::mam::solver_mam_basic_mmap (const qn::NetworkStruct< T > &L, const MamOptions &opt)
	Port of solver_mam_basic_mmap.m, the top-level dispatcher of the MMAP fork-join decomposition: an open model goes straight to the inner algorithm with the arrival rates its sources declare, a closed one through the bisection wrapper.

Detailed Description

Port of solver_mam_basic_mmap.m, solver_mam_basic_mmap_inner.m and solver_mam_basic_mmap_closed.m: the MMAP fork-join decomposition, reached as the dec.source.mmap method and as branch 2b of the dispatch (every open fork-join model that is not in the homogeneous class solver_mam_fj serves).

THE METHOD. It is a PARAMETRIC DECOMPOSITION, not a per-station isolation: unlike dec.source, which hands every station a rescaled copy of the chain's source process, this one carries a per-node DEPARTURE process table and recomputes the arrival stream at every node from the traffic equations each sweep (solver_mam_traffic_mmap, the fork-join aware traffic step). The departure process of an FCFS or PS station is the ETAQA truncation of its own QBD (qbd_depproc_etaqa, qbd_depproc_etaqa_ps), so the correlation a queue introduces travels downstream instead of being discarded. The fixed point is driven on the station queue lengths by da_fpi with a RELATIVE increment norm, and the reference starts testing convergence only from the third sweep (config.da_miniter = 3).

WHAT MAKES IT THE FORK-JOIN ANALYZER. Two things, and neither is in dec.source:

the traffic step SYNCHRONIZES the flows arriving at a join along one sync group with mmap_max rather than superposing them, so the join's output process is the slowest branch's, blocking included;
the join's own metrics are derived AFTER the fixed point from the branch response times, as the expected maximum of independent exponentials with rates 1/R_b minus their mean. That difference is the synchronization delay, and QN = (sum of branch throughputs) * delay is Little's law on it.

THE CLOSED WRAPPER has no source to fix the arrival rates, so it wraps the inner analyzer in a per-class BISECTION on a surrogate arrival rate, driven against the population, exactly as solver_mna_closed does. Three details of the reference are reproduced rather than tidied: the bracket's upper bound is the SLOWEST rate over the finite-server stations (the fallback to the infinite-server ones, and then to 1, is the reference's own); the loop breaks when every bracket has collapsed below the precision floor, undoing its own iteration count as it does so; and a diverged inner call is caught, treated as an overload, and the last successful metrics are restored if the FINAL trial is the one that diverged.

SELF-LOOPING CLASSES. sn.isslc guards the surrogate-rate zeroing, the queue clamp and the final throughput pin in the reference's closed wrapper, and the PS denominator and the FCFS saturation test in the inner analyzer. The C++ JobClassType is OPEN or CLOSED only, so no model this port can build enters them, and they are not transcribed – the same decision solver_mna.h and solver_mam_ag.h record.

THE REFERENCE'S OWN QUIRKS, REPRODUCED. XN is initialised to zeros and never assigned by either the inner analyzer or the closed wrapper, so the per-class throughput column is zero however the model is solved; the station throughputs in TN are the real ones. The inner analyzer's try/catch around the ETAQA departure process, and the closed wrapper's around the whole inner call, are the reference's control flow and not defensive additions: the first falls back to the scaled service process, the second to a bisection step downwards.

ARITHMETIC. Double (or real) only, for the reasons solver_mam_basic.h lists: the fixed point stops on a tolerance, MMAP[K]/PH[K]/1 runs the ADDA doubling iteration, and both ETAQA departure processes static_assert on transcendental arithmetic.

Definition in file solver_mam_basic_mmap.h.

Classes

Namespaces

Functions

Detailed Description