Classes
struct	CacheIsolateResult
	Return value of da_cache_isolate, mirroring [gamma,lambda_cache,Rcost]. More...
struct	CacheParam
	The fields of sn.nodeparam{cache} that da_cache_isolate reads. More...
struct	CacheqnInfo
	The converged isolated-cache inputs, kept for per-item occupancy reporting. More...
struct	CacheqnResult
struct	CacheqnRetrievalResult
	What the delayed-hit decomposition returns. More...
struct	FpiOptions
	Options mirroring the fields MATLAB reads off the options struct. More...
struct	FpiResult

Functions
template<class T>
CacheIsolateResult< T >	da_cache_isolate (const CacheParam< T > &ch, const std::vector< T > &lambda)
	Isolated-cache input construction for the decomposition methods.
template<class T>
std::vector< Matrix< T > >	da_cacheqn_itemprob (const CacheqnInfo< T > &info)
	Per-item occupancy of every cache from the CONVERGED access factors.
template<class T>
CacheqnResult< T >	da_cacheqn (qn::NetworkStruct< T > sn, bool exact, const mva::MvaOptions &opt, const std::function< mva::MvaSolution< T >(const qn::NetworkStruct< T > &)> &netfun, const std::function< std::vector< T >(const Matrix< T > &, const std::vector< int > &, const std::vector< Matrix< T > > &, const qn::CacheParam< T > &)> &missfun=nullptr)
	Decomposition-aggregation driver for integrated cache-queueing models, a port of matlab/src/api/da/da_cacheqn.m.
template<class T>
CacheqnRetrievalResult< T >	da_cacheqn_retrieval (qn::NetworkStruct< T > sn, const std::function< mva::MvaSolution< T >(const qn::NetworkStruct< T > &)> &netfun, const mva::MvaOptions &opt)
	Port of da_cacheqn_retrieval.
template<class T>
FpiResult< T >	da_fpi (const std::function< std::pair< std::vector< T >, std::vector< T > >(const std::vector< T > &, std::size_t)> &iterfun, const std::vector< T > &x0, const FpiOptions &options=FpiOptions())
	Damped fixed-point iteration, the shared driver of the decomposition algorithms.
template<class T>
T	da_traffic_superpos (const std::vector< T > &lambda, const std::vector< T > &a2)
	Superposition of independent renewal flows (Whitt's QNA stationary-interval method).

Function Documentation

◆ da_cache_isolate()

template<class T>

CacheIsolateResult< T > line::da::da_cache_isolate	(	const CacheParam< T > &	ch,
		const std::vector< T > &	lambda )

Isolated-cache input construction for the decomposition methods.

Parameters

ch	cache node parameters
lambda	(u) per-class arrival rates at the cache

Definition at line 82 of file da_cache_isolate.h.

References line::da::CacheParam< T >::accost, line::cache::cache_gamma_lp(), da_cache_isolate(), line::da::CacheIsolateResult< T >::gamma, line::InputError::InputError(), line::da::CacheParam< T >::itemcap, line::da::CacheIsolateResult< T >::lambda_cache, line::da::CacheParam< T >::nitems, line::da::CacheParam< T >::pread, and line::da::CacheIsolateResult< T >::Rcost.

Referenced by da_cache_isolate(), da_cacheqn(), da_cacheqn_retrieval(), and line::mva::solver_mva_cache_analyzer().

◆ da_cacheqn()

template<class T>

CacheqnResult< T > line::da::da_cacheqn	(	qn::NetworkStruct< T >	sn,
		bool	exact,
		const mva::MvaOptions &	opt,
		const std::function< mva::MvaSolution< T >(const qn::NetworkStruct< T > &)> &	netfun,
		const std::function< std::vector< T >(const Matrix< T > &, const std::vector< int > &, const std::vector< Matrix< T > > &, const qn::CacheParam< T > &)> &	missfun = nullptr )

Decomposition-aggregation driver for integrated cache-queueing models, a port of matlab/src/api/da/da_cacheqn.m.

Parameters

sn	the model struct, taken by value and mutated (caches relabelled)
exact	true selects the exact isolated-cache miss, false the approximation; consulted only when missfun is empty
opt	iteration controls (iter_max, tol)
netfun	solves the surrounding queueing network on the mutated struct; its MvaSolution.X is read as the per-class system throughput
missfun	THE ISOLATED-CACHE MISS ALGORITHM, as the reference's missfun handle. Empty selects the MVA pair (cache_mva / cache_miss_fpi), which is what SolverMVA passes; SolverNC supplies cache_prob_erec / cache_miss_spm instead. The reference has always taken a handle here – an earlier version of this port collapsed it to exact, which hardcoded one solver's pair into a driver both solvers share.

THE FOURTH ARGUMENT IS THE CACHE ITSELF, as the reference's missfun(gamma, m, lambda_cache, ch) passes it. Without it a handle cannot see the replacement strategy or the access graph of the cache it is being asked about, so a model with two caches under different policies would be solved by whichever one the handle was written for. SolverFLD reads exactly those two fields; SolverMVA and SolverNC ignore the argument.

Definition at line 133 of file da_cacheqn.h.

References line::da::CacheParam< T >::accost, line::qn::CacheParam< T >::accost, line::cache::cache_miss_fpi(), line::cache::cache_mva(), da_cache_isolate(), da_cacheqn(), da_fpi(), line::da::CacheIsolateResult< T >::gamma, line::qn::CacheParam< T >::hitclass, line::da::CacheqnResult< T >::hitprob, line::da::CacheqnResult< T >::info, line::da::CacheParam< T >::itemcap, line::qn::CacheParam< T >::itemcap, line::da::CacheqnResult< T >::iter, line::da::FpiOptions::iter_max, line::da::FpiOptions::iter_tol, line::da::FpiResult< T >::iterations, line::da::CacheIsolateResult< T >::lambda_cache, line::Matrix< T >::Matrix(), line::qn::CacheParam< T >::missclass, line::da::CacheqnResult< T >::missprob, line::cache::CacheMissResult< T >::MU, line::da::CacheParam< T >::nitems, line::qn::CacheParam< T >::nitems, line::cache::CacheMvaResult< T >::pij, line::da::CacheParam< T >::pread, line::qn::CacheParam< T >::pread, line::da::CacheIsolateResult< T >::Rcost, line::qn::CacheParam< T >::replacestrat, line::da::CacheqnResult< T >::res, and line::mva::MvaSolution< T >::X.

Referenced by da_cacheqn(), line::fluid::solver_fld_cacheqn_analyzer(), line::fluid::solver_fld_cacheqn_tran(), line::mva::solver_mva_cacheqn_analyzer(), and line::nc::solver_nc_cacheqn_analyzer().

◆ da_cacheqn_itemprob()

template<class T>

std::vector< Matrix< T > > line::da::da_cacheqn_itemprob ( const CacheqnInfo< T > & info )

Per-item occupancy of every cache from the CONVERGED access factors.

This is the EMBEDDED (per-request) law: the stationary law of the cache-content chain seen at request instants, which coincides with the time-stationary one only under PASTA. SolverCTMC reports the time-weighted counterpart instead.

RR/FIFO past 10 items is NaN, not the fixed point's marginals: the exact recursion is what makes these a distribution, and an approximation of it is not one. SolverMVA and SolverNC read the same law off their own fixed points, so it is derived here rather than in either analyzer.

Returns: one (n x h+1) matrix per cache, column 0 the miss probability; an EMPTY matrix where the cache carries no access factors

Definition at line 82 of file da_cacheqn.h.

References line::cache::cache_prob_erec(), line::cache::cache_ttl_lrua(), da_cacheqn_itemprob(), line::lang::GlobalConstants::FineTol, line::da::CacheqnInfo< T >::gamma, line::da::CacheqnInfo< T >::itemcap, line::da::CacheqnInfo< T >::lambda_cache, line::lang::LRU, line::Matrix< T >::Matrix(), line::da::CacheqnInfo< T >::Rcost, and line::da::CacheqnInfo< T >::strat.

Referenced by da_cacheqn_itemprob(), line::mva::solver_mva_cacheqn_analyzer(), and line::nc::solver_nc_cacheqn_analyzer().

◆ da_cacheqn_retrieval()

template<class T>

CacheqnRetrievalResult< T > line::da::da_cacheqn_retrieval	(	qn::NetworkStruct< T >	sn,
		const std::function< mva::MvaSolution< T >(const qn::NetworkStruct< T > &)> &	netfun,
		const mva::MvaOptions &	opt )

Port of da_cacheqn_retrieval.

Parameters

sn	the model struct, taken by value and MUTATED (the cache becomes a ClassSwitch and the fetch station gains lldscaling)
netfun	solves the surrounding queueing network on the mutated struct
opt	iteration controls

Definition at line 91 of file da_cacheqn_retrieval.h.

References line::da::CacheParam< T >::accost, line::qn::CacheParam< T >::accost, line::cache::cache_miss_fpi(), da_cache_isolate(), da_cacheqn_retrieval(), da_fpi(), line::da::CacheqnRetrievalResult< T >::delayedprob, line::da::CacheIsolateResult< T >::gamma, line::qn::CacheParam< T >::hitclass, line::da::CacheqnRetrievalResult< T >::hitprob, line::da::CacheParam< T >::itemcap, line::qn::CacheParam< T >::itemcap, line::da::CacheqnRetrievalResult< T >::iter, line::da::FpiOptions::iter_max, line::da::FpiOptions::iter_tol, line::da::FpiResult< T >::iterations, line::da::CacheIsolateResult< T >::lambda_cache, line::qn::CacheParam< T >::missclass, line::da::CacheqnRetrievalResult< T >::missprob, line::da::CacheParam< T >::nitems, line::qn::CacheParam< T >::nitems, line::cache::CacheMissResult< T >::pi0, line::da::CacheParam< T >::pread, line::qn::CacheParam< T >::pread, line::da::CacheqnRetrievalResult< T >::res, line::qn::CacheParam< T >::retrieval_classes, line::qn::CacheParam< T >::retrieval_queues, line::da::CacheqnRetrievalResult< T >::sn, and line::UnsupportedError::UnsupportedError().

Referenced by da_cacheqn_retrieval(), line::mva::solver_mva_cacheqn_retrieval_analyzer(), and line::nc::solver_nc_cacheqn_retrieval_analyzer().

◆ da_fpi()

template<class T>

FpiResult< T > line::da::da_fpi	(	const std::function< std::pair< std::vector< T >, std::vector< T > >(const std::vector< T > &, std::size_t)> &	iterfun,
		const std::vector< T > &	x0,
		const FpiOptions &	options = FpiOptions() )

Damped fixed-point iteration, the shared driver of the decomposition algorithms.

Parameters

iterfun	(x, iteration) -> (xnew, xref); xref is the point the damping and the increment norm are taken against
x0	initial iterate
options	fixed-point options (tolerance, iteration cap, damping)

Definition at line 92 of file da_fpi.h.

References line::da::FpiResult< T >::converged, da_fpi(), line::InputError::InputError(), line::da::FpiResult< T >::iterations, and line::da::FpiResult< T >::x.

Referenced by da_cacheqn(), da_cacheqn_retrieval(), da_fpi(), line::lossn::lossn_erlangfp(), line::mam::solver_mam_basic_mmap_inner(), line::mam::solver_mam_decmmap(), line::mam::solver_mna_closed(), line::mam::solver_mna_open(), and line::mva::solver_qna().