Classes
struct	BndBgt
struct	BndBpt
struct	DpsMorrisonResult
	Mean queue lengths, sojourn times and throughputs, with Morrison's intermediate constants. More...
struct	FeedbackElimResult
	Outcome of the feedback elimination. More...
struct	MergeConfig
	MATLAB's config struct. More...
struct	NonexpApproxResult
	Return value, mirroring MATLAB's [ST,gamma,nservers,rho,scva,scvs,eta]. More...
struct	SqdOptions
	The four option switches of the reference, with its defaults. More...
struct	SqdResult
	Return value of npfqn_sqd, mirroring [X, Q, U, R]. More...
struct	TrafficIdcContext
	Context returned by npfqn_traffic_idc, mirroring the MATLAB ctx struct. More...
struct	TrafficIdcCorrections
	Toggle for the two correction terms, mirroring MATLAB's corrections. More...
struct	TrafficRqt

Typedefs
template<class T>
using	Mmap = std::vector<Matrix<T>>
	An MMAP as the MATLAB cell {D0, D1, D1^(1), ..., D1^(R)}.

Enumerations
enum class	Merge { Default , Super , Mixture , Interpos }
	Merge rule, MATLAB's config.merge. More...
enum class	Compress { Default , None }
	Post-merge compression, MATLAB's config.compress. More...

Functions
template<class T>
BndBgt< T >	npfqn_bnd_bgt (const std::vector< T > &lambda, const std::vector< std::vector< T > > &mu, const std::vector< std::vector< std::size_t > > &sigma, std::size_t J)
	Piecewise-linear Lyapunov UPPER bound on the steady-state queue lengths of a multitype (deterministic-routing) multiclass Markovian queueing network, valid for EVERY work-conserving Markovian policy.
template<class T>
BndBpt< T >	npfqn_bnd_bpt (const std::vector< T > &lambda0, const std::vector< T > &mu, const Matrix< T > &P, const std::vector< std::size_t > &stationOf, const std::vector< T > &c)
	First-order linear-programming relaxation of the achievable region of a multiclass open Markovian queueing network.
template<class T>
DpsMorrisonResult< T >	npfqn_dps_morrison (const std::vector< T > &N, const std::vector< T > &Z, const std::vector< T > &S, const std::vector< T > &w)
	Evaluates Morrison's two-term approximation.
template<class T>
FeedbackElimResult< T >	npfqn_feedback_elim (const Matrix< T > &P, const std::vector< T > &rho, const std::vector< T > &cs2=std::vector< T >(), const std::vector< T > &lambda=std::vector< T >(), bool immediateOnly=false)
	Near-immediate feedback elimination for the robust queueing network analyzer.
template<class T>
NonexpApproxResult< T >	npfqn_nonexp_approx (const std::string &method, const std::vector< bool > &isFCFS, const Matrix< T > &rates, const Matrix< T > &ST, const Matrix< T > &V, const Matrix< T > &SCV, const Matrix< T > &Tput, const Matrix< T > &U, const std::vector< T > &gamma, const std::vector< T > &nservers)
	Handler for non-exponential service and arrival processes in AMVA and NC.
template<class T>
T	npfqn_rqna_weight (const T &t)
	Canonical reflected-Brownian-motion correlation weight w*(t) used by the Robust Queueing Network Analyzer (RQNA).
template<class T>
std::vector< T >	npfqn_rqna_weight (const std::vector< T > &t)
	Elementwise form, mirroring the MATLAB array argument.
template<class T>
SqdResult< T >	npfqn_sqd (const std::vector< T > &ST, const std::vector< T > &V, const std::vector< T > &cap, const std::vector< bool > &isDelay, const Matrix< T > &rt, const std::vector< std::size_t > &stationToStateful, std::size_t nclasses, int N, const SqdOptions< T > &opt)
	Smith Queue Decomposition (SQD): approximate MVA for closed networks under Blocking-After-Service (manufacturing / transfer blocking).
template<class T>
SqdResult< T >	npfqn_sqd (const std::vector< T > &ST, const std::vector< T > &V, const std::vector< T > &cap, const std::vector< bool > &isDelay, const Matrix< T > &rt, const std::vector< std::size_t > &stationToStateful, std::size_t nclasses, int N)
	Overload with the reference's default option switches.
template<class T>
TrafficIdcContext< T >	npfqn_traffic_idc (const std::vector< T > &lambda0, const Matrix< T > &P, const std::vector< T > &c2a0, const std::vector< T > &mu, const std::vector< T > &cs2, const TrafficIdcCorrections &corrections)
	Traffic variability equations of the Robust Queueing Network Analyzer (W.
template<class T>
TrafficIdcContext< T >	npfqn_traffic_idc (const std::vector< T > &lambda0, const Matrix< T > &P, const std::vector< T > &c2a0, const std::vector< T > &mu, const std::vector< T > &cs2)
	Default corrections (both on), matching MATLAB's nargin < 8 branch.
template<class T>
std::vector< T >	npfqn_traffic_idc_at (const TrafficIdcContext< T > &ctx, const T &t, const std::function< std::vector< T >(const T &)> &a0IdcFun, const std::function< std::vector< T >(const std::vector< T > &)> &sIdcFun)
	Time-dependent IDC equations (eq.
template<class T>
mam::Mmap< T >	mmap_super_match (const mam::Mmap< T > &a, const mam::Mmap< T > &b)
	Superposition matching classes one to one (mmap_super.m, option 'match').
template<class T>
mam::Mmap< T >	mmap_mark_types (const mam::Mmap< T > &m, const Matrix< T > &prob)
	Re-mark an MMAP's K types into R classes (mmap_mark.m).
template<class T>
mam::Mmap< T >	npfqn_traffic_merge (const std::vector< mam::Mmap< T > > &flows, const MergeConfig &config=MergeConfig())
	Merge a list of MMAPs carrying the same classes.
template<class T>
mam::Mmap< T >	npfqn_traffic_merge_cs (const std::vector< mam::Mmap< T > > &flows, const Matrix< T > &prob, Merge merge=Merge::Default)
	Merge flows that switch class on departure.
template<class T>
TrafficRqt< T >	npfqn_traffic_rqt (const std::vector< T > &lambda0, const std::vector< T > &Gamma0, const std::vector< T > &alpha0, const Matrix< T > &F)
	Effective arrival processes of a network under the Robust Queueing calculus.
template<class T>
std::vector< Mmap< T > >	npfqn_traffic_split_cs (const Mmap< T > &MMAP, const Matrix< T > &P)
	Splitting of a marked MAP departure flow with class switching.
template<class T>
Matrix< T >	npfqn_traffic_split_rr (const qn::NetworkStruct< T > &sn)
	Port of npfqn_traffic_split_rr.m.

Typedef Documentation

◆ Mmap

template<class T>

using line::npfqn::Mmap = std::vector<Matrix<T>>

An MMAP as the MATLAB cell {D0, D1, D1^(1), ..., D1^(R)}.

Definition at line 53 of file npfqn_traffic_split_cs.h.

Enumeration Type Documentation

◆ Compress

enum class line::npfqn::Compress

strong

Post-merge compression, MATLAB's config.compress.

Enumerator
Default	'default', mmap_compress with its own default method
None	'none'

Definition at line 156 of file npfqn_traffic_merge.h.

◆ Merge

enum class line::npfqn::Merge

strong

Merge rule, MATLAB's config.merge.

Enumerator
Default	'default', identical to 'super'
Super	'super'
Mixture	'mixture', not ported
Interpos	'interpos', lumped interleaving of per-flow M3PP(2, m) fits

Definition at line 148 of file npfqn_traffic_merge.h.

Function Documentation

◆ mmap_mark_types()

template<class T>

mam::Mmap< T > line::npfqn::mmap_mark_types	(	const mam::Mmap< T > &	m,
		const Matrix< T > &	prob )

Re-mark an MMAP's K types into R classes (mmap_mark.m).

Parameters

m	an MMAP with K marked types
prob	(K x R); prob(k, r) is the probability that a type-k arrival is marked as class r

D0 and D1 are untouched and D1^(r) = sum_k D1^(k) prob(k, r). MATLAB does not normalize here, so neither does this: the caller's mmap_super does it.

Distinct from line::mam::mmap_mark, which marks a plain MAP with phase-dependent weights; MATLAB's mmap_mark is this one.

Definition at line 125 of file npfqn_traffic_merge.h.

References line::mam::Mmap< T >::classes(), line::Matrix< T >::cols(), line::mam::Mmap< T >::D0, line::mam::Mmap< T >::D1, line::mam::Mmap< T >::Dc, line::InputError::InputError(), mmap_mark_types(), line::mam::Mmap< T >::order(), and line::Matrix< T >::rows().

Referenced by mmap_mark_types(), and npfqn_traffic_merge_cs().

◆ mmap_super_match()

template<class T>

mam::Mmap< T > line::npfqn::mmap_super_match	(	const mam::Mmap< T > &	a,
		const mam::Mmap< T > &	b )

Superposition matching classes one to one (mmap_super.m, option 'match').

Every component of the MATLAB cell, D0 and D1 included, is combined with the same Kronecker sum, so the result carries the same class list as its operands. This is NOT line::mam::mmap_super, which is the 'default' option and CONCATENATES the two class lists; the merge needs the matching form, because merging n flows of R classes must yield R classes and not n R. MATLAB errors when the class counts differ; so does this.

It lives in the npfqn namespace, next to its only caller, rather than in the mam domain: the mam MMAP algebra is owned elsewhere in this tree and this option is not part of it.

Definition at line 99 of file npfqn_traffic_merge.h.

References line::mam::Mmap< T >::classes(), line::mam::Mmap< T >::D0, line::mam::Mmap< T >::D1, line::mam::Mmap< T >::Dc, line::InputError::InputError(), line::mam::krons(), line::mam::mmap_normalize(), and mmap_super_match().

Referenced by mmap_super_match(), npfqn_traffic_merge(), and npfqn_traffic_merge_cs().

◆ npfqn_bnd_bgt()

template<class T>

BndBgt< T > line::npfqn::npfqn_bnd_bgt	(	const std::vector< T > &	lambda,
		const std::vector< std::vector< T > > &	mu,
		const std::vector< std::vector< std::size_t > > &	sigma,
		std::size_t	J )

Piecewise-linear Lyapunov UPPER bound on the steady-state queue lengths of a multitype (deterministic-routing) multiclass Markovian queueing network, valid for EVERY work-conserving Markovian policy.

Parameters

lambda	Poisson arrival rate of each type
mu	mu[i][k] = service rate of stage k of type i
sigma	sigma[i][k] = zero-based station of stage k of type i
J	number of stations

Definition at line 107 of file npfqn_bnd_bgt.h.

Referenced by npfqn_bnd_bgt(), and line::ba::solver_ba_bgt().

◆ npfqn_bnd_bpt()

template<class T>

BndBpt< T > line::npfqn::npfqn_bnd_bpt	(	const std::vector< T > &	lambda0,
		const std::vector< T > &	mu,
		const Matrix< T > &	P,
		const std::vector< std::size_t > &	stationOf,
		const std::vector< T > &	c )

First-order linear-programming relaxation of the achievable region of a multiclass open Markovian queueing network.

Parameters

lambda0	external Poisson arrival rate into each class (0 if none)
mu	exponential service rate of each class
P	K x K routing, P(r,r') = P(class r becomes r' after service)
stationOf	zero-based station index of each class
c	objective weights; empty means all ones

Definition at line 94 of file npfqn_bnd_bpt.h.

References line::Matrix< T >::cols(), line::lp::LpModel< T >::emit(), line::lp::EQ, line::InputError::InputError(), line::inverse(), line::npfqn::BndBpt< T >::lambda, line::lp::lp_solve(), line::lp::lp_status_name(), line::matmul(), npfqn_bnd_bpt(), line::npfqn::BndBpt< T >::nrows, line::lp::LpModel< T >::num_rows(), line::lp::LpModel< T >::num_vars(), line::npfqn::BndBpt< T >::nvars, line::lp::LpSolution< T >::objective, line::lp::LpSolution< T >::ok(), line::npfqn::BndBpt< T >::rho, line::npfqn::BndBpt< T >::rhoStation, line::lp::LpModel< T >::row_add(), line::lp::LpModel< T >::row_clear(), line::Matrix< T >::rows(), line::lp::LpModel< T >::set_cost(), line::lp::LpModel< T >::set_maximize(), line::lp::LpSolution< T >::status, line::UnsupportedError::UnsupportedError(), line::lp::LpSolution< T >::x, line::npfqn::BndBpt< T >::x, and line::npfqn::BndBpt< T >::zlb.

Referenced by npfqn_bnd_bpt(), and line::ba::solver_ba_bpt().

◆ npfqn_dps_morrison()

template<class T>

DpsMorrisonResult< T > line::npfqn::npfqn_dps_morrison	(	const std::vector< T > &	N,
		const std::vector< T > &	Z,
		const std::vector< T > &	S,
		const std::vector< T > &	w )

Evaluates Morrison's two-term approximation.

Parameters

N	per-class populations, finite and positive
Z	per-class mean think times, finite and positive
S	per-class mean DPS service times, finite and positive
w	per-class DPS weights, finite and positive

Returns: the mean performance measures and the intermediate constants

Definition at line 196 of file npfqn_dps_morrison.h.

Referenced by npfqn_dps_morrison(), and line::nc::solver_nc_dps_analyzer().

◆ npfqn_feedback_elim()

template<class T>

FeedbackElimResult< T > line::npfqn::npfqn_feedback_elim	(	const Matrix< T > &	P,
		const std::vector< T > &	rho,
		const std::vector< T > &	cs2 = std::vector<T>(),
		const std::vector< T > &	lambda = std::vector<T>(),
		bool	immediateOnly = false )

Near-immediate feedback elimination for the robust queueing network analyzer.

Parameters

P	routing matrix, substochastic
rho	traffic intensity of each station
cs2	service SCV of each station, empty to skip modifiedScv
lambda	arrival rate of each station, empty to skip modifiedRates
immediateOnly	keep only the self-loops, i.e. Section 4.1 feedback

Definition at line 78 of file npfqn_feedback_elim.h.

References line::Matrix< T >::cols(), line::npfqn::FeedbackElimResult< T >::feedbackProb, line::InputError::InputError(), line::npfqn::FeedbackElimResult< T >::modifiedRates, line::npfqn::FeedbackElimResult< T >::modifiedRouting, line::npfqn::FeedbackElimResult< T >::modifiedScv, npfqn_feedback_elim(), line::num_abs(), line::npfqn::FeedbackElimResult< T >::reductionExact, line::Matrix< T >::rows(), line::solve(), and line::npfqn::FeedbackElimResult< T >::visitInflation.

Referenced by npfqn_feedback_elim().

◆ npfqn_nonexp_approx()

template<class T>

NonexpApproxResult< T > line::npfqn::npfqn_nonexp_approx	(	const std::string &	method,
		const std::vector< bool > &	isFCFS,
		const Matrix< T > &	rates,
		const Matrix< T > &	ST,
		const Matrix< T > &	V,
		const Matrix< T > &	SCV,
		const Matrix< T > &	Tput,
		const Matrix< T > &	U,
		const std::vector< T > &	gamma,
		const std::vector< T > &	nservers )

Handler for non-exponential service and arrival processes in AMVA and NC.

Parameters

method	'default', 'none', 'hvmva' (all no-ops) or 'interp'
isFCFS	(M) sn.sched(i) == SchedStrategy.FCFS
rates	(M x R) sn.rates
ST	(M x R) service times
V	(M x R) visit ratios; present in the MATLAB signature but never read by it, kept here for a 1:1 argument list
SCV	(M x R) service SCVs
Tput	(M x R) per-class throughputs
U	(M x R) per-class utilizations
gamma	(M) input decay rates
nservers	(M) input server counts

Definition at line 91 of file npfqn_nonexp_approx.h.

References line::Matrix< T >::cols(), line::npfqn::NonexpApproxResult< T >::eta, line::npfqn::NonexpApproxResult< T >::gamma, line::InputError::InputError(), npfqn_nonexp_approx(), line::npfqn::NonexpApproxResult< T >::nservers, line::num_pow_int(), line::npfqn::NonexpApproxResult< T >::rho, line::Matrix< T >::rows(), line::npfqn::NonexpApproxResult< T >::scva, line::npfqn::NonexpApproxResult< T >::scvs, and line::npfqn::NonexpApproxResult< T >::ST.

Referenced by npfqn_nonexp_approx(), line::nc::solver_nc(), and line::nc::solver_ncld().

◆ npfqn_rqna_weight() [1/2]

template<class T>

std::vector< T > line::npfqn::npfqn_rqna_weight ( const std::vector< T > & t )

Elementwise form, mirroring the MATLAB array argument.

Definition at line 81 of file npfqn_rqna_weight.h.

References npfqn_rqna_weight().

◆ npfqn_rqna_weight() [2/2]

template<class T>

T line::npfqn::npfqn_rqna_weight ( const T & t )

Canonical reflected-Brownian-motion correlation weight w*(t) used by the Robust Queueing Network Analyzer (RQNA).

Parameters

t	nonnegative time argument; t <= 0 gives 0 and t = Inf gives 1

Returns: the weight w*(t), clamped to [0,1] as in MATLAB and the JAR

Definition at line 47 of file npfqn_rqna_weight.h.

References npfqn_rqna_weight().

Referenced by npfqn_rqna_weight(), npfqn_rqna_weight(), and npfqn_traffic_idc_at().

◆ npfqn_sqd() [1/2]

template<class T>

SqdResult< T > line::npfqn::npfqn_sqd	(	const std::vector< T > &	ST,
		const std::vector< T > &	V,
		const std::vector< T > &	cap,
		const std::vector< bool > &	isDelay,
		const Matrix< T > &	rt,
		const std::vector< std::size_t > &	stationToStateful,
		std::size_t	nclasses,
		int	N )

Overload with the reference's default option switches.

Eight arguments, so it cannot collide with a MATLAB call transcribed positionally (the reference accepts at most seven, starting with an sn).

Definition at line 397 of file npfqn_sqd.h.

References npfqn_sqd().

◆ npfqn_sqd() [2/2]

template<class T>

SqdResult< T > line::npfqn::npfqn_sqd	(	const std::vector< T > &	ST,
		const std::vector< T > &	V,
		const std::vector< T > &	cap,
		const std::vector< bool > &	isDelay,
		const Matrix< T > &	rt,
		const std::vector< std::size_t > &	stationToStateful,
		std::size_t	nclasses,
		int	N,
		const SqdOptions< T > &	opt )

Smith Queue Decomposition (SQD): approximate MVA for closed networks under Blocking-After-Service (manufacturing / transfer blocking).

Parameters

ST	(M) chain-aggregated service times, STchain(:,1)
V	(M) chain-aggregated visit ratios, Vchain(:,1)
cap	(M) buffer capacities; use infinity for unbounded
isDelay	(M) true at the INF / EXT stations
rt	stateful-indexed routing matrix (sn.rt)
stationToStateful	(M) ONE-based station-to-stateful map
nclasses	class count, the stride of rt
N	total closed population
opt	the four option switches and the initial V1

Definition at line 248 of file npfqn_sqd.h.

References line::InputError::InputError(), npfqn_sqd(), line::npfqn::SqdResult< T >::Q, line::npfqn::SqdResult< T >::R, line::npfqn::SqdResult< T >::U, and line::npfqn::SqdResult< T >::X.

Referenced by npfqn_sqd(), npfqn_sqd(), and line::mva::solver_sqd().

◆ npfqn_traffic_idc() [1/2]

template<class T>

TrafficIdcContext< T > line::npfqn::npfqn_traffic_idc	(	const std::vector< T > &	lambda0,
		const Matrix< T > &	P,
		const std::vector< T > &	c2a0,
		const std::vector< T > &	mu,
		const std::vector< T > &	cs2 )

Default corrections (both on), matching MATLAB's nargin < 8 branch.

Definition at line 258 of file npfqn_traffic_idc.h.

References npfqn_traffic_idc().

◆ npfqn_traffic_idc() [2/2]

template<class T>

TrafficIdcContext< T > line::npfqn::npfqn_traffic_idc	(	const std::vector< T > &	lambda0,
		const Matrix< T > &	P,
		const std::vector< T > &	c2a0,
		const std::vector< T > &	mu,
		const std::vector< T > &	cs2,
		const TrafficIdcCorrections &	corrections )

Traffic variability equations of the Robust Queueing Network Analyzer (W.

Whitt and W. You 2018, "A Robust Queueing Network Analyzer Based on Indices of Dispersion").

Parameters

lambda0	(K) external arrival rate into each queue
P	(K x K) routing matrix among the queues, P(i,j) = p_{i,j}
c2a0	(K) asymptotic IDC (SCV) of each external arrival process
mu	(K) service rate at each queue
cs2	(K) service SCV c2_{s,i}
corrections	which of the two correction terms to include

Definition at line 121 of file npfqn_traffic_idc.h.

Referenced by npfqn_traffic_idc(), npfqn_traffic_idc(), and line::mva::solver_rqna().

◆ npfqn_traffic_idc_at()

template<class T>

std::vector< T > line::npfqn::npfqn_traffic_idc_at	(	const TrafficIdcContext< T > &	ctx,
		const T &	t,
		const std::function< std::vector< T >(const T &)> &	a0IdcFun,
		const std::function< std::vector< T >(const std::vector< T > &)> &	sIdcFun )

Time-dependent IDC equations (eq.

43) at a single time t, the port of the MATLAB nested function local_idc_at reached through ctx.IaFun.

Parameters

ctx	context from npfqn_traffic_idc
t	time argument
a0IdcFun	external-arrival IDC, a0IdcFun(t) -> (K) vector
sIdcFun	service IDC, sIdcFun(rho .* t) -> (K) vector

Returns: (K) total arrival IDCs I_{a,i}(t)

Definition at line 275 of file npfqn_traffic_idc.h.

References line::npfqn::TrafficIdcContext< T >::c2alpha, line::npfqn::TrafficIdcContext< T >::c2x, line::InputError::InputError(), line::npfqn::TrafficIdcContext< T >::K, line::npfqn::TrafficIdcContext< T >::lam_ji, line::npfqn::TrafficIdcContext< T >::lambda, line::npfqn::TrafficIdcContext< T >::lambda0, npfqn_rqna_weight(), npfqn_traffic_idc_at(), line::npfqn::TrafficIdcContext< T >::P, line::npfqn::TrafficIdcContext< T >::rho, line::solve(), and line::npfqn::TrafficIdcContext< T >::zetaAll.

Referenced by npfqn_traffic_idc_at(), and line::mva::solver_rqna().

◆ npfqn_traffic_merge()

template<class T>

mam::Mmap< T > line::npfqn::npfqn_traffic_merge	(	const std::vector< mam::Mmap< T > > &	flows,
		const MergeConfig &	config = MergeConfig() )

Merge a list of MMAPs carrying the same classes.

Parameters

flows	the MMAPs to superpose; empty ones are dropped, as in MATLAB
config	merge rule and compression

Returns: the merged MMAP, normalized

Definition at line 197 of file npfqn_traffic_merge.h.

References Default, line::InputError::InputError(), Interpos, line::mam::m3pp2m_fitc_theoretical(), line::mam::m3pp2m_interleave(), Mixture, line::mam::mmap_normalize(), mmap_super_match(), npfqn_traffic_merge(), Super, and line::UnsupportedError::UnsupportedError().

Referenced by npfqn_traffic_merge(), line::mam::solver_mam_traffic(), and line::mam::solver_mam_traffic_mmap().

◆ npfqn_traffic_merge_cs()

template<class T>

mam::Mmap< T > line::npfqn::npfqn_traffic_merge_cs	(	const std::vector< mam::Mmap< T > > &	flows,
		const Matrix< T > &	prob,
		Merge	merge = Merge::Default )

Merge flows that switch class on departure.

Parameters

flows	n MMAPs, each carrying R marked classes
prob	(n R x R), prob((i-1)R + r, s) in MATLAB 1-based terms
merge	merge rule; only Default and Super are ported

Returns: the merged MMAP with R classes

Definition at line 73 of file npfqn_traffic_merge_cs.h.

References line::Matrix< T >::cols(), Default, line::InputError::InputError(), mmap_mark_types(), mmap_super_match(), npfqn_traffic_merge_cs(), line::Matrix< T >::rows(), Super, and line::UnsupportedError::UnsupportedError().

Referenced by npfqn_traffic_merge_cs().

◆ npfqn_traffic_rqt()

template<class T>

TrafficRqt< T > line::npfqn::npfqn_traffic_rqt	(	const std::vector< T > &	lambda0,
		const std::vector< T > &	Gamma0,
		const std::vector< T > &	alpha0,
		const Matrix< T > &	F )

Effective arrival processes of a network under the Robust Queueing calculus.

Parameters

lambda0	external arrival rate at each node, 0 where there is none
Gamma0	variability parameter of each external arrival process, which for a renewal stream is the interarrival standard deviation
alpha0	tail coefficient in (1,2] of each external arrival process
F	routing probabilities, F(i,j) = fraction of the jobs leaving node i that go to node j (row sums <= 1)

Definition at line 70 of file npfqn_traffic_rqt.h.

References line::npfqn::TrafficRqt< T >::alpha, line::npfqn::TrafficRqt< T >::Gamma, line::inverse(), line::npfqn::TrafficRqt< T >::lambda, line::matmul(), and npfqn_traffic_rqt().

Referenced by npfqn_traffic_rqt(), and line::mva::solver_rqt().

◆ npfqn_traffic_split_cs()

template<class T>

std::vector< Mmap< T > > line::npfqn::npfqn_traffic_split_cs	(	const Mmap< T > &	MMAP,
		const Matrix< T > &	P )

Splitting of a marked MAP departure flow with class switching.

Parameters

MMAP	the departure MMAP {D0, D1, D1^(1), ..., D1^(R)}
P	(R x J) with J = M*R, P(r, (j-1)R + s) in MATLAB 1-based terms

Returns: one MMAP per destination station, in destination order

Definition at line 106 of file npfqn_traffic_split_cs.h.

References line::Matrix< T >::cols(), line::InputError::InputError(), npfqn_traffic_split_cs(), and line::Matrix< T >::rows().

Referenced by npfqn_traffic_split_cs(), line::mam::solver_mam_traffic(), and line::mam::solver_mam_traffic_mmap().

◆ npfqn_traffic_split_rr()

template<class T>

Matrix< T > line::npfqn::npfqn_traffic_split_rr ( const qn::NetworkStruct< T > & sn )

Port of npfqn_traffic_split_rr.m.

Parameters

sn	the model, after refresh(): rtnodes carries the expanded routing

Returns: an (nstations x nclasses) matrix of split degrees, 1 where the split is Markovian

Definition at line 94 of file npfqn_traffic_split_rr.h.

References line::lang::GlobalConstants::FineTol, npfqn_traffic_split_rr(), and line::qn::NodeDef::routing.

Referenced by npfqn_traffic_split_rr(), line::mam::solver_mna_open(), and line::mva::solver_qna().

Classes

Typedefs

Enumerations

Functions

Typedef Documentation

◆ Mmap

Enumeration Type Documentation

◆ Compress

◆ Merge

Function Documentation

◆ mmap_mark_types()

◆ mmap_super_match()

◆ npfqn_bnd_bgt()

◆ npfqn_bnd_bpt()

◆ npfqn_dps_morrison()

◆ npfqn_feedback_elim()

◆ npfqn_nonexp_approx()

◆ npfqn_rqna_weight() [1/2]

◆ npfqn_rqna_weight() [2/2]

◆ npfqn_sqd() [1/2]

◆ npfqn_sqd() [2/2]

◆ npfqn_traffic_idc() [1/2]

◆ npfqn_traffic_idc() [2/2]

◆ npfqn_traffic_idc_at()

◆ npfqn_traffic_merge()

◆ npfqn_traffic_merge_cs()

◆ npfqn_traffic_rqt()

◆ npfqn_traffic_split_cs()

◆ npfqn_traffic_split_rr()