Classes
class	MDD
	The diagram: insert / member / index / enumerate / cardinality. More...
struct	MddClosedQnResult
	Result of the MDD-stored exact closed-network solve. More...
struct	MddDescriptor
	Kronecker rate descriptor of a structured model, the input of mdd_mcd. More...
struct	MddEvent
	One event of the Kronecker rate descriptor. More...
struct	MddLocalMatrix
	A local rate matrix W_k^e of the Kronecker descriptor, held row-compressed. More...
struct	MddMcdOptions
	Knobs of the level iteration in mdd_mcd. More...
struct	MddMcdResult
	Result of the Miner-Ciardo-Donatelli level aggregation. More...
struct	MddServiceLaw
	Phase-type service law of one station, as a Markovian (D0,D1) pair. More...
struct	MddStats
	Storage description of the set held in an MDD. More...
struct	MddStruct
	Plain-array export of an MDD, the input contract of mdd_mcd. More...

Typedefs
typedef std::vector< std::vector< bool > >	MddMask
	Per-level admissible local values, the restriction of Sec.
typedef std::function< std::vector< std::vector< int > >(const std::vector< int > &)>	MddNextState
	Successor function over local indices, for mdd_reachset.

Functions
std::string	mdd_to_string (const MDD &m)
	Human-readable storage summary, the twin of MDD.toString.
template<class T>
MddClosedQnResult< T >	mdd_closedqn (const std::vector< T > &mu, const Matrix< T > &P, const std::vector< double > &servers, int N, const MDD *reuse=nullptr)
	Exact solve of a single-class closed exponential queueing network whose CTMC state space (reachable occupancy vectors) is stored in a Multi-valued Decision Diagram instead of an explicit state list.
template<class T>
MddDescriptor< T >	mdd_descriptor (const std::vector< T > &mu, const Matrix< T > &P, const std::vector< double > &servers, int N, const std::vector< MddServiceLaw< T > > &proc=std::vector< MddServiceLaw< T > >(), const std::vector< std::string > &sched=std::vector< std::string >())
	Build the descriptor.
template<class T>
MddMcdResult< T >	mdd_mcd (const MddStruct &mdds, const MddDescriptor< T > &desc, const MddMcdOptions &options=MddMcdOptions())
	Approximate stationary measures by decision-diagram-guided aggregation.
template<class T>
MddDescriptor< T >	mdd_ps (const std::vector< T > &mu, const Matrix< T > &P, const std::vector< double > &servers, int N, const std::vector< MddServiceLaw< T > > &proc=std::vector< MddServiceLaw< T > >())
	Build the descriptor.
MDD	mdd_reachset (const std::vector< int > &domain, const std::vector< int > &init, const MddNextState &nextfun)
	Generate and store the reachability set into a quasi-reduced ordered MDD.
template<class T>
T	mdd_rec_masked (const MddStruct &mdds, const std::vector< std::vector< T > > &g, const MddMask &mask)
	Unnormalised mass of the masked subset of the reachable set (Algorithm 1).
template<class T>
T	mdd_rec (const MddStruct &mdds, const std::vector< std::vector< T > > &g)
	The normalising constant G = sum_{s in S} prod_l g_l(s_l).
template<class T>
std::vector< T >	mdd_rec_marginal (const MddStruct &mdds, const std::vector< std::vector< T > > &g, std::size_t l)
	Unnormalised masses of {s in S : s_l = k}, one per local value k of level l.
template<class T>
std::vector< T >	mdd_entry_law (const std::vector< T > &given, const Matrix< T > &D1, std::size_t h, std::size_t i, const std::string &caller)
	Entry law of a phase-type station, taken as given or derived from D1.

Variables
const int	TERM_TRUE = -1
	Terminal node "1": a completed path is accepted.
const int	TERM_FALSE = 0
	Terminal node "0": empty subgraph.

Typedef Documentation

◆ MddMask

typedef std::vector<std::vector<bool> > line::mdd::MddMask

Per-level admissible local values, the restriction of Sec.

5.3.

mask[l][v] false drops local value v of level l from the sum. An EMPTY mask admits everything, which is the plain MDD-rec of Algorithm 1.

Definition at line 65 of file mdd_rec.h.

◆ MddNextState

typedef std::function<std::vector<std::vector<int> >(const std::vector<int>&)> line::mdd::MddNextState

Successor function over local indices, for mdd_reachset.

Definition at line 155 of file mdd_types.h.

Function Documentation

◆ mdd_closedqn()

template<class T>

MddClosedQnResult< T > line::mdd::mdd_closedqn	(	const std::vector< T > &	mu,
		const Matrix< T > &	P,
		const std::vector< double > &	servers,
		int	N,
		const MDD *	reuse = nullptr )

Exact solve of a single-class closed exponential queueing network whose CTMC state space (reachable occupancy vectors) is stored in a Multi-valued Decision Diagram instead of an explicit state list.

Parameters

mu	per-station exponential service rates, length M
P	M x M Markovian routing matrix (row-stochastic, irreducible)
servers	servers per station; infinite for a delay/IS station
N	closed population
reuse	an already-built reachable set (the mdd of a previous result on the same mu/P/servers/N) to skip regeneration, or nullptr

Definition at line 84 of file mdd_closedqn.h.

Referenced by mdd_closedqn().

◆ mdd_descriptor()

template<class T>

MddDescriptor< T > line::mdd::mdd_descriptor	(	const std::vector< T > &	mu,
		const Matrix< T > &	P,
		const std::vector< double > &	servers,
		int	N,
		const std::vector< MddServiceLaw< T > > &	proc = std::vector<MddServiceLaw<T>>(),
		const std::vector< std::string > &	sched = std::vector<std::string>() )

Build the descriptor.

Parameters

mu	station service rates, 1/E[S]; entry i is ignored when station i is given a phase-type law through proc
P	station-to-station routing matrix, row-stochastic
servers	servers per station, infinite for delay/IS
N	closed population
proc	per-station service law; an absent or present == false entry is an exponential station
sched	per-station discipline names, consulted only to REJECT a phase-type law at a preemptive-resume or shared-server station; may be empty when every station is non-preemptive

Definition at line 269 of file mdd_descriptor.h.

Referenced by mdd_descriptor(), and line::ctmc::solver_ctmc_mdd_analyzer().

◆ mdd_entry_law()

template<class T>

std::vector< T > line::mdd::mdd_entry_law	(	const std::vector< T > &	given,
		const Matrix< T > &	D1,
		std::size_t	h,
		std::size_t	i,
		const std::string &	caller )

Entry law of a phase-type station, taken as given or derived from D1.

A {D0,D1} pair carries its own restart law: for a renewal process D1 = t0*pie, so every row with a positive exit rate is proportional to pie. Deriving it is not optional – defaulting to e_1 instead silently replaces a hyperexponential (whose D0 is diagonal, so a job entering phase 1 can never leave it) by an exponential at the phase-1 rate.

Definition at line 268 of file mdd_types.h.

References line::InputError::InputError(), and mdd_entry_law().

Referenced by mdd_descriptor(), mdd_entry_law(), mdd_ps(), and line::spn::spn_mdd().

◆ mdd_mcd()

template<class T>

MddMcdResult< T > line::mdd::mdd_mcd	(	const MddStruct &	mdds,
		const MddDescriptor< T > &	desc,
		const MddMcdOptions &	options = MddMcdOptions() )

Approximate stationary measures by decision-diagram-guided aggregation.

Parameters

mdds	the reachable set, in MDD orientation
desc	the Kronecker rate descriptor
options	level-iteration knobs

Definition at line 384 of file mdd_mcd.h.

Referenced by mdd_mcd(), and line::ctmc::solver_ctmc_mdd_analyzer().

◆ mdd_ps()

template<class T>

MddDescriptor< T > line::mdd::mdd_ps	(	const std::vector< T > &	mu,
		const Matrix< T > &	P,
		const std::vector< double > &	servers,
		int	N,
		const std::vector< MddServiceLaw< T > > &	proc = std::vector<MddServiceLaw<T>>() )

Build the descriptor.

Parameters

mu	station service rates, ignored where proc gives a law
P	station-to-station routing matrix, row-stochastic
servers	servers per station, 1 (PS) or infinite (IS); no other value has a per-phase-count encoding here
N	closed population
proc	per-station service law; an absent or present == false entry is an exponential station

Definition at line 242 of file mdd_ps.h.

Referenced by mdd_ps(), and line::ctmc::solver_ctmc_mdd_analyzer().

◆ mdd_reachset()

MDD line::mdd::mdd_reachset	(	const std::vector< int > &	domain,
		const std::vector< int > &	init,
		const MddNextState &	nextfun )

inline

Generate and store the reachability set into a quasi-reduced ordered MDD.

Parameters

domain	per-level local-state counts, values 0..domain[k]-1
init	the initial global state, 0-based local values
nextfun	the next-state function

Returns: an MDD holding every state reachable from init

Definition at line 44 of file mdd_reachset.h.

References line::mdd::MDD::compact(), line::mdd::MDD::insert(), mdd_reachset(), and line::mdd::MDD::member().

Referenced by mdd_closedqn(), mdd_reachset(), and line::ctmc::solver_ctmc_mdd_analyzer().

◆ mdd_rec()

template<class T>

T line::mdd::mdd_rec	(	const MddStruct &	mdds,
		const std::vector< std::vector< T > > &	g )

The normalising constant G = sum_{s in S} prod_l g_l(s_l).

Definition at line 139 of file mdd_rec.h.

References mdd_rec(), and mdd_rec_masked().

Referenced by mdd_rec(), and line::spn::spn_metrics().

◆ mdd_rec_marginal()

template<class T>

std::vector< T > line::mdd::mdd_rec_marginal	(	const MddStruct &	mdds,
		const std::vector< std::vector< T > > &	g,
		std::size_t	l )

Unnormalised masses of {s in S : s_l = k}, one per local value k of level l.

Divided by G these are P(m_l = k) of Sec. 5.3: the mean occupancy of a level is sum_k k * P(m_l = k), and its utilization 1 - P(m_l = 0).

Definition at line 150 of file mdd_rec.h.

References line::mdd::MddStruct::domain, line::InputError::InputError(), line::mdd::MddStruct::K, mdd_rec_marginal(), and mdd_rec_masked().

Referenced by line::lossn::lossn_rec(), mdd_rec_marginal(), and line::spn::spn_metrics().

◆ mdd_rec_masked()

template<class T>

T line::mdd::mdd_rec_masked	(	const MddStruct &	mdds,
		const std::vector< std::vector< T > > &	g,
		const MddMask &	mask )

Unnormalised mass of the masked subset of the reachable set (Algorithm 1).

Parameters

mdds	the reachable set, in MDD orientation (level 0 is the root)
g	g[l][v] is g_l(v), the per-level factor of the product form
mask	per-level admissible values; empty admits everything and returns G

Definition at line 123 of file mdd_rec.h.

References line::mdd::MddStruct::K, mdd_rec_masked(), line::mdd::MddStruct::nnodes, line::mdd::MddStruct::root, and TERM_FALSE.

Referenced by mdd_rec(), mdd_rec_marginal(), mdd_rec_masked(), and line::spn::spn_rec_enabled().

◆ mdd_to_string()

std::string line::mdd::mdd_to_string ( const MDD & m )

inline

Human-readable storage summary, the twin of MDD.toString.

Definition at line 377 of file mdd.h.

References line::mdd::MddStats::explicit_ints, line::mdd::MDD::K(), line::mdd::MddStats::mdd_ints, mdd_to_string(), line::mdd::MddStats::num_nodes, line::mdd::MddStats::num_states, line::mdd::MDD::stats(), and line::mdd::MddStats::table_nodes.

Referenced by mdd_to_string().

Variable Documentation

◆ TERM_FALSE

const int line::mdd::TERM_FALSE = 0

Terminal node "0": empty subgraph.

Definition at line 50 of file mdd.h.

Referenced by line::mdd::MDD::compact(), line::mdd::MDD::enumerate(), line::mdd::MDD::index(), line::mdd::MDD::MDD(), mdd_rec_masked(), and line::mdd::MDD::member().

◆ TERM_TRUE

const int line::mdd::TERM_TRUE = -1

Terminal node "1": a completed path is accepted.

Definition at line 48 of file mdd.h.

Referenced by line::mdd::MDD::index(), mdd_mcd(), and line::mdd::MDD::member().

Classes

Typedefs

Functions

Variables

Typedef Documentation

◆ MddMask

◆ MddNextState

Function Documentation

◆ mdd_closedqn()

◆ mdd_descriptor()

◆ mdd_entry_law()

◆ mdd_mcd()

◆ mdd_ps()

◆ mdd_reachset()

◆ mdd_rec()

◆ mdd_rec_marginal()

◆ mdd_rec_masked()

◆ mdd_to_string()

Variable Documentation

◆ TERM_FALSE

◆ TERM_TRUE