line::me Namespace Reference

Classes
struct	GegecnResult
	What me_gegecn returns: the law and the four means read off it. More...
struct	MeBlkOptions
	Controls of the blocking fixed point, me_oqn_blk's options struct. More...
struct	MeBlkResult
	What me_oqn_blk returns, per station. More...
struct	MeOptions
	Iteration control, mirroring the MATLAB options struct. More...
struct	MeResult
	Mean-value results shared by the open, closed and mixed algorithms. More...

Functions
template<class T>
MeResult< T >	me_cqn (std::size_t M, std::size_t R, const std::vector< long > &N, const Matrix< T > &mu, const Matrix< T > &Cs, const std::vector< Matrix< T > > &P, const std::vector< long > &c, const std::vector< long > &refstat_in, const std::vector< char > &insens, const MeOptions &opt=MeOptions())
	Maximum-entropy algorithm for closed multiclass queueing networks.
template<class T>
T	me_gegec_mql (const T &lambda, const T &Ca, const T &mu, const T &Cs, long c)
	Port of me_gegec_mql.
template<class T>
GegecnResult< T >	me_gegecn (const T &lambda, const T &Ca, const T &mu, const T &Cs, long c, long K, long N)
	Port of me_gegecn.
template<class T>
T	me_gegecn_pb (const std::vector< T > &p, long K, long N, long c, const T &Cs, const T &Ca)
	Port of me_gegecn_pb.
template<class T>
MeResult< T >	me_mqn (std::size_t M, std::size_t R, const std::vector< char > &open_classes, const Matrix< T > &lambda0, const Matrix< T > &Ca0, const std::vector< long > &N, const Matrix< T > &mu, const Matrix< T > &Cs, const std::vector< Matrix< T > > &P, const std::vector< long > &c, const std::vector< long > &refstat, const std::vector< char > &insens, const MeOptions &opt=MeOptions())
	Maximum-entropy algorithm for mixed open/closed multiclass networks.
template<class T>
MeResult< T >	me_oqn (std::size_t M, std::size_t R, const Matrix< T > &lambda0, const Matrix< T > &Ca0, const Matrix< T > &mu, const Matrix< T > &Cs, const std::vector< Matrix< T > > &P, const std::vector< long > &c, const std::vector< char > &insens, const MeOptions &opt=MeOptions())
	Maximum-entropy algorithm for open multiclass queueing networks.
template<class T>
MeBlkResult< T >	me_oqn_blk (std::size_t M, const std::vector< T > &lambda0, const std::vector< T > &Ca0, const std::vector< T > &mu, const std::vector< T > &Cs, const Matrix< T > &P, const std::vector< long > &c, const std::vector< long > &N, const std::vector< int > &blockrule, const MeBlkOptions &opt=MeBlkOptions())
	Port of me_oqn_blk.

Function Documentation

me_cqn()

template<class T>

MeResult< T > line::me::me_cqn	(	std::size_t	M,
		std::size_t	R,
		const std::vector< long > &	N,
		const Matrix< T > &	mu,
		const Matrix< T > &	Cs,
		const std::vector< Matrix< T > > &	P,
		const std::vector< long > &	c,
		const std::vector< long > &	refstat_in,
		const std::vector< char > &	insens,
		const MeOptions &	opt = MeOptions() )

Maximum-entropy algorithm for closed multiclass queueing networks.

Parameters

M	number of stations
R	number of classes
N	class populations (R)
mu	service rates (M x R)
Cs	service scvs (M x R)
P	routing, R matrices (M x M)
c	servers per station, 0 for an infinite-server station; finite values must be 1
refstat_in	reference station per class, or -1 for the first station the class is served at
insens	insensitive discipline flags per station
opt	tolerance and iteration budget

Definition at line 463 of file me_cqn.h.

References line::me::MeResult< T >::Ca, line::me::MeResult< T >::Cd, line::me::MeResult< T >::converged, line::InputError::InputError(), line::me::MeResult< T >::iter, line::me::MeResult< T >::L, line::me::MeResult< T >::lambda, line::Matrix< T >::Matrix(), me_cqn(), line::num_abs(), line::me::MeResult< T >::rho, line::me::MeResult< T >::W, and line::me::MeResult< T >::X.

Referenced by me_cqn(), me_mqn(), and line::nc::solver_nc_mem().

me_gegec_mql()

template<class T>

T line::me::me_gegec_mql	(	const T &	lambda,
		const T &	Ca,
		const T &	mu,
		const T &	Cs,
		long	c )

Port of me_gegec_mql.

Parameters

lambda	arrival rate
Ca	squared coefficient of variation of the interarrival times
mu	service rate of ONE server
Cs	squared coefficient of variation of the service times
c	number of servers, finite and at least 1

Returns

the mean number of jobs in the queue

Definition at line 53 of file me_gegec_mql.h.

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

Referenced by me_gegec_mql(), and me_oqn_blk().

me_gegecn()

template<class T>

GegecnResult< T > line::me::me_gegecn	(	const T &	lambda,
		const T &	Ca,
		const T &	mu,
		const T &	Cs,
		long	c,
		long	K,
		long	N )

Port of me_gegecn.

Parameters

lambda	arrival rate OFFERED to the queue, the arrivals turned away included
Ca	squared coefficient of variation of the interarrival times; the GE distribution needs at least 1
mu	service rate of ONE server
Cs	squared coefficient of variation of the service times, >= 1
c	number of servers, finite and at least 1
K	minimum number of jobs in the queue, >= 0
N	buffer capacity in jobs, service included, finite and > K

Definition at line 75 of file me_gegecn.h.

References line::InputError::InputError(), line::me::GegecnResult< T >::L, line::me::GegecnResult< T >::Lq, me_gegecn(), me_gegecn_pb(), line::me::GegecnResult< T >::p, line::me::GegecnResult< T >::PB, and line::me::GegecnResult< T >::U.

Referenced by me_gegecn(), and me_oqn_blk().

me_gegecn_pb()

template<class T>

T line::me::me_gegecn_pb	(	const std::vector< T > &	p,
		long	K,
		long	N,
		long	c,
		const T &	Cs,
		const T &	Ca )

Port of me_gegecn_pb.

Parameters

p	queue-length distribution, p[idx] = Pr{n = K + idx}
K	minimum number of jobs in the queue
N	buffer capacity in jobs
c	number of servers
Cs	squared coefficient of variation of the service times
Ca	squared coefficient of variation of the interarrival times OF THE STREAM whose blocking probability is requested

Returns

the probability that an arrival of this stream finds the queue full

Definition at line 58 of file me_gegecn_pb.h.

References line::InputError::InputError(), me_gegecn_pb(), and line::num_pow_int().

Referenced by me_gegecn(), me_gegecn_pb(), and me_oqn_blk().

me_mqn()

template<class T>

MeResult< T > line::me::me_mqn	(	std::size_t	M,
		std::size_t	R,
		const std::vector< char > &	open_classes,
		const Matrix< T > &	lambda0,
		const Matrix< T > &	Ca0,
		const std::vector< long > &	N,
		const Matrix< T > &	mu,
		const Matrix< T > &	Cs,
		const std::vector< Matrix< T > > &	P,
		const std::vector< long > &	c,
		const std::vector< long > &	refstat,
		const std::vector< char > &	insens,
		const MeOptions &	opt = MeOptions() )

Maximum-entropy algorithm for mixed open/closed multiclass networks.

Parameters

M	number of stations
R	number of classes
open_classes	per-class flag, nonzero for an open class
lambda0	external arrival rates (M x R), zero for closed classes
Ca0	external arrival scvs (M x R)
N	populations (R); the entries of open classes are unused
mu	service rates (M x R)
Cs	service scvs (M x R)
P	routing, R matrices (M x M)
c	servers per station, 0 for an infinite-server station
refstat	reference station per class, -1 for the default
insens	insensitive discipline flags per station
opt	tolerance and iteration budget

Definition at line 78 of file me_mqn.h.

References line::me::MeResult< T >::Ca, line::me::MeResult< T >::Cd, line::me::MeResult< T >::converged, line::InputError::InputError(), line::me::MeResult< T >::iter, line::me::MeResult< T >::L, line::me::MeResult< T >::lambda, line::Matrix< T >::Matrix(), me_cqn(), me_mqn(), me_oqn(), line::me::MeResult< T >::rho, line::me::MeResult< T >::W, and line::me::MeResult< T >::X.

Referenced by me_mqn(), and line::nc::solver_nc_mem().

me_oqn()

template<class T>

MeResult< T > line::me::me_oqn	(	std::size_t	M,
		std::size_t	R,
		const Matrix< T > &	lambda0,
		const Matrix< T > &	Ca0,
		const Matrix< T > &	mu,
		const Matrix< T > &	Cs,
		const std::vector< Matrix< T > > &	P,
		const std::vector< long > &	c,
		const std::vector< char > &	insens,
		const MeOptions &	opt = MeOptions() )

Maximum-entropy algorithm for open multiclass queueing networks.

Parameters

M	number of stations
R	number of classes
lambda0	external arrival rates (M x R)
Ca0	external arrival scvs (M x R)
mu	service rates (M x R)
Cs	service scvs (M x R)
P	routing, R matrices (M x M), P[r](j,i)
c	servers per station, 0 for an infinite-server station
insens	insensitive discipline flags per station
opt	tolerance and iteration budget

Definition at line 121 of file me_oqn.h.

References line::me::MeResult< T >::Ca, line::me::MeResult< T >::Cd, line::Matrix< T >::cols(), line::me::MeResult< T >::converged, line::InputError::InputError(), line::me::MeResult< T >::iter, line::me::MeResult< T >::L, line::me::MeResult< T >::lambda, line::Matrix< T >::Matrix(), me_oqn(), line::num_abs(), line::NumericError::NumericError(), line::me::MeResult< T >::rho, line::Matrix< T >::rows(), line::me::MeResult< T >::W, and line::me::MeResult< T >::X.

Referenced by me_mqn(), me_oqn(), and line::nc::solver_nc_mem().

me_oqn_blk()

template<class T>

MeBlkResult< T > line::me::me_oqn_blk	(	std::size_t	M,
		const std::vector< T > &	lambda0,
		const std::vector< T > &	Ca0,
		const std::vector< T > &	mu,
		const std::vector< T > &	Cs,
		const Matrix< T > &	P,
		const std::vector< long > &	c,
		const std::vector< long > &	N,
		const std::vector< int > &	blockrule,
		const MeBlkOptions &	opt = MeBlkOptions() )

Port of me_oqn_blk.

Parameters

M	number of stations
lambda0	external arrival rates (M)
Ca0	external interarrival scv (M), at least 1 where lambda0 > 0
mu	service rates (M)
Cs	service scv (M), at least 1 at every finite-buffer station
P	routing (M x M), P(i,j) = p_ij; a row sum below one sends the residual flow out of the network
c	servers per station (M); 0 marks an infinite server, as everywhere else in api/me
N	buffer capacity per station (M) in jobs, service included; 0 marks an unbounded buffer
blockrule	per station (M): 0 = loss, 1 = transfer blocking
opt	tolerance, iteration budget and relaxation weight

Definition at line 113 of file me_oqn_blk.h.

References line::me::MeBlkResult< T >::Ca, line::me::MeBlkResult< T >::Cd, line::Matrix< T >::cols(), line::me::MeBlkResult< T >::converged, line::InputError::InputError(), line::me::MeBlkResult< T >::iter, line::me::GegecnResult< T >::L, line::me::MeBlkResult< T >::lambda, me_gegec_mql(), me_gegecn(), me_gegecn_pb(), me_oqn_blk(), line::NumericError::NumericError(), line::me::GegecnResult< T >::p, line::me::MeBlkResult< T >::PBa, line::me::MeBlkResult< T >::Q, line::Matrix< T >::rows(), line::solve(), line::me::MeBlkResult< T >::T_, line::me::GegecnResult< T >::U, line::me::MeBlkResult< T >::U, and line::me::MeBlkResult< T >::W.

Referenced by me_oqn_blk(), and line::nc::solver_nc_mem().