line::dqsys Namespace Reference

Classes
struct	Bernoulli1Result
	Steady-state quantities of a finite-buffer Bernoulli server. More...
struct	GeoGeo1Result
struct	GeoXGeo1Result

Enumerations
enum class	GeoConvention { LAS_DA , EAS }

Functions
template<class T>
Bernoulli1Result< T >	dqsys_bernoulli1 (const std::vector< T > &b, const std::vector< T > &p, std::size_t L)
	Finite buffer of L jobs.
template<class T>
T	dqsys_geogeo1_pmf (const GeoGeo1Result< T > &r, int n)
	Stationary queue-length pmf under the convention of the result.
template<class T>
GeoGeo1Result< T >	dqsys_geogeo1 (const T &a, const T &s, GeoConvention convention=GeoConvention::LAS_DA)
	Geo/Geo/1: the discrete-time single-server queue with geometric interarrival and service times.
template<class T>
GeoXGeo1Result< T >	dqsys_geoxgeo1_moments (const T &a, const T &batchMean, const T &batchSecondFactorial, const T &s, GeoConvention convention=GeoConvention::LAS_DA)
	Geo^X/Geo/1 for an arbitrary batch law given by its first two factorial moments.
template<class T>
GeoXGeo1Result< T >	dqsys_geoxgeo1 (const T &a, const T &beta, const T &s, GeoConvention convention=GeoConvention::LAS_DA)
	Geo^X/Geo/1: the discrete-time single-server queue with batch arrivals.
template<class T>
T	dqsys_geoxgeo1_pgf (const GeoXGeo1Result< T > &r, const T &z, const T &Az)
	Probability generating function of the stationary queue length.

Enumeration Type Documentation

GeoConvention

enum class line::dqsys::GeoConvention

strong

Enumerator
LAS_DA
EAS

Definition at line 45 of file dqsys_geogeo1.h.

Function Documentation

dqsys_bernoulli1()

template<class T>

Bernoulli1Result< T > line::dqsys::dqsys_bernoulli1	(	const std::vector< T > &	b,
		const std::vector< T > &	p,
		std::size_t	L )

Finite buffer of L jobs.

An arrival in a slot that finds L jobs present is lost, which is the loss system of corollary 2.8.

Parameters

b	offered arrival probabilities b(n) for n = 0..L, or one entry for a state independent stream
p	service probabilities p(n) for n = 1..L, or one entry for a state independent server
L	buffer capacity in jobs

Definition at line 78 of file dqsys_bernoulli1.h.

References line::dqsys::Bernoulli1Result< T >::arrivalPmf, line::dqsys::Bernoulli1Result< T >::arrivalProb, line::dqsys::Bernoulli1Result< T >::capacity, dqsys_bernoulli1(), line::dqsys::Bernoulli1Result< T >::emptyProb, line::InputError::InputError(), line::dqsys::Bernoulli1Result< T >::lossProb, line::dqsys::Bernoulli1Result< T >::meanQueueLength, line::dqsys::Bernoulli1Result< T >::meanSojournTime, line::dqsys::Bernoulli1Result< T >::meanWaitingQueue, line::dqsys::Bernoulli1Result< T >::meanWaitingTime, line::dqsys::Bernoulli1Result< T >::normConst, line::dqsys::Bernoulli1Result< T >::pmf, line::dqsys::Bernoulli1Result< T >::serviceProb, line::dqsys::Bernoulli1Result< T >::throughput, and line::dqsys::Bernoulli1Result< T >::utilization.

Referenced by dqsys_bernoulli1(), and line::nc::solver_nc_dt().

dqsys_geogeo1()

template<class T>

GeoGeo1Result< T > line::dqsys::dqsys_geogeo1	(	const T &	a,
		const T &	s,
		GeoConvention	convention = GeoConvention::LAS_DA )

Geo/Geo/1: the discrete-time single-server queue with geometric interarrival and service times.

Parameters

a	arrival probability per slot, in (0,1]
s	service completion probability per slot, in (0,1]
convention	slot-boundary convention (late arrival, early arrival)

Definition at line 84 of file dqsys_geogeo1.h.

References line::dqsys::GeoGeo1Result< T >::arrivalProb, line::dqsys::GeoGeo1Result< T >::convention, dqsys_geogeo1(), line::dqsys::GeoGeo1Result< T >::emptyProb, line::InputError::InputError(), LAS_DA, line::dqsys::GeoGeo1Result< T >::meanQueueLength, line::dqsys::GeoGeo1Result< T >::meanServiceTime, line::dqsys::GeoGeo1Result< T >::meanSojournTime, line::dqsys::GeoGeo1Result< T >::meanWaitingQueue, line::dqsys::GeoGeo1Result< T >::meanWaitingTime, line::dqsys::GeoGeo1Result< T >::ratio, line::dqsys::GeoGeo1Result< T >::serviceProb, line::dqsys::GeoGeo1Result< T >::throughput, and line::dqsys::GeoGeo1Result< T >::utilization.

Referenced by dqsys_geogeo1().

dqsys_geogeo1_pmf()

template<class T>

T line::dqsys::dqsys_geogeo1_pmf	(	const GeoGeo1Result< T > &	r,
		int	n )

Stationary queue-length pmf under the convention of the result.

Definition at line 65 of file dqsys_geogeo1.h.

References line::dqsys::GeoGeo1Result< T >::arrivalProb, line::dqsys::GeoGeo1Result< T >::convention, dqsys_geogeo1_pmf(), EAS, line::dqsys::GeoGeo1Result< T >::emptyProb, line::InputError::InputError(), line::num_pow_int(), line::dqsys::GeoGeo1Result< T >::ratio, and line::dqsys::GeoGeo1Result< T >::utilization.

Referenced by dqsys_geogeo1_pmf().

dqsys_geoxgeo1()

template<class T>

GeoXGeo1Result< T > line::dqsys::dqsys_geoxgeo1	(	const T &	a,
		const T &	beta,
		const T &	s,
		GeoConvention	convention = GeoConvention::LAS_DA )

Geo^X/Geo/1: the discrete-time single-server queue with batch arrivals.

Parameters

a	per-slot probability that a batch arrives, in (0,1]
beta	geometric batch-size parameter, in (0,1]; E[X] = 1/beta
s	per-slot service completion probability, in (0,1]
convention	slot-boundary convention (late arrival, early arrival)

Definition at line 148 of file dqsys_geoxgeo1.h.

References dqsys_geoxgeo1(), dqsys_geoxgeo1_moments(), line::InputError::InputError(), and LAS_DA.

Referenced by dqsys_geoxgeo1().

dqsys_geoxgeo1_moments()

template<class T>

GeoXGeo1Result< T > line::dqsys::dqsys_geoxgeo1_moments	(	const T &	a,
		const T &	batchMean,
		const T &	batchSecondFactorial,
		const T &	s,
		GeoConvention	convention = GeoConvention::LAS_DA )

Geo^X/Geo/1 for an arbitrary batch law given by its first two factorial moments.

This is MATLAB's local dqsys_geoxgeo1_moments, exposed here because a C++ caller has no other way to reach it.

Definition at line 74 of file dqsys_geoxgeo1.h.

References line::dqsys::GeoXGeo1Result< T >::arrivalRate, line::dqsys::GeoXGeo1Result< T >::batchArrivalProb, line::dqsys::GeoXGeo1Result< T >::batchMean, line::dqsys::GeoXGeo1Result< T >::batchSecondFactorialMoment, line::dqsys::GeoXGeo1Result< T >::boundaryEmptyProb, line::dqsys::GeoXGeo1Result< T >::convention, dqsys_geoxgeo1_moments(), line::InputError::InputError(), LAS_DA, line::dqsys::GeoXGeo1Result< T >::meanQueueLength, line::dqsys::GeoXGeo1Result< T >::meanServiceTime, line::dqsys::GeoXGeo1Result< T >::meanSojournTime, line::dqsys::GeoXGeo1Result< T >::meanWaitingQueue, line::dqsys::GeoXGeo1Result< T >::meanWaitingTime, line::dqsys::GeoXGeo1Result< T >::serviceProb, line::dqsys::GeoXGeo1Result< T >::throughput, and line::dqsys::GeoXGeo1Result< T >::utilization.

Referenced by dqsys_geoxgeo1(), and dqsys_geoxgeo1_moments().

dqsys_geoxgeo1_pgf()

template<class T>

T line::dqsys::dqsys_geoxgeo1_pgf	(	const GeoXGeo1Result< T > &	r,
		const T &	z,
		const T &	Az )

Probability generating function of the stationary queue length.

Parameters

r	a result of dqsys_geoxgeo1
z	argument in (0,1]
Az	the value A(z) of the slot-arrival pgf at the same z

No pmf is offered: for a general batch law the stationary distribution has no elementary closed form, so only the generating function is exact.

Definition at line 170 of file dqsys_geoxgeo1.h.

References line::dqsys::GeoXGeo1Result< T >::boundaryEmptyProb, line::dqsys::GeoXGeo1Result< T >::convention, dqsys_geoxgeo1_pgf(), line::InputError::InputError(), LAS_DA, line::NumericError::NumericError(), and line::dqsys::GeoXGeo1Result< T >::serviceProb.

Referenced by dqsys_geoxgeo1_pgf().