Package jline.api.pfqn.nc

Class Pfqn_cub

java.lang.Object

jline.api.pfqn.nc.Pfqn_cub

public final class Pfqn_cub
extends Object

Field Summary

Fields

Modifier and Type	Field	Description
static final double	CUB_MAX_EVALS	integrand-evaluation budget above which pfqn_nc prefers le over cub
static final int	CUB_THINK_STEPS	quadrature points of v in the think-time branch; pfqn_nc prices CUB against it

Method Summary

Modifier and Type	Method	Description
static Ret.pfqnNc	pfqn_cub(Matrix L, Matrix N, Matrix Z)	Cubature method to compute the normalizing constant of a load-independent closed queueing network model
static Ret.pfqnNc	pfqn_cub(Matrix L, Matrix N, Matrix Z, int order, double atol)	Cubature method to compute the normalizing constant of a load-independent closed queueing network model
static double	pfqn_cub_evals(int M, int order, Matrix Z)	Number of integrand evaluations pfqn_cub performs at this order.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Details

CUB_THINK_STEPS

public static final int CUB_THINK_STEPS

quadrature points of v in the think-time branch; pfqn_nc prices CUB against it

See Also:

• Constant Field Values

CUB_MAX_EVALS

public static final double CUB_MAX_EVALS

integrand-evaluation budget above which pfqn_nc prefers le over cub

See Also:

• Constant Field Values

Method Details

pfqn_cub_evals

public static double pfqn_cub_evals(int M,
 int order,
 Matrix Z)

Number of integrand evaluations pfqn_cub performs at this order. The Grundmann-Moeller rule of degree order on the (M-1)-simplex evaluates sum_{d=0..order} binom(M-1+2d, M-1) points, and a non-zero think time repeats the whole rule at every v-quadrature step.

Parameters:

M - - number of queueing stations

order - - cubature order

Z - - think time per class, summed over delay stations

Returns:

the integrand-evaluation count

pfqn_cub

public static Ret.pfqnNc pfqn_cub(Matrix L,
 Matrix N,
 Matrix Z)

Cubature method to compute the normalizing constant of a load-independent closed queueing network model

pfqn_cub

public static Ret.pfqnNc pfqn_cub(Matrix L,
 Matrix N,
 Matrix Z,
 int order,
 double atol)

Cubature method to compute the normalizing constant of a load-independent closed queueing network model

Parameters:

L - - demands at all stations

N - - number of jobs for each class

Z - - think time for each class

order - - cubature order ( ceil((|N|-1)/2) or above is exact)

atol - - numerical tolerance for simplex quadrature

Returns:

normalizing constant, its logarithm, and mean performance metrics computed as a by-product