Package jline.api.pfqn.nc

Class Pfqn_dnc

java.lang.Object

jline.api.pfqn.nc.Pfqn_dnc

public final class Pfqn_dnc
extends Object

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	Pfqn_dnc.Result	Result of the DNC evaluation at a real population.

Method Summary

Modifier and Type	Method	Description
static Pfqn_dnc.Result	pfqn_dnc(Matrix L, double N)	Normalizing constant and throughput at a real-valued population.

Methods inherited from class java.lang.Object

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

Method Details

pfqn_dnc

public static Pfqn_dnc.Result pfqn_dnc(Matrix L,
 double N)

Normalizing constant and throughput at a real-valued population.

With distinct loads x_1..x_G of multiplicities m_1..m_G the generating function prod_g (1-x_g u)^{-m_g} expands as G(n) = sum_g sum_{j=1..m_g} A_gj C(n+j-1,j-1) x_g^n, every term of which is analytic in n, so evaluating at a real n interpolates the integral normalizing constants exactly and gives a smooth throughput curve through the integral points. For all-distinct loads A_g = prod_{l!=g} x_g/(x_g - x_l) is used directly; with repeated loads the coefficients are recovered from G(0..M-1).

Only the queueing part admits this continuation: the delay sequence Z^n/n! is entire and has no partial-fraction expansion, so a think time is not accepted here. Use Pfqn_nintmva for nonintegral populations with a delay.

Parameters:

L - service demand vector (M x 1) of the queueing stations

N - population (real, nonnegative; may be fractional)

Returns:

throughput, normalizing constant and its logarithm