Package jline.api.pfqn.nc

Class Pfqn_is

java.lang.Object

jline.api.pfqn.nc.Pfqn_is

public final class Pfqn_is
extends Object

Importance-sampling (IS) estimate of the normalizing constant of a closed LOAD-INDEPENDENT product-form queueing network with M single-server queues of per-class demand L and an aggregated delay of think time Z.

This is the load-independent case of Pfqn_ld_is (capacities mu_i(k) = 1), and the ordinary-network counterpart of the order-independent

invalid reference

Pfqn_oi_is

and the pass-and-swap Pfqn_pas_is: all four are the same sample-an-ordering estimator, differing only in the per-position factor of each station's balance function. For a single-server queue that factor is the demand of the class at that position, L(i,q_p); for the delay it is Z(q_p)/p; for an OI/P&S station it is the reciprocal rank rate 1/mu_i(supp(q_1..q_p)).

Writing ell = sum(N), an ordering c of all ell jobs is drawn by placing a uniformly random present class at each step (probability p(c) = product of the reciprocal branching factors), and the sum over ALL ways of cutting c into contiguous per-station segments is computed exactly by dynamic programming: G(N) = E_{C~p}[ S(C)/p(C) ], which is unbiased for the exact constant of Pfqn_nc.

Port of matlab/src/api/pfqn/pfqn_is.m.

See Also:

• Pfqn_ld_is
• invalid reference

  Pfqn_oi_is

• Pfqn_pas_is

Method Summary

Modifier and Type	Method	Description
static Ret.pfqnNc	pfqn_is(Matrix L, Matrix N, Matrix Z, SolverOptions options)	Importance-sampling estimate of the load-independent normalizing constant.

Methods inherited from class java.lang.Object

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

Method Details

pfqn_is

public static Ret.pfqnNc pfqn_is(Matrix L,
 Matrix N,
 Matrix Z,
 SolverOptions options)

Importance-sampling estimate of the load-independent normalizing constant.

Parameters:

L - (M x R) per-class service demands at the M single-server queues.

N - (1 x R) closed population vector, finite.

Z - (1 x R) aggregated think time (delay) demand; null or zeros if none.

options - solver options; uses options.samples and options.seed.

Returns:

G and lG = log(G).