Package jline.api.lossn

Class Lossn_rec

java.lang.Object

jline.api.lossn.Lossn_rec

public class Lossn_rec
extends Object

Exact analysis of a loss network by MDD-rec: the normalising constant is the sum of a product form over the admissible set {n >= 0 : A n <= C}, which is what a decision diagram holding that set computes in one memoised walk.

A Kelly loss network carries offered load nu_r on route r and admits a call only while the resource constraint A n <= C still holds after it. The stationary law is the truncation of independent Poisson counts to that set, P(n) = (1/G) prod_r nu_r^(n_r)/n_r!, so g_r(k) = nu_r^k/k! and Mdd_rec returns G. By PASTA the acceptance probability of a class-r call is the ratio of two such constants, 1 - B_r = G(C - A e_r) / G(C), which is one further diagram per class.

Why this exists alongside Lossn_manjunath. The Manjunath-Sikdar transform evaluates G exactly as a multidimensional residue, and the residue argument counts WHOLE UNITS: it needs an integral A and C. On a region declaring a fractional class size or capacity the analyzer had no exact route at all and fell back to the Erlang fixed point, an approximation. MDD-rec needs only that the admissible set be finite and bounded coordinate by coordinate, which a fractional constraint still is, so it is exact there too. It is also an exact alternative to the Monte Carlo summation Lossn_mci estimates.

References: F. P. Kelly, "Loss networks", Annals of Applied Probability 1(3), 1991. S. Balsamo, A. Marin, I. Stojic, "Computation of the normalising constant for product-form models of distributed systems with synchronisation", Future Generation Computer Systems 111 (2020) 475-490.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	Lossn_rec.LossnRecResult	Carried load, blocking, log normalising constant and walk count.

Method Summary

Modifier and Type	Method	Description
static Lossn_rec.LossnRecResult	lossn_rec(Matrix nu, Matrix A, Matrix C)	Exact loss-network analysis by MDD-rec.

Methods inherited from class java.lang.Object

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

Method Details

lossn_rec

public static Lossn_rec.LossnRecResult lossn_rec(Matrix nu,
 Matrix A,
 Matrix C)

Exact loss-network analysis by MDD-rec.

Parameters:

nu - offered load per class, length K

A - J x K non-negative resource requirement matrix

C - capacity vector, length J