Package jline.api.lossn

Class Lossn_kr

java.lang.Object

jline.api.lossn.Lossn_kr

public final class Lossn_kr
extends Object

Kaufman-Roberts recursion for the multirate single-link loss system (stochastic knapsack).

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	Lossn_kr.LossnKrResult	Result of lossn_kr(Matrix, Matrix, double).

Method Summary

Modifier and Type	Method	Description
static Lossn_kr.LossnKrResult	lossn_kr(Matrix rho, Matrix b, double C)	Exact occupancy distribution and per-class blocking of a stochastic knapsack.

Methods inherited from class java.lang.Object

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

Method Details

lossn_kr

public static Lossn_kr.LossnKrResult lossn_kr(Matrix rho,
 Matrix b,
 double C)

Exact occupancy distribution and per-class blocking of a stochastic knapsack.

A single link of C bandwidth units is offered K classes of calls. Class k arrives as a Poisson process with offered load rho_k (arrival rate times mean holding time) and holds b_k units for the whole call; a call that finds fewer than b_k free units is lost. The occupancy distribution q(n) = P(n units busy), n = 0..C, satisfies the Kaufman-Roberts recursion

      n q(n) = sum_k b_k rho_k q(n - b_k),   q(n) = 0 for n < 0,
 

and a class-k call is blocked when more than C - b_k units are busy,

      B_k = sum_{n = C-b_k+1}^{C} q(n).
 

The result is insensitive to the holding-time distributions beyond their means. A class with b_k = 0 is never blocked; a class with b_k > C always is.

References: J. S. Kaufman, "Blocking in a Shared Resource Environment", IEEE Trans. Commun. 29(10), 1981. J. W. Roberts, "A Service System with Heterogeneous User Requirements", 1981. K. W. Ross, "Multiservice Loss Models for Broadband Telecommunication Networks", Springer, 1995, Sec. 2.2.

Parameters:

rho - offered load of class k (1xK, nonnegative)

b - bandwidth units held by a class-k call (1xK, nonnegative integers)

C - link capacity in bandwidth units (nonnegative integer)

Returns:

occupancy distribution q, blocking B and mean calls in progress QLen