Package jline.api

Class LOSSN

java.lang.Object

jline.api.LOSSN

public class LOSSN
extends Object

APIs for stochastic models of loss networks

Constructor Summary

Constructors

Constructor	Description
LOSSN()

Method Summary

Modifier and Type	Method	Description
static double	ErlangB(double nu, double C)	Calculates the Erlang B formula for a given arrival rate and capacity.
static Ret.lossnErlangFP	lossn_erlangfp(Matrix nuVec, Matrix Amat, Matrix cVec)	This method calculates the Erlang fixed point approximation for loss networks.

Methods inherited from class java.lang.Object

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

Constructor Details

LOSSN

public LOSSN()

Method Details

lossn_erlangfp

public static Ret.lossnErlangFP lossn_erlangfp(Matrix nuVec,
 Matrix Amat,
 Matrix cVec)

This method calculates the Erlang fixed point approximation for loss networks.

Calls (jobs) on route (class) r arrive according to a Poisson rate nu_r, r=1,...,R. Call service times on route r have unit mean.

The link capacity requirements are defined as: sum_r A(j, r) n(j, r) < C(j) for all links j=1,...,J, where n(j, r) counts the calls on route r on link j.

Parameters:

nuVec - A Matrix (1xR) representing the arrival rate of route (class) r = 1,...,R.

Amat - A Matrix (J,R) representing the capacity requirement of link j for route r = 1,...,R.

cVec - A Matrix (J,1) representing the available capacity of link j.

Returns:

lossnErlangFPReturn which contains: - qLen (1xR): mean queue-length for route r = 1,...,R calls. - loss (1xR): loss probability for route r = 1,...,R calls. - eBlock (Jx1): blocking probability for link j = 1,...,J.

Note: nu_r may be replaced by a utilization rho_r=nu_r/mu_r, where mu_r is the service rate for route r. Example: lossn_erlangfp(new Matrix("[0.3,0.1]"), new Matrix("[1,1;1,4]"), new Matrix("[1,3]")).qLen.print();

ErlangB

public static double ErlangB(double nu,
 double C)

Calculates the Erlang B formula for a given arrival rate and capacity.

The Erlang B formula is used to compute the blocking probability in a loss system where calls arrive according to a Poisson process and there are a fixed number of servers.

Parameters:

nu - The traffic intensity or offered load, which is the product of the arrival rate and the average service time.

C - The total capacity or number of servers.

Returns:

The blocking probability, which is the probability that a call is blocked due to all servers being busy.