Package jline.api.pfqn.sens

Class Pfqn_sens_ldmx_ec

java.lang.Object

jline.api.pfqn.sens.Pfqn_sens_ldmx_ec

public final class Pfqn_sens_ldmx_ec
extends Object

Method Summary

Modifier and Type	Method	Description
static Ret.pfqnSensLdmxEc	pfqn_sens_ldmx_ec(Matrix lambda, Matrix D, Matrix mu)	Computes the effective capacity terms EC, E and Eprime of the mixed load-dependent MVA of Bruell-Balbo-Afshari, exactly as Pfqn_ldmx_ec does, and additionally their exact analytic derivatives with respect to the open-class load Lo(i) of each station.

Methods inherited from class java.lang.Object

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

Method Details

pfqn_sens_ldmx_ec

public static Ret.pfqnSensLdmxEc pfqn_sens_ldmx_ec(Matrix lambda,
 Matrix D,
 Matrix mu)

Computes the effective capacity terms EC, E and Eprime of the mixed load-dependent MVA of Bruell-Balbo-Afshari, exactly as Pfqn_ldmx_ec does, and additionally their exact analytic derivatives with respect to the open-class load Lo(i) of each station.

Lo(i) = sum_r lambda(r)*D(i,r) is the only channel through which a service demand enters E, Eprime and EC: the load-dependent rates mu are independent of the demands. Station i's terms depend on Lo(i) alone, so a single derivative per station is enough, and the chain rule then yields the derivative with respect to any demand-scaling parameter. This is the factorization behind equations (19), (21) and (24)-(31) of the reference, which are reproduced here term by term.

Reference: I. F. Akyildiz and J. C. Strelen, "Moment Analysis for Load-Dependent Mixed Product Form Queueing Networks", IEEE Trans. Communications 39(6):828-832, 1991.

The column index n of E, Eprime, dE and dEprime carries the value of the corresponding term at population n, i.e. it matches the MATLAB column 1+n; the column index n of EC and dEC carries the term at population n+1, i.e. the MATLAB column 1+n. This is the same convention used by Pfqn_ldmx_ec, so the two are interchangeable.

Parameters:

lambda - arrival rate vector (1 x R); zero for closed classes

D - service demand matrix (M x R)

mu - load-dependent rate matrix (M x Nt), limited load dependence

Returns:

EC, E, Eprime, Lo and their derivatives with respect to Lo