pfqn_sens_ldmx_ec.h File Reference

Effective capacity terms of the mixed load-dependent MVA of Bruell-Balbo-Afshari, together with their exact derivatives with respect to the open-class load Lo(i) of each station. More...

#include <cstddef>
#include <vector>
#include "line/num/number.h"
#include "line/util/error.h"
#include "line/util/matrix.h"

Include dependency graph for pfqn_sens_ldmx_ec.h:

Go to the source code of this file.

Classes
struct	line::pfqn::SensLdmxEcResult< T >

Namespaces
namespace	line
namespace	line::pfqn

Functions
template<class T>
SensLdmxEcResult< T >	line::pfqn::pfqn_sens_ldmx_ec (const std::vector< T > &lambda, const Matrix< T > &D, const Matrix< T > &mu)
	Effective capacity terms of the mixed load-dependent MVA of Bruell-Balbo-Afshari, together with their exact derivatives with respect to the open-class load Lo(i) of each station.

Detailed Description

Effective capacity terms of the mixed load-dependent MVA of Bruell-Balbo-Afshari, together with their exact derivatives with respect to the open-class load Lo(i) of each station.

Templated port of matlab/src/api/pfqn/pfqn_sens_ldmx_ec.m. The primal terms duplicate pfqn_ldmx_ec.h; they are recomputed here rather than reused because every intermediate (E1, F2, F3, F2prime) has to be carried alongside its derivative, and the reference does the same.

Lo(i) = sum_r lambda(r) D(i,r) is the only channel through which a demand enters E, Eprime and EC, since the load-dependent rates mu do not depend on the demands. Station i's terms depend on Lo(i) alone, so one derivative per station suffices and the chain rule then gives the derivative with respect to any demand-scaling parameter. This is the factorization behind equations (19), (21) and (24)-(31) of the reference, reproduced here term by term.

Arithmetic. Every term is a rational function of Lo and of the reciprocal rates, differentiated symbolically, so the routine stays in the field and instantiates at line::Rational with no gate.

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.

Definition in file pfqn_sens_ldmx_ec.h.