lossn_links.h File Reference

Per-link blocking and occupancy of a loss network. More...

#include <algorithm>
#include <cctype>
#include <cmath>
#include <cstddef>
#include <cstdint>
#include <string>
#include <vector>
#include "line/api/lossn/lossn_asy.h"
#include "line/api/lossn/lossn_erlangfp.h"
#include "line/api/lossn/lossn_manjunath.h"
#include "line/api/lossn/lossn_mci.h"
#include "line/api/lossn/lossn_rec.h"
#include "line/num/number.h"
#include "line/util/error.h"
#include "line/util/matrix.h"

Include dependency graph for lossn_links.h:

Go to the source code of this file.

Classes
struct	line::lossn::LossnLinksResult< T >
	Result of lossn_links. More...

Namespaces
namespace	line
	Conservation laws of a layered queueing network, enumerated from its structure.
namespace	line::lossn

Functions
template<class T>
LossnLinksResult< T >	line::lossn::lossn_links (const std::vector< T > &nu, const Matrix< T > &A, const std::vector< T > &C, const std::string &method="exact", const LossnMciOptions< T > &mciopt=LossnMciOptions< T >(), std::uint64_t seed=0)
	Per-link blocking and occupancy of a loss network.

Detailed Description

Per-link blocking and occupancy of a loss network.

Templated port of matlab/src/api/lossn/lossn_links.m.

Returns, for every link j and route r with A(j,r) > 0, the probability that link j alone cannot accept a route-r call, E(j,r) = P(fewer than A(j,r) free units on link j), together with the mean occupancy of each link, Occ_j = sum_r A(j,r) E[n_r]. Under the product form the link blocking is a ratio of normalizing constants, E(j,r) = 1 - G(C - A(j,r) e_j)/G(C), which the exact methods evaluate directly. The route loss satisfies Loss_r >= max_j E(j,r), with equality only when no two links block route r in different states.

Methods:

• 'exact' (also 'manjunath', 'ms'): one Manjunath-Sikdar evaluation per distinct (link, requirement) pair; needs integral A and C.
• 'rec': as exact with MDD-rec, also for fractional A and C.
• 'erlangfp': the Erlang fixed-point blocking matrix (independence approximation).
• 'asy': the Kelly limit, E(j,r) = 1 - (1-a_j)^A(j,r).
• 'mci': the importance-sampling estimator of lossn_mci (the options carry the sample count and the seed).

ARITHMETIC. The fixed point, the fluid limit and the Monte Carlo estimator are all transcendental, so the header is gated on num_traits<T>::has_transcendental.

Reference: K. W. Ross, "Multiservice Loss Models for Broadband Telecommunication Networks", Springer, 1995, Sec. 5.1-5.3.

See also

lossn_revsens, lossn_mci, lossn_asy, lossn_erlangfp

Definition in file lossn_links.h.