qsys_engset.h File Reference

Exact analysis of the Engset loss system M/G/c/c/K: K sources, each idle for an Exp(alpha) time, c servers and no waiting room. More...

#include <algorithm>
#include <cmath>
#include <string>
#include <vector>
#include "line/api/qsys/qsys_res.h"
#include "line/util/error.h"

Include dependency graph for qsys_engset.h:

Go to the source code of this file.

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

Functions
std::vector< double >	line::qsys::engsetdetail::engset_dist (double beta, unsigned c, unsigned K)
	The truncated binomial occupancy law, normalized in log space.
QsysRes	line::qsys::qsys_engset (double alpha, double mu, unsigned c, unsigned K)
	Exact Engset M/G/c/c/K loss system.

Detailed Description

Exact analysis of the Engset loss system M/G/c/c/K: K sources, each idle for an Exp(alpha) time, c servers and no waiting room.

Port of matlab/src/api/qsys/qsys_engset.m. The number of busy servers has the truncated binomial law p_n ~ C(K, n) beta^n, n = 0..c, beta = alpha/mu, which is insensitive to the service law. Time congestion is p_c; call congestion (what an arriving request sees) is the time congestion of the same system with K-1 sources.

ARITHMETIC: double (gammaln, log-space normalization), as the reference.

Definition in file qsys_engset.h.