qsys_mg1k_loss_mgs.h File Reference

MacGregor Smith's closed-form approximation of the M/G/1/K loss probability. More...

#include "line/api/qsys/qsys_types.h"
#include "line/num/number.h"
#include "line/util/error.h"

Include dependency graph for qsys_mg1k_loss_mgs.h:

Go to the source code of this file.

Classes
struct	line::qsys::Mg1kLossMgsResult< T >

Namespaces
namespace	line
namespace	line::qsys

Functions
template<class T>
Mg1kLossMgsResult< T >	line::qsys::qsys_mg1k_loss_mgs (const T &lambda, const T &mu, const T &mu_scv, unsigned K)
	MacGregor Smith's closed-form approximation of the M/G/1/K loss probability.

Detailed Description

MacGregor Smith's closed-form approximation of the M/G/1/K loss probability.

Templated port of matlab/src/api/qsys/qsys_mg1k_loss_mgs.m, cross-checked against jar/src/main/java/jline/api/qsys/Qsys_mg1k_loss_mgs.java (identical).

rho = lambda/mu, s = sqrt(scv), r = sqrt(rho), b = 2 + r s^2 - r Ploss = rho^((r s^2 - r + 2K)/b) (rho - 1) / ( rho^(2(1 + r s^2 - r + K)/b) - 1 )

The exponents interpolate the exact M/M/1/K expression in the service variability: at scv = 1 they are K and K+1 and the formula reduces to qsys_mm1k_loss.

ARITHMETIC. Both the square root of rho and the real-valued exponents are transcendental, so the function is gated. There is no exact instantiation even in principle: for scv != 1 the exponents are irrational.

Reference: J. MacGregor Smith, Optimal design and performance modelling of M/G/1/K queueing systems.

Definition in file qsys_mg1k_loss_mgs.h.