qsys_mm1k_loss.h File Reference

Blocking probability of the M/M/1/K queue. More...

#include <cmath>
#include "line/api/qsys/qsys_types.h"
#include "line/lang/lang_types.h"
#include "line/num/number.h"
#include "line/util/error.h"

Include dependency graph for qsys_mm1k_loss.h:

Go to the source code of this file.

Classes
struct	line::qsys::Mm1kLossResult< T >

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

Functions
template<class T>
Mm1kLossResult< T >	line::qsys::qsys_mm1k_loss (const T &lambda, const T &mu, unsigned K)
	Blocking probability of the M/M/1/K queue.

Detailed Description

Blocking probability of the M/M/1/K queue.

Templated port of matlab/src/api/qsys/qsys_mm1k_loss.m, cross-checked against jar/src/main/java/jline/api/qsys/Qsys_mm1k_loss.java (identical).

rho = lambda/mu Ploss = (1-rho)/(1-rho^(K+1)) * rho^K

Only integer powers appear, so this is exact for T = Rational. It is the closed form the Niu-Cooper transform-free M/G/1/K analysis collapses onto when the service is exponential, and qsys_mg1k_loss must reproduce it.

The formula has a removable singularity at rho = 1, where the true value is 1/(K+1): the stationary law is uniform over 0..K, so the full state carries 1/(K+1) like every other. This port RAISED there until 2026-09-13, while MATLAB, the JAR and python all returned the limit, so the one caller that reaches a saturated M/M/1/K got an exception from C++ and a number from the other three. The limit is a rational, not an approximation, so it is exact for T = Rational as well.

Definition in file qsys_mm1k_loss.h.