qsys_mmk.h File Reference

Exact mean response time of the M/M/k queue (Erlang-C). More...

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

Include dependency graph for qsys_mmk.h:

Go to the source code of this file.

Namespaces
namespace	line
namespace	line::qsys

Functions
template<class T>
QsysResult< T >	line::qsys::qsys_mmk (const T &lambda, const T &mu, unsigned k)
	Exact mean response time of the M/M/k queue (Erlang-C).

Detailed Description

Exact mean response time of the M/M/k queue (Erlang-C).

Templated port of matlab/src/api/qsys/qsys_mmk.m, cross-checked against jar/src/main/java/jline/api/qsys/Qsys_mmk.java. The JAR accumulates the factorials incrementally and writes C = 1/(1+(1-rho)*(C*(C-1)!)/(C rho)^C*S), which is the same k! as MATLAB's factorial(k); the two agree.

rho = lambda/(mu k) S = sum_{j=0}^{k-1} (k rho)^j / j! C = 1 / (1 + (1-rho) k! / (k rho)^k * S) Q = rho/(1-rho) C + k rho, W = Q/lambda

Every exponent is an integer, so this stays in the field of the inputs and is exact for T = Rational.

Definition in file qsys_mmk.h.