aoi_fcfs_mm1.h File Reference

Mean, variance and peak Age of Information of an M/M/1 FCFS queue. More...

#include "line/api/aoi/aoi_types.h"
#include "line/num/number.h"

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Namespaces
namespace	line
namespace	line::aoi

Functions
template<class T>
AoiResult< T >	line::aoi::aoi_fcfs_mm1 (const T &lambda, const T &mu)
	Mean, variance and peak Age of Information of an M/M/1 FCFS queue.

Detailed Description

Mean, variance and peak Age of Information of an M/M/1 FCFS queue.

Templated port of matlab/src/api/aoi/aoi_fcfs_mm1.m, cross-checked against jar/src/main/java/jline/api/aoi/Aoi_fcfs_mm1.java (identical).

E[A] = (1/mu)(1 + 1/rho + rho^2/(1-rho)) E[Apeak] = (1/mu)(1 + 1/rho + rho/(1-rho)) E[A^2] = (2/mu^2)(1 - rho - rho^3 + 4 rho^4 - 2 rho^5)/(rho^2 (1-rho)^2) Var[A] = E[A^2] - E[A]^2

from Inoue, Masuyama, Takine and Tanaka (IEEE Trans. IT 65(12), 2019). Every quantity is a rational function of rho, so the triple is exact in the field. This is the reference AoI closed form: E[A] has an interior minimum in rho near 0.53, and the exact instantiation locates it as the root of a polynomial rather than by a rounded search.

MATLAB clamps a negative variance to zero as a numerical safety net; the port keeps the clamp so the two agree, but note that in exact arithmetic the clamp can never fire, because E[A^2] - E[A]^2 is then evaluated without cancellation error.

Definition in file aoi_fcfs_mm1.h.