aoi_lcfspr_mm1.h File Reference

Mean, variance and peak Age of Information of an M/M/1 preemptive LCFS 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_lcfspr_mm1 (const T &lambda, const T &mu)
	Mean, variance and peak Age of Information of an M/M/1 preemptive LCFS queue.

Detailed Description

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

Templated port of matlab/src/api/aoi/aoi_lcfspr_mm1.m, cross-checked against jar/src/main/java/jline/api/aoi/Aoi_lcfspr_mm1.java (identical).

E[A] = (1/mu)(1 + 1/rho) = 1/mu + 1/lambda E[Apeak] = 1/(lambda+mu) + 1/lambda + 1/mu E[A^2] = 2 (1/lambda^2 + 1/(lambda mu) + 1/mu^2)

from Inoue et al. (2019, Section IV). Rational throughout, hence exact in the field. The identity worth checking is E[A]_LCFSPR < E[A]_FCFS at every rho in (0,1): both sides are exact rationals, so the comparison is a theorem rather than a numerical observation.

Definition in file aoi_lcfspr_mm1.h.