aoi_lcfspr_md1.h File Reference

Mean, variance and peak Age of Information of an M/D/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_md1 (const T &lambda, const T &d)
	Mean, variance and peak Age of Information of an M/D/1 preemptive LCFS queue.

Detailed Description

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

Templated port of matlab/src/api/aoi/aoi_lcfspr_md1.m, cross-checked against jar/src/main/java/jline/api/aoi/Aoi_lcfspr_md1.java (identical).

E[A] = 1/lambda + d E[Apeak] = d + exp(lambda d)/lambda Var[A] = 1/lambda^2 (the service time is constant)

from Inoue et al. (2019, Section IV). Under preemption an update is delivered only if no arrival occurs during its service, which happens with probability exp(-lambda d); the reciprocal of that probability is the exp(lambda d) in the peak age.

static_assert(num_traits<T>::has_transcendental) – the exp in the peak age. The mean and the variance are rational and could be evaluated exactly, but the triple is returned as a unit, as in MATLAB.

Definition in file aoi_lcfspr_md1.h.