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
	Conservation laws of a layered queueing network, enumerated from its structure.
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] = exp(lambda d)/lambda E[Apeak] = d + exp(lambda d)/lambda Var[A] = (exp(2 lambda d) - 2 lambda d exp(lambda d))/lambda^2

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 mean and peak age. The moments follow from the M/GI/1 preemptive transform A*(s) = f(s)/(s + f(s)), f(s) = lambda H*(s+lambda).

static_assert(num_traits<T>::has_transcendental) – the exp in all three.

Definition in file aoi_lcfspr_md1.h.