aoi_lcfspr_mgi1.h File Reference

Mean Age of Information, its transform and the peak age of an M/GI/1 preemptive LCFS queue. More...

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

Include dependency graph for aoi_lcfspr_mgi1.h:

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Namespaces
namespace	line
namespace	line::aoi

Functions
template<class T>
AoiLstResult< T >	line::aoi::aoi_lcfspr_mgi1 (const T &lambda, const Lst< T > &H_lst, const T &E_H)
	Mean Age of Information, its transform and the peak age of an M/GI/1 preemptive LCFS queue.

Detailed Description

Mean Age of Information, its transform and the peak age of an M/GI/1 preemptive LCFS queue.

Templated port of matlab/src/api/aoi/aoi_lcfspr_mgi1.m, cross-checked against jar/src/main/java/jline/api/aoi/Aoi_lcfspr_mgi1.java (identical).

E[A] = 1/lambda + E[H] q = P(S < Y) = H*(lambda) E[Apeak] = -H*'(lambda)/H*(lambda) + 1/(lambda H*(lambda)) A*(s) = lambda/(s + lambda) * H*(s)

from Inoue et al. (2019, Section IV). Under preemption the age at delivery is the sum of an interarrival time and the successful service time, so the AoI transform is simply the product of the two transforms.

static_assert(num_traits<T>::has_transcendental) – the peak age uses MATLAB's finite-difference derivative of H* at lambda, with step 1e-6 max(1,lambda). The mean is rational in lambda and E_H and is exact; the transform is exact wherever H* is.

Definition in file aoi_lcfspr_mgi1.h.