aoi_lcfsd_gim1.h File Reference

Mean and peak Age of Information of a GI/M/1 non-preemptive LCFS queue with discarding (LCFS-D, equivalently GI/M/1/2*). More...

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

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Namespaces
namespace	line
namespace	line::aoi

Functions
template<class T>
AoiLstResult< T >	line::aoi::aoi_lcfsd_gim1 (const Lst< T > &Y_lst, const T &mu, const T &E_Y)
	Mean and peak Age of Information of a GI/M/1 non-preemptive LCFS queue with discarding (LCFS-D, equivalently GI/M/1/2*).

Detailed Description

Mean and peak Age of Information of a GI/M/1 non-preemptive LCFS queue with discarding (LCFS-D, equivalently GI/M/1/2*).

Templated port of matlab/src/api/aoi/aoi_lcfsd_gim1.m, cross-checked against jar/src/main/java/jline/api/aoi/Aoi_lcfsd_gim1.java (identical).

sigma solves Y*(mu - mu sigma) = sigma in (0,1) E[S] = 1/mu, E[T_eff] = E[S](1 + sigma) E[A] = E[Y] + E[S](1 + sigma) + sigma E[S]/(1 + sigma) E[Apeak] = E[Y] + E[T_eff]

from Inoue et al. (2019, Section VI) adapted to GI/M/1: an arriving update finds the server busy with probability sigma, and by memorylessness the remaining service is again exponential with rate mu.

static_assert(num_traits<T>::has_transcendental) – sigma is a bracketed root of a transcendental equation. Everything downstream of sigma is rational.

MATLAB falls back to sigma = rho when fzero fails to bracket; this port instead reports the failure, since a silent substitution of the utilization for the busy probability changes the answer without saying so. MATLAB returns an empty LST handle, reported here as has_lst = false.

Definition in file aoi_lcfsd_gim1.h.