aoi_lcfspr_gim1.h File Reference

Mean Age of Information, its transform and the peak age of a GI/M/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_gim1.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>
AoiLstResult< T >	line::aoi::aoi_lcfspr_gim1 (const Lst< T > &Y_lst, const T &mu, const T &E_Y, const T &E_Y2)
	Mean Age of Information, its transform and the peak age of a GI/M/1 preemptive LCFS queue.

Detailed Description

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

Templated port of matlab/src/api/aoi/aoi_lcfspr_gim1.m, cross-checked against jar/src/main/java/jline/api/aoi/Aoi_lcfspr_gim1.java (identical).

E[A] = lambda E[Y^2]/2 + 1/mu q = P(S < Y) = 1 - Y*(mu) E[S|succ] = (1/mu + Y*'(mu) - Y*(mu)/mu) / q E[Apeak] = E[S|succ] + 1/(lambda q) A*(s) = mu/(s + mu) * lambda (1 - Y*(s))/s

With memoryless service the age is the backward recurrence time of the arrivals plus an independent Exp(mu); the old E[Y] + 1/mu and Y*(s) mu/(s+mu) hold only for Poisson arrivals (general age formula of Inoue et al. 2019).

static_assert(num_traits<T>::has_transcendental) – MATLAB's finite-difference derivative of Y* at mu. The mean is rational in E_Y, E_Y2 and mu and is exact; the transform is exact wherever Y* is.

Definition in file aoi_lcfspr_gim1.h.