aoi_lcfss_mgi1.h File Reference

Mean Age of Information, its transform and the peak age of an M/GI/1 non-preemptive LCFS queue with set-aside (LCFS-S), i.e. More...

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

Include dependency graph for aoi_lcfss_mgi1.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_lcfss_mgi1 (const T &lambda, const Lst< T > &H_lst, const T &E_H, const T &E_H2)
	Mean Age of Information, its transform and the peak age of an M/GI/1 non-preemptive LCFS queue with set-aside (LCFS-S).

Detailed Description

Mean Age of Information, its transform and the peak age of an M/GI/1 non-preemptive LCFS queue with set-aside (LCFS-S), i.e.

LCFS without discarding: older waiting updates are still served, after fresher ones.

Templated port of matlab/src/api/aoi/aoi_lcfss_mgi1.m, cross-checked against jar/src/main/java/jline/api/aoi/Aoi_lcfss_mgi1.java (identical).

Exact, Inoue et al. (2019, Section 3.3, NP-LCFS (D)), H* the service LST:

E[A] = lambda E[H^2]/2 + ((1-rho)^2/(rho H*(lambda)) + 2) E[H] (eq. 70) E[Apeak] = E[H] + E[W] + 1/(lambda (2 - rho - H*(lambda))) E[W] = ((1 - H*(lambda))/lambda + H*'(lambda))/(2 - rho - H*(lambda)) A*(s) = eq. (66)

static_assert(num_traits<T>::has_transcendental) – MATLAB's finite-difference derivative of H* at lambda.

Definition in file aoi_lcfss_mgi1.h.