aoi_lcfsd_mgi1.h File Reference

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

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

Include dependency graph for aoi_lcfsd_mgi1.h:

Go to the source code of this file.

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_lcfsd_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 discarding (LCFS-D).

Detailed Description

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

Templated port of matlab/src/api/aoi/aoi_lcfsd_mgi1.m, cross-checked against jar/src/main/java/jline/api/aoi/Aoi_lcfsd_mgi1.java (identical).

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

E[A] = (lambda E[H^2]/2 + H*(lambda)/lambda - H*'(lambda))/(rho + H*(lambda))

• (1 - H*(lambda))/lambda + H*'(lambda) + E[H] (eq. 68) E[Apeak] = 1/lambda + H*'(lambda) + 2 E[H] A*(s) = eq. (64)

Discarding keeps at most one update waiting, so rho >= 1 is accepted.

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

Definition in file aoi_lcfsd_mgi1.h.