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:

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

Looking back from any instant, each earlier update is delivered iff its service ends before the next arrival, so the age is a geometric sum of Exp(lambda) gaps ending at the first delivered update. The old 1/lambda + E[H] and lambda/(s+lambda) H*(s) hold only for exponential service.

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 and the transform are exact wherever H* is.

Definition in file aoi_lcfspr_mgi1.h.