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

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

Include dependency graph for aoi_lcfsd_gim1.h:

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_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 non-preemptive LCFS queue with discarding (LCFS-D).

Detailed Description

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

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).

Exact, Inoue et al. (2019, Section 3.3, NP-LCFS (C)), G* the interarrival LST and rho = 1/(E_Y mu):

E[A] = 1/mu + E[G^2]/(2E[G])

rho (-G*'(mu) + mu G*(mu) G*''(mu)/(1 + mu G*'(mu))) (eq. 69) E[Apeak] = P0 (E[G] + (1+G*(mu))/mu) + Pw (E[G]/(1-G*(mu)) + 1/mu) P0 = q/(q + G*(mu)), Pw = 1 - P0, q = 1 + mu G*'(mu)/(1-G*(mu)) (eq. 91) A*(s) = eq. (65)

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

static_assert(num_traits<T>::has_transcendental) – finite-difference first and second derivatives of G* at mu, with the steps MATLAB uses.

Definition in file aoi_lcfsd_gim1.h.

Namespaces