aoi_lcfss_gim1.h File Reference

Mean Age of Information, its transform and the peak age of a GI/M/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_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_lcfss_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 set-aside (LCFS-S).

Detailed Description

Mean Age of Information, its transform and the peak age of a GI/M/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_gim1.m, cross-checked against jar/src/main/java/jline/api/aoi/Aoi_lcfss_gim1.java (identical).

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

E[A] = 1/mu + E[G^2]/(2E[G]) + rho (-G*'(mu - mu gamma)) (eq. 71) E[Apeak] = P0 (E[G] + (1+G*(mu))/mu)

• Pw (1/mu + (E[G] + G*'(mu) + (gamma - G*(mu))/(gamma mu))/(1 - G*(mu))) P0 = (1-gamma)/(1 - gamma G*(mu)), Pw = 1 - P0 (eqs. 100-103) A*(s) = eq. (67)

static_assert(num_traits<T>::has_transcendental) – gamma is a bracketed root of a transcendental equation and G*' is a finite difference. A bracketing failure is an error, never a gamma = rho fallback.

Definition in file aoi_lcfss_gim1.h.