The Waiting Time Distribution in Poisson-Driven Deterministic Systems - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports Year : 1997

The Waiting Time Distribution in Poisson-Driven Deterministic Systems

Abstract

We consider systems with Poisson arrivals and a deterministic delay structure given by some increasing sequence. We characterize the distribution of waiting times in the transient regime, and describe effective ways to evaluate it. We also compute the stationary waiting time distribution in the case where the deterministic structure becomes ultimately periodic. This analysis is strongly connected to the theory of linear $(\max,+)$ systems and has the same range of applications: we give examples from stochastic Petri Net theory and stochastic task graph theory. It also applies in general to single server queues with Poisson arrivals and known service times, in particular to the $M/D/1$ queue with periodic service durations and the $E/D/1$ queue.
Fichier principal
Vignette du fichier
RR-3083.pdf (530.47 Ko) Télécharger le fichier

Dates and versions

inria-00073608 , version 1 (24-05-2006)

Identifiers

  • HAL Id : inria-00073608 , version 1

Cite

Alain Jean-Marie. The Waiting Time Distribution in Poisson-Driven Deterministic Systems. RR-3083, INRIA. 1997. ⟨inria-00073608⟩
90 View
13386 Download

Share

Gmail Facebook Twitter LinkedIn More