Sobre um sistema de fila com chegadas programadas sujeitas a perturbações do tipo Pareto

Abstract

We discuss the results and proofs presented in the article by Araman et al. (On a Single Server Queue Fed by a Scheduled Traffic with Pareto Perturbations), which studies queueing systems with scheduled arrivals affected by perturbations and deterministic service times. In this context, the n-th arrival is scheduled at time n but actually occurs at time n+ξn, where ξn are i.i.d. random variables. The behavior of the single-server system is analyzed under the assumption that the perturbations follow heavy-tailed distributions similar to the Pareto distribution, with finite mean. Despite the heavy tails of the perturbations, the system maintains unit intensity and exhibits light tails, indicating that individual perturbations do not dominate the global behavior of the system. The paper analyzes the queue behavior resulting from a sum of independent Bernoulli random variables. Assuming perturbations with finite mean, the use of these Bernoulli-type variables allows for a decomposition of the scheduled arrival process. This representation facilitates the mathematical characterization of the influence of perturbations and aids in obtaining an approximation for the stationary workload queue, both in the critically loaded case and in the heavy traffic scenario.