Fernando Miguelez | Searcharxiv

arXiv2025

On the Age of Information in Single-Server Queues with Aged Updates

The Age of Information (AoI) is a performance metric that quantifies the freshness of data in systems where timely updates are critical. Most state-of-the-art methods typically assume that packets enter the monitored system with zero age, neglecting situations, such as those prevalent in multi-hop networks or distributed sensing, where packets experience prior delays. In this paper, the AoI is investigated when packets have a non-zero initial age. We derive an expression for the average AoI in this setting, showing that it equals the standard AoI plus a correction term involving the correlation between packet age and inter-departure times. When these variables are independent, the expression simplifies to an additive correction equal to the mean initial age. In cases where the dependency structure is unknown, we also establish lower and upper bounds for the correction term. We demonstrate the applicability of our approach across various queueing scenarios, such as forwarding, tandem, and retrial queues. Additionally, we explore the accuracy of the derived bounds on a tandem composed of several queues, a model that has not yet been analytically solved from an age perspective.

cs.IT↗

arXiv2024

An Adaptive Learning Approach to Multivariate Time Forecasting in Industrial Processes

Industrial processes generate a massive amount of monitoring data that can be exploited to uncover hidden time losses in the system. This can be used to enhance the accuracy of maintenance policies and increase the effectiveness of the equipment. In this work, we propose a method for one-step probabilistic multivariate forecasting of time variables involved in a production process. The method is based on an Input-Output Hidden Markov Model (IO-HMM), in which the parameters of interest are the state transition probabilities and the parameters of the observations' joint density. The ultimate goal of the method is to predict operational process times in the near future, which enables the identification of hidden losses and the location of improvement areas in the process. The input stream in the IO-HMM model includes past values of the response variables and other process features, such as calendar variables, that can have an impact on the model's parameters. The discrete part of the IO-HMM models the operational mode of the process. The state transition probabilities are supposed to change over time and are updated using Bayesian principles. The continuous part of the IO-HMM models the joint density of the response variables. The estimate of the continuous model parameters is recursively computed through an adaptive algorithm that also admits a Bayesian interpretation. The adaptive algorithm allows for efficient updating of the current parameter estimates as soon as new information is available. We evaluate the method's performance using a real data set obtained from a company in a particular sector, and the results are compared with a collection of benchmark models.

stat.AP↗