Notas sobre Teor\'ia de colas y algunas aplicaciones

TL;DR

This paper reviews stochastic processes, especially Markov chains and jump processes, focusing on queuing systems, their stability conditions, and analysis tools like the Probability Generating Function, from a queuing theory perspective.

Contribution

It provides a comprehensive overview of stability conditions and performance analysis methods for queuing systems and networks, emphasizing the role of the Probability Generating Function.

Findings

Stability conditions for queuing systems are detailed.

Performance measures can be computed using the Probability Generating Function.

Extensions to queuing networks and visiting systems are discussed.

Abstract

This paper presents a comprehensive review of stochastic processes, with a particular focus on Markov chains and jump processes. The main results related to queuing systems are analyzed. Additionally, conditions that ensure the stability, or ergodicity, of such systems are presented. The paper also discusses stability results for queuing networks and their extension to visiting systems. Finally, key contributions concerning the Probability Generating Function, an essential tool in the analysis of the aforementioned processes, are introduced. The review is conducted from the perspective of queuing theory, grounded in the Kendall-Lee notation, emphasizing stability results and the computation of performance measures based on the specific characteristics of each process.