Notas sobre Teoría de colas y algunas aplicaciones

Carlos E. Martínez-Rodríguez
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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.
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排队理论及一些应用说明
本文全面评述了随机过程,尤其侧重于马尔可夫链和跳跃过程。本文分析了与排队系统相关的主要结果。此外,还介绍了确保此类系统稳定性或遍历性的条件。论文还讨论了排队网络的稳定性结果,并将其扩展到驻留系统。最后,介绍了概率生成函数的主要贡献,它是分析上述过程的重要工具。这篇综述从排队理论的角度出发,以肯达尔-李符号为基础,强调稳定性结果和基于每个过程具体特征的性能指标的计算。
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