RT Journal Article
T1 Discrete-Time Retrial Queuing Systems with Last-Come-First-Served (LCFS) and First-Come-First-Served (FCFS) Disciplines: Negative Customer Impact and Stochastic Analysis
A1 Atencia-McKillop, Iván
A1 Sánchez-Merino, Sixto
A1 Fortes-Ruiz, Inmaculada
A1 Galán-García, José Luis
K1 Colas de espera, Teoría de
K1 Análisis estocástico
AB This paper examines a discrete-time retrial queuing system that incorporates negative customers, system breakdowns, and repairs. In this model, an arriving customer has the option to go directly to the server, pushing the currently served customer, if any, to the front of the orbit queue, or to join the orbit based on a First-Come-First-Served (FCFS) discipline. The study also considers negative customers who not only remove the customer currently being served but also cause a server breakdown. An in-depth analysis of the model is conducted using a generating function approach, leading to the determination of the distribution and expected values of the number of customers in the orbit and the entire system. The paper explores the stochastic decomposition law and provides bounds for the difference between the steady-state distribution of this system and a comparable standard system. Recursive formulas for the steady-state distributions of the orbit and the system are developed. Additionally, it is shown that the studied discrete-time system can approximate the M/G/1 continuous-time version of the model. The research includes a detailed examination of the customer’s sojourn time distribution in the orbit and the system, utilizing the busy period of an auxiliary system. The paper concludes with numerical examples that highlight how different system parameters affect various performance characteristics, and a section summarizing the key research contributions.
PB MDPI
YR 2025
FD 2025
LK https://hdl.handle.net/10630/40419
UL https://hdl.handle.net/10630/40419
LA eng
NO Atencia-Mckillop, I., Sánchez-Merino, S., Fortes-Ruiz, I., & Galán-García, J. L. (2025). Discrete-Time Retrial Queuing Systems with Last-Come-First-Served (LCFS) and First-Come-First-Served (FCFS) Disciplines: Negative Customer Impact and Stochastic Analysis. Mathematics, 13(1), 107. https://doi.org/10.3390/math13010107
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 13 abr 2026