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Discrete-Time Retrial Queuing Systems with Last-Come-First-Served (LCFS) and First-Come-First-Served (FCFS) Disciplines: Negative Customer Impact and Stochastic Analysis

Author

Listed:
  • Iván Atencia-Mckillop

    (Department of Applied Mathematics, School of Industrial Engineering, University of Málaga, 29071 Málaga, Spain
    Current address: Avda. Cervantes, 2, University of Málaga, 29071 Málaga, Spain.
    These authors contributed equally to this work.)

  • Sixto Sánchez-Merino

    (Department of Applied Mathematics, School of Industrial Engineering, University of Málaga, 29071 Málaga, Spain
    Current address: Avda. Cervantes, 2, University of Málaga, 29071 Málaga, Spain.
    These authors contributed equally to this work.)

  • Inmaculada Fortes-Ruiz

    (Department of Applied Mathematics, School of Industrial Engineering, University of Málaga, 29071 Málaga, Spain
    Current address: Avda. Cervantes, 2, University of Málaga, 29071 Málaga, Spain.
    These authors contributed equally to this work.)

  • José Luis Galán-García

    (Department of Applied Mathematics, School of Industrial Engineering, University of Málaga, 29071 Málaga, Spain
    Current address: Avda. Cervantes, 2, University of Málaga, 29071 Málaga, Spain.
    These authors contributed equally to this work.)

Abstract

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.

Suggested Citation

  • Iván Atencia-Mckillop & Sixto Sánchez-Merino & Inmaculada Fortes-Ruiz & José Luis Galán-García, 2024. "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, MDPI, vol. 13(1), pages 1-24, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:107-:d:1556356
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    References listed on IDEAS

    as
    1. N. Nithya & N. Anbazhagan & S. Amutha & K. Jeganathan & Gi-Cheon Park & Gyanendra Prasad Joshi & Woong Cho, 2023. "Controlled Arrivals on the Retrial Queueing–Inventory System with an Essential Interruption and Emergency Vacationing Server," Mathematics, MDPI, vol. 11(16), pages 1-24, August.
    2. J. Artalejo & J. Falin, 1994. "Stochastic decomposition for retrial queues," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 2(2), pages 329-342, December.
    Full references (including those not matched with items on IDEAS)

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