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

Iván Atencia-Mckillop (), Sixto Sánchez-Merino, Inmaculada Fortes-Ruiz and José Luis Galán-García
Additional contact information
Iván Atencia-Mckillop: Department of Applied Mathematics, School of Industrial Engineering, University of Málaga, 29071 Málaga, Spain
Sixto Sánchez-Merino: Department of Applied Mathematics, School of Industrial Engineering, University of Málaga, 29071 Málaga, Spain
Inmaculada Fortes-Ruiz: Department of Applied Mathematics, School of Industrial Engineering, University of Málaga, 29071 Málaga, Spain
José Luis Galán-García: Department of Applied Mathematics, School of Industrial Engineering, University of Málaga, 29071 Málaga, Spain

Mathematics, 2024, vol. 13, issue 1, 1-24

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.

Keywords: discrete-time retrial queue; negative customers; stochastic decomposition; recursive formulae; sojourn times (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/1/107/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/1/107/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2024:i:1:p:107-:d:1556356

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().