A Discrete-Time Single-Server Retrial Queue with Preemption and Adaptive Retrial Times: Theoretical Analysis and Telecommunication Insights

Iván Atencia-Mckillop (), José Luis Galán-García, María Ángeles Galán-García, Yolanda Padilla-Domínguez, Pedro Rodríguez-Cielos and Pablo Rodríguez-Padilla
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Iván Atencia-Mckillop: Department of Applied Mathematics, Escuela de Ingenierías Industriales, University of Málaga, Campus de Teatinos, Dr. Ortiz Ramos s/n, 29071 Málaga, Spain
José Luis Galán-García: Department of Applied Mathematics, Escuela de Ingenierías Industriales, University of Málaga, Campus de Teatinos, Dr. Ortiz Ramos s/n, 29071 Málaga, Spain
María Ángeles Galán-García: Department of Applied Mathematics, Escuela de Ingenierías Industriales, University of Málaga, Campus de Teatinos, Dr. Ortiz Ramos s/n, 29071 Málaga, Spain
Yolanda Padilla-Domínguez: Department of Applied Mathematics, Escuela de Ingenierías Industriales, University of Málaga, Campus de Teatinos, Dr. Ortiz Ramos s/n, 29071 Málaga, Spain
Pedro Rodríguez-Cielos: Department of Applied Mathematics, Escuela de Ingenierías Industriales, University of Málaga, Campus de Teatinos, Dr. Ortiz Ramos s/n, 29071 Málaga, Spain
Pablo Rodríguez-Padilla: Department of Applied Mathematics, Escuela de Ingenierías Industriales, University of Málaga, Campus de Teatinos, Dr. Ortiz Ramos s/n, 29071 Málaga, Spain

Mathematics, 2025, vol. 13, issue 21, 1-14

Abstract: This paper analyzes a discrete-time single-server retrial queue with preemptive service, Bernoulli arrivals, and adaptive retrial times, tailored to telecommunications systems. In call centers, the model captures caller retries and priority interruptions, while in cellular networks, it represents user channel access attempts with preemption for emergency calls. Using a Markov chain framework, we derive the stationary distribution, establish a stability condition, and compute performance metrics, including the mean number of retrying callers or users and orbit size probabilities. The model incorporates a novel retrial time adaptation probability, reflecting dynamic retry behaviors in telecommunications. Numerical results demonstrate the impact of arrival rates, preemption probabilities, and retrial adaptations on system performance, offering insights for optimizing call center staffing and cellular network protocols. Applications to slotted ALOHA and TDMA systems highlight the model’s practical relevance.

Keywords: discrete-time queue; retrial queue; preemption; Markov chain; call centers; cellular networks; stationary distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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