Revue d'économie et de statistique appliquée
Volume 22, Numéro 1, Pages 72-90
2025-06-03
Modeling A Retrial Queue With Batch Arrivals And Impatient Customers Under Server Failures And Bernoulli-controlled Availability
Authors : Moulai Ratiba . Benrais Isma . Boualem Mohamed .
Abstract
This paper analyzes an MX/G/1 retrial queueing model with batch arrivals and impatient customers, where the server is subject to active breakdowns and follows a Bernoulli vacation schedule that incorporates a reservation period. When primary customers arrive and find the server unavailable—due to service, breakdown, reservation, or vacation—they may either leave the system permanently or enter an orbit, generating future retrial attempts. In case of a server failure during service, the interrupted customer may wait near the server until it is repaired or move to the orbit, which initiates a reservation period. After each service completion, the server may take a vacation with a certain probability or remain active. The supplementary variable technique is used to derive the system’s steady-state performance measures. Numerical experiments are conducted through a sensitivity analysis to investigate the effects of key parameters. From a managerial perspective, this model offers valuable insights for the design and control of systems with unreliable servers, limited waiting spaces, and retrial behavior, such as in call centers, air traffic control, and smart service systems, where balancing server availability and customer patience is critical to performance.
Keywords
Retrial queues ; batch customer arrivals ; server breakdown and repair ; Bernoulli-type server vacations ; supplementary variable method
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