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Sensitivity analysis of feedback multiple vacation queueing system with differentiated vacations, vacation interruptions and impatient customers

Amina Angelika Bouchentouf, Abdelhak Guendouzi


The purpose of this paper is to study an infinite-buffer single-server queueing system with Bernoulli feedback, multiple vacations, differentiated vacations, vacation interruptions and impatient customers (balking and reneging). Two types of vacation are considered; type 1 vacation taken after the busy period and type 2 vacation taken when the server returns from a vacation and finds the system empty. Each vacation type may be interrupted when the number of customers in the system reaches a predefined threshold (each type of vacation has a different threshold). Via certain mechanism, reneged customers may be retained in the system. Using the recursive method, we obtain explicit expressions of the steady-state probabilities of the queueing system. Further, we present important performance measures and formulate a cost model. Finally, we carry out a sensitivity analysis through numerical experiments.


Multiple vacations, differentiated vacations, vacation interruptions, impatient customers, Bernoulli feedback, cost model

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