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