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Abstract

We consider a queueing system that utilizes a single server to manage product flow through bulk and overload service modes, depending on queue length. Balking occurs when the queue length reaches ‘N’. After completion of service, products undergo quality inspection, with defective products sent for rework based on specific probabilities. If the product is non-defective, the server continues processing until the queue length exceeds a certain threshold; beyond this point, the server is either routed back to bulk service or directed to an overload service. Also, the server goes into a vacation mode when the queue size is below a certain limit to ensure that resources are well utilized. Through steady-state analysis using the supplementary variable technique, key performance metrics and stability conditions were determined. Cost functions are established for the concerned model. The results, supported by illustrative numerical data, shed light on the effectiveness of the proposed model.

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