Background: This study examines a non-Markovian two-stage bulk tandem queueing system with vacation, aiming to model real-world service environments involving batch processing and intermittent server availability. Practical applications, such as IoT-based port crane operations, often encounter conditions where batch arrivals, batch services, and vacation policies influence system performance. Traditional queueing models fail to capture this complexity, necessitating a more realistic framework to analyze system behavior and optimize operational efficiency. Methods: The system comprises two service nodes Node 1 and Node 2 where customers arrive in batches and are served in bulk at both nodes. A vacation policy is applied at Node 1: if the queue length after service completion is less than a threshold value “a,” the server goes on vacation and remains dormant upon return until the queue length reaches “a.” After receiving service at Node 1, customers proceed to Node 2 for further batch service. The Supplementary Variable Technique (SVT) is used to derive the probability generating functions for queue sizes at both nodes, allowing the computation of key performance metrics. Additionally, an optimal cost analysis is performed to minimize the total average cost, with practical relevance demonstrated through its application in IoT-enabled logistics systems using RFID technology for dynamic inventory and service optimization. Result: Numerical results highlight how system parameters affect queue performance and identify optimal thresholds for cost minimization. Conclusion: An optimal cost analysis is performed to minimize the total average cost, with consideration of practical applications.
Niranjan et al. (Tue,) studied this question.