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This paper introduces a focused model for analyzing congestion in finite tandem networks, a crucial aspect in queueing theory with far-reaching implications for system efficiency. By examining job flow through nodes, Node-1 and Node-2, it reveals intricate relationships between latent and processing times, exploring system dynamics. Incorporating Poisson arrivals, balking, and diverse processing mechanisms, the model encompasses both direct job progression and potential balking, offering a comprehensive view. Additionally, it accounts for waiting job processing, reneging, and Node-2's breakdown vulnerabilities and recovery. The model's independence of processes amplifies its depth. This analysis enriches our understanding of finite tandem queueing networks and their congestion intricacies. The model aids in optimal resource allocation and system design, enhancing congestion and delay management in practical settings like transportation and communication networks. It forms a foundation for informed operational strategies, bolstering customer satisfaction and resource utilization in complex service systems |
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