Comprehensive Anaysis on Effective Queue System as an Effective Tool of Crowd Management

Queueing theory studies the formation and management of lines or queues, playing a crucial role in solving real- world problems where resources are limited, and efficiency is essential. This research paper outlines the fundamental principles of queueing theory, including arrival rates, service rates, and system utilization. It also explores advanced concepts, such as using multiple servers, prioritizing tasks, and managing unpredictable events. Through practical examples like traffic control, optimizing hospital operations, managing customer service calls, and designing communication networks, the paper demonstrates how queueing theory minimizes waiting times, improves service, and maximizes resource utilization. It further examines various queue management strategies, such as serving customers in order of arrival or prioritizing tasks based on specific scenarios. Lastly, the paper highlights the role of modern tools, such as computer simulations and advanced technologies, in tackling complex queueing challenges, such as hospital overcrowding during pandemics or automating logistics systems. By connecting mathematical principles with practical applications, this research showcases how queueing theory enhances the efficiency of everyday systems.