Authors : Dr. D.P. Siva Sakti Balan; P. Sri Lekha; A. Azlina; I. RayYana

Volume/Issue : Volume 10 - 2025, Issue 3 - March

Google Scholar : https://tinyurl.com/yc35xafv

Scribd : https://tinyurl.com/yvk32pxf

DOI : https://doi.org/10.38124/ijisrt/25mar1215

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Abstract : 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.

Keywords : Queue: A Line of customers or Tasks Awaiting Service. Arrival rate (λ): The Average Number of Arrivals Per Time Unit. Lamda Service rate (μ): The Average Number of Services Completed Per Time Unit. Meu Utilization (⍴): The Ratio of Arrival rate to Service Rate. Row Queue discipline: The Rule for Serving Customers, e.g., First Come First Serve (FCFS)

References :

1. Kendall, 1953; Little, 1961; Gross & Harris, 1998; Bertsimas & Tsitsiklis, 1997).
2. John D. C. Little’s seminal 1961 paper, "A Proof for the Queuing Formula: L = λW," established what is now known as Little’s law, providing a fundamental relationship between the average number of items in a system, the arrival rate, and the average waiting time (Little, 1961).
3. Larson's 1987 work, "Perspectives on Queues: Theory and Practice," published in Operations Research.
4. Gross and Harris further enriched the field with their 1998 book “Fundamentals of Queueing Theory,”
5. Bertsimas and Tsitsiklis’s 1997 book “Introduction to Linear Optimization”
6. Kelley (1975). "Networks of Queues with Customers of Different Types". Journal of Applied Probability. 12 (3): 542–554. doi:10.2307/3212869. JSTOR 3212869. S2CID 51917794
7. Chen, H.; Whitt, W. (1993). "Diffusion approximations for open queueing networks with service interruptions"