Maximum Entropy Principle for an Unreliable Server Queue with second optional service, Repair and Vacation

Author(s)	Dr. Rekha Kumari
Country	India
Abstract	Queueing systems with unreliable servers are widely used in communication networks, manufacturing industries, computer systems, and service organizations. In many practical situations, the server may fail during operation, require repair, or take vacations when the system becomes idle. Additionally, customers may request a second optional service after completion of the first service. This paper studies an M/M/1 queueing model with server breakdowns, repair facility, vacation policy, and second optional service using the Maximum Entropy Principle (MEP). The entropy maximization approach is applied to derive the steady-state probability distribution of the system under limited statistical information. Expressions for important performance measures such as average queue length, waiting time, utilization factor, and vacation probability are obtained. The study demonstrates that the Maximum Entropy Principle provides a simple and efficient method for analyzing complex queueing systems where exact analytical solutions become difficult. The proposed model is useful in the analysis of cloud computing systems, communication networks, production systems, and computer repair environments.
Keywords	queiuing, unreliable, Repair, vacation
Field	Mathematics > Statistics
Published In	Volume 7, Issue 3, May-June 2026
Published On	2026-05-18

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