Analysis of a Repairable M/G/1 Queue with the Gated Service and Multiple Adaptive Vacation.

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Bibliographic Details
Title:	Analysis of a Repairable M/G/1 Queue with the Gated Service and Multiple Adaptive Vacation.
Authors:	Tongyu Xu¹ 15194908257@163.com, Zhanyou Ma² mzhy55@ysu.edu.cn, Ying Sun¹ S1041942326@163.com
Source:	IAENG International Journal of Applied Mathematics. May2025, Vol. 55 Issue 5, p1419-1427. 9p.
Subjects:	Setup time, Consumers, Vacations, Probability theory, Queuing theory
Abstract:	This paper considered a repairable MX/G/1 queueing system with the gated service, setup time and multiple adaptive vacation rules. Customers arrive according to Markov flow. The system has a main queue and an infinite buffer queue separated by a gate. After the customers arrival, they enter the buffer and wait for service in order. Before each service period begins, the system has a random setup period. After the setup period ends, the system opens the gate and customers waiting in the buffer zone enter the main queue according to the original order to receive the service. This paper uses tools such as the intuitive total probability decomposition theorem, regeneration cycle method, PGF and LST transform to analyze the system's queue length and waiting time. The probabilities for the server being in the states of general service, idle, setup, and vacation are presented individually. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	This paper considered a repairable MX/G/1 queueing system with the gated service, setup time and multiple adaptive vacation rules. Customers arrive according to Markov flow. The system has a main queue and an infinite buffer queue separated by a gate. After the customers arrival, they enter the buffer and wait for service in order. Before each service period begins, the system has a random setup period. After the setup period ends, the system opens the gate and customers waiting in the buffer zone enter the main queue according to the original order to receive the service. This paper uses tools such as the intuitive total probability decomposition theorem, regeneration cycle method, PGF and LST transform to analyze the system's queue length and waiting time. The probabilities for the server being in the states of general service, idle, setup, and vacation are presented individually. [ABSTRACT FROM AUTHOR]
ISSN:	19929978