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We study a single server queue with general service time distribution and two types of random system failures categorized as major or minor failures. We assume that customers arrive at the system in batches of variable size in accordance with a compound Poisson process and they are provided one by one service on a first-come, first-served basis. As soon as there is a major failure, the repairs do not start immediately resulting in delay. The delay time in starting repairs of this type of failures follows a general distribution. However, if the system fails due to a minor failure, it instantly enters a repair process with a deterministic repair time. We further assume that customers may become impatient during the breakdown periods of the system and may renege from the system. We obtain steady-state results in terms of the probability generating functions of the number of customers in the queue. Some special cases of interest are discussed, and some known results have been derived.

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On a \({{\varvec{M}}}^{\left[{\varvec{X}}\right]}/{\varvec{G}}\) /1 Queue with Two Types of Random Failures, Delay in Starting the Major Repairs and Reneging During the Down Time

  • 会议论文

  • 发表日期：

    2025年

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  • Kailash C. Madan

摘要

We study a single server queue with general service time distribution and two types of random system failures categorized as major or minor failures. We assume that customers arrive at the system in batches of variable size in accordance with a compound Poisson process and they are provided one by one service on a first-come, first-served basis. As soon as there is a major failure, the repairs do not start immediately resulting in delay. The delay time in starting repairs of this type of failures follows a general distribution. However, if the system fails due to a minor failure, it instantly enters a repair process with a deterministic repair time. We further assume that customers may become impatient during the breakdown periods of the system and may renege from the system. We obtain steady-state results in terms of the probability generating functions of the number of customers in the queue. Some special cases of interest are discussed, and some known results have been derived.