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A discrete-time Geom/G/1 retrial queue with balking customers and second optional service

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Abstract

In this paper, we discuss a discrete-time Geom/G/1 retrial queue with balking customers and second optional service where the retrial time follows a geometrical distribution. If an arriving customer finds the server is busy, he will leave the service area and go to the orbit with probability θ or leave the system with probability 1−θ; otherwise, he will begin his service immediately. In this model, after a customer finishes his first essential service, he may leave the system with probability 1−α or asks for a second optional service with probability α. Through studying the Markov chain underlying the model, we establish the probability generating functions of the orbit size and system size. Finally, some performance measures and numerical examples are presented.

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Acknowledgments

This research was supported by the National Natural Science Foundation of China (71062008), and the National Foundation Cultivation of Shantou University (NFC12002).

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Authors and Affiliations

  1. Department of Mathematics, Shantou University, Shantou, 515063, People’s Republic of China

    Cai-Min Wei & Li Cai

  2. School of Management and Engineering, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    Jian-Jun Wang

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  1. Cai-Min Wei
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  2. Li Cai
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  3. Jian-Jun Wang
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Correspondence to Cai-Min Wei.

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Wei, CM., Cai, L. & Wang, JJ. A discrete-time Geom/G/1 retrial queue with balking customers and second optional service. OPSEARCH 53, 344–357 (2016). https://doi.org/10.1007/s12597-015-0232-7

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