A single-server discrete-time retrial <Emphasis Type="Italic">G</Emphasis>-queue with server breakdowns and repairs |
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Authors: | Jin-ting Wang Peng Zhang |
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Institution: | [1]Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China [2]Qingdao Branch, The Bank of Communication, Qingdao 266001, China |
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Abstract: | This paper concerns a discrete-time Geo/Geo/1 retrial queue with both positive and negative customers where the server is subject to breakdowns and repairs due to negative
arrivals. The arrival of a negative customer causes one positive customer to be killed if any is present, and simultaneously
breaks the server down. The server is sent to repair immediately and after repair it is as good as new. The negative customer
also causes the server breakdown if the server is found idle, but has no effect on the system if the server is under repair.
We analyze the Markov chain underlying the queueing system and obtain its ergodicity condition. The generating function of
the number of customers in the orbit and in the system are also obtained, along with the marginal distributions of the orbit
size when the server is idle, busy or down. Finally, we present some numerical examples to illustrate the influence of the
parameters on several performance characteristics of the system. |
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Keywords: | Discrete-time retrial queue G-queue Markov chain unreliable server |
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