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- W2991266552 abstract "This paper presents a discrete-time Geo/G/1 retrial queue with two waiting buffers to model an ATM network, in which the server begins a single vacation in cases where the system is empty at the instant of a service completion. New arriving customer who finds the server being on vacation can decide to either enter the retrial buffer with some probability <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mi>p</mml:mi></mml:math> or leave the system with complementary probability <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>p</mml:mi></mml:mrow></mml:math>. But the new arriving customer can begin its service immediately if he finds the server idle and join the original buffer if he finds the server busy. We first carry out an extensive analysis of the model by using the supplementary variable method and the generating function approach, and give some performance measures, such as server’s state probabilities and mean queue lengths in the original buffer, retrial buffer, and in the system. Secondly, we give the generating function of the sojourn time of a customer in the system and prove that Little’s law still holds in our model. Sensitivity analysis and cost optimization are finally given for illustrative purposes." @default.
- W2991266552 created "2019-12-05" @default.
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- W2991266552 date "2019-11-27" @default.
- W2991266552 modified "2023-10-17" @default.
- W2991266552 title "Analysis of a Single Server Retrial Queue with Server Vacation and Two Waiting Buffers Based on ATM Networks" @default.
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- W2991266552 doi "https://doi.org/10.1155/2019/4193404" @default.
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