A Discrete-Time Geo/G/1 Retrial Queue with Balking Customer, Second Optional Service, Bernoulli Vacation and General Retrial Time

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 367)


In this paper, we study a discrete-time Geo/G/1 retrial queue with a balking customer and a second optional service where retrial time follows a general distribution. If an arriving customer finds the server free, he begins the service immediately. If an arriving customer finds the server busy or to be on vacation, then he will consider whether he enters into the system. After a customer accepts his first essential service, he may leave the system or ask for a second service. In this model, we assume that the server, after each service completion, may begin a vacation or wait to serve the following customer. This paper studies the Markov chain underlying this model, we establish the probability generating functions of the orbit size and system size. Finally, some performance measures and some numerical examples are presented.


Retrial queue Balking customer Optional service Bernoulli vacation 



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


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Natural SciencesShantou PolytechnicShantouPeople’s Republic of China
  2. 2.Guangdong Provincial Key Laboratory of Digital Signal and Image Processing TechniquesShantou UniversityShantouPeople’s Republic of China
  3. 3.Department of MathematicsShantou UniversityShantouPeople’s Republic of China

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