Abstract
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.
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References
Artalejo, J.: A classified bibliography of research on retrial queues: progress in 1990–1999. Top 7(2), 187–211 (1999)
Artalejo, J.: Accessible bibliography on retrial queues: progress in 2000–2009. Math. Comput. Modell. 51, 1071–1081 (2010)
Falin, G., Templeton, J.: Retrial Queues. Chapman and Hall, London (1997)
G\(\acute{o}\)mezC Corral, A.: A bibliographical guide to analysis of retrial queues through matrix analytic techniques. Ann. Oper. Res. 141, 163–191 (2006)
Takagi, H.: Queueing analysis: a foundation of performance evaluation. Discrete-time systems, Vol. 3. North-Holland, Amsterdam (1993)
Woodward, M.: Communication and computer networks: modelling with discrete-time queues. IEEE Computer Society Press, Los Alamitos, California (1994)
Tian, N., Xu, X., Ma, Z.: Discrete-time queueing theory. Science Press, Beijing (2008)
Aboul-Hassan, A., Rabia, S., Kadry, A.: A recursive approach for analyzing a discrete-time retrial queue with balking customers and early arrival scheme. Alexandria Eng. J. 44, 919–925 (2005)
Aboul-Hassan, A., Rabia, S., Taboly, F.: A discrete time Geo/G/1 retrial queue with general retrial times and balking customers. Journal of the Korean Statistical Society 37, 335–48 (2008)
Atencia, I., Morena, P.: A discrete-time retrial queue with optional service. In: Proceeding of the Fifth International Workshop On Retrial Queues, Seoul, vol. 9, pp. 117–121 (2004)
Wang, J., Zhao, Q.: A discrete-time Geo/G/1 retrial queue with starting failures and second optional service. Comput. Math. Appl. 53, 115–127 (2007)
Wang, J.: Discrete-time Geo/G/1 retrial queues with general retrial time and Bernoulli vacation. J. Syst. Sci. Complex. 25(3), 504–513 (2012)
Chen, P., Zhu, Y., Chen, Y.: A discrete-time Geo/G/1 retrial queue with Bernoulli vacation and Second optional service. Math. Pract. Theory 41(3), 121–128 (2011)
Wei, C., Cai, L., Wang, J.: A discrete-time Geom/G/1 retrial queue with balking customers and second optional service. OPSEARCH, revision (2014)
Acknowledgments
Research supported by the National Natural Science Foundation of China (71062008), and the National Foundation Cultivation of Shantou University (NFC12002).
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Chen, Y., Cai, L., Wei, Cm. (2016). A Discrete-Time Geo/G/1 Retrial Queue with Balking Customer, Second Optional Service, Bernoulli Vacation and General Retrial Time. In: Cao, BY., Liu, ZL., Zhong, YB., Mi, HH. (eds) Fuzzy Systems & Operations Research and Management. Advances in Intelligent Systems and Computing, vol 367. Springer, Cham. https://doi.org/10.1007/978-3-319-19105-8_24
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DOI: https://doi.org/10.1007/978-3-319-19105-8_24
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