Abstract
In this paper we analyze a discrete-time queueing system in which an arriving customer can decide, with a certain probability, to go directly to the server expelling out of the system the customer that is currently in service or to join the queue in the last place. The arrivals are assumed to be geometrical and the service times are arbitrarily distributed. We present some numerical examples in order to illustrate the effect of the parameters on several performance characteristics.
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References
Atencia, I., Pechinkin, A.V.: A discrete-time queueing system with optional LCFS discipline. Ann. Oper. Res. (2012), doi:10.1007/s10479-012-1097-2
Birdsall, T., Ristenbatt, M., Weinstein, S.: Analysis of asynchronous time multiplexing of speech sources. IRE Transactions on Communication Systems 10, 390–397 (1962)
Bruneel, H., Kim, B.G.: Discrete-time models for communication systems including ATM. Kluwer Academic Publishers, Boston (1993)
Cascone, A., Manzo, P., Pechinkin, A., Shorgin, S.: A Geom/G/1/n system with a LIFO discipline without interruptions in the service and with a limitation for the total capacity for the customers. Avtomatika i Telemejanika 1, 107–120 (2011) (in Russian)
Hunter, J.: Mathematical Techniques of Applied Probability. Operations Research and Industrial Engineering, vol. 1. Academic Press, New York (1983)
Hunter, J.: Mathematical Techniques of Applied Probability, Discrete-Time Models: Techniques and Applications. Operations Research and Industrial Engineering, vol. 2. Academic Press, New York (1983)
Meisling, T.: Discrete time queueing theory. Oper. Res. 6, 96–105 (1958)
Pechinkin, A., Svischeva, T.: The stationary state probability in the BMAP/G/1/r queueing system with inverse discipline and probabilistic priority. In: Transactions of XXIV International Seminar on Stability Problems for Stochastic Models, Jurmala, Latvia, September 10-17, pp. 141–174 (2004)
Pechinkin, A., Shorgin, S.: A Geo/G/1/ ∞ system with a one non-standard discipline for the service. Informatics and it Applications 2, 55–62 (2008) (in Russian)
Powell, B., Avi-Itzhak, B.: Queueing systems with enforced idle times. Operations Research 15(6), 1145–1156 (1967)
Takagi, H.: Queueing analysis: A foundation of performance evaluation. Discrete-Time Systems, vol. 3. North-Holland, Amsterdam (1993)
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Atencia, I., Fortes, I., Sánchez, S. (2013). Discrete-Time Queueing System with Expulsions. In: Dudin, A., Klimenok, V., Tsarenkov, G., Dudin, S. (eds) Modern Probabilistic Methods for Analysis of Telecommunication Networks. BWWQT 2013. Communications in Computer and Information Science, vol 356. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35980-4_3
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DOI: https://doi.org/10.1007/978-3-642-35980-4_3
Publisher Name: Springer, Berlin, Heidelberg
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