Abstract
In the paper, the retrial queueing system of M/M/N type with Poisson flow of events and impatient calls is considered. The delay time of calls in the orbit, the calls service time and the impatience time of calls in the system have exponential distribution. Asymptotic analysis method is proposed for the solving problem of finding distribution of the number of calls in the orbit under a system heavy load and long time patience of calls in the orbit condition. The theorem about the Gauss form of the asymptotic probability distribution of the number of calls in the orbit is formulated and proved. Numerical illustrations, results are also given.
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References
Wilkinson, R.I.: Theories for toll traffic engineering in the USA. Bell Syst. Tech. J. 35(2), 421–507 (1956)
Cohen, J.W.: Basic problems of telephone traffic and the influence of repeated calls. Philips Telecommun. Rev. 18(2), 49–100 (1957)
Gosztony, G.: Repeated call attempts and their effect on traffic engineering. Budavox Telecommun. Rev. 2, 16–26 (1976)
Elldin, A., Lind, G.: Elementary Telephone Traffic Theory. Ericsson Public Telecommunications, Stockholm (1971)
Artalejo, J.R., Gomez-Corral, A.: Retrial Queueing Systems. A Computational Approach. Springer, Stockholm (2008). https://doi.org/10.1007/978-3-540-78725-9
Falin, G.I., Templeton, J.G.C.: Retrial Queues. Chapman & Hall, London (1997)
Artalejo, J.R., Falin, G.I.: Standard and retrial queueing systems: a comparative analysis. Revista Matematica Complutense 15, 101–129 (2002)
Roszik, J., Sztrik, J., Kim, C.: Retrial queues in the performance modelling of cellular mobile networks using MOSEL. Int. J. Simul. 6, 38–47 (2005)
Aguir, S., Karaesmen, F., Askin, O.Z., Chauvet, F.: The impact of retrials on call center performance. OR Spektrum 26, 353–376 (2004)
Nazarov, A., Sztrik, J., Kvach, A.: Comparative analysis of methods of residual and elapsed service time in the study of the closed retrial queuing system M/GI/1//N with collision of the customers and unreliable server. In: Dudin, A., Nazarov, A., Kirpichnikov, A. (eds.) ITMM 2017. CCIS, vol. 800, pp. 97–110. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-68069-9_8
Dudin, A., Deepak, T.G., Joshua, V.C., Krishnamoorthy, A., Vishnevsky, V.: On a BMAP/G/1 retrial system with two types of search of customers from the orbit. In: Dudin, A., Nazarov, A., Kirpichnikov, A. (eds.) ITMM 2017. CCIS, vol. 800, pp. 1–12. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-68069-9_1
Dudin, A.N., Klimenok, V.I.: Queueing system BMAP/G/1 with repeated calls. Math. Comput. Model. 30(3–4), 115–128 (1999)
Yang, T., Posner, M., Templeton, J.: The M/G/1 retrial queue with non-persistent customers. Queueing Syst. 7(2), 209–218 (1990)
Krishnamoorthy, A., Deepak, T.G., Joshua, V.C.: An M/G/1 retrial queue with non-persistent customers and orbital search. Stochast. Anal. Appl. 23, 975–997 (2005)
Kim, J.: Retrial queueing system with collision and impatience. Commun. Korean Math. Soc. 4, 647–653 (2010)
Martin, M., Artalejo, J.: Analysis of an M/G/1 queue with two types of impatient units. Adv. Appl. Probab. 27, 647–653 (1995)
Kumar, M., Arumuganathan, R.: Performance analysis of single server retrial queue with general retrial time, impatient subscribers, two phases of service and Bernoulli schedule. Tamkang J. Sci. Eng. 13(2), 135–143 (2010)
Fedorova, E., Voytikov, K.: Retrial queue M/G/1 with impatient calls under heavy load condition. In: Dudin, A., Nazarov, A., Kirpichnikov, A. (eds.) ITMM 2017. CCIS, vol. 800, pp. 347–357. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-68069-9_28
Berczes, T., Sztrik, J., Toth, A., Nazarov, A.: Performance modeling of finite-source retrial queueing systems with collisions and non-reliable server using MOSEL. In: Dudin, A., Nazarov, A. (eds.) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2017, CCIS, vol. 800, pp. 248–258, Springer, Cham (2017).https://doi.org/10.1007/978-3-319-68069-9
Artalejo, J.R., Pozo, M.: Numerical calculation of the stationary distribution of the main multiserver retrial queue. Ann. Oper. Res. 116, 41–56 (2002)
Neuts, M.F., Rao, B.M.: Numerical investigation of a multiserver retrial model. Queueing Syst. 7(2), 169–189 (1990)
Borovkov, A.A.: Asymptotic Methods in Queueing Theory. Wiley, New York (1984)
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Danilyuk, E., Vygoskaya, O., Moiseeva, S. (2018). Retrial Queue M/M/N with Impatient Customer in the Orbit. In: Vishnevskiy, V., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2018. Communications in Computer and Information Science, vol 919. Springer, Cham. https://doi.org/10.1007/978-3-319-99447-5_42
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DOI: https://doi.org/10.1007/978-3-319-99447-5_42
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