Abstract
We consider a multi-server queueing system with session arrivals that operates in random environment. A session consists of a random number of customers. Sessions arrive to the system in Markovian arrival flow. Inter-arrival times of customers within each session are random. The service time of a customer has a phase type distribution. A numerically stable algorithm for calculation of the stationary distribution of system states is presented. The main performance measures are calculated.
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References
Lee, M.H., Dudin, S., Klimenok, V.: Queueing Model with Time-Phased Batch Arrivals. In: Mason, L.G., Drwiega, T., Yan, J. (eds.) ITC 2007. LNCS, vol. 4516, pp. 719–730. Springer, Heidelberg (2007)
Kim, C.S., Dudin, S.A., Klimenok, V.I.: The MAP/PH/1/N queue with time phased arrivals as model for traffic control in telecommunication networks. Performance Evaluation 66, 564–579 (2009)
Kim, C.S., Dudin, A., Dudin, S., Klimenok, V.: A Queueing System with Batch Arrival of Customers in Sessions. Computers and Industrial Engeneering 62, 890–897 (2012)
Dudin, S.A.: The MAP/M/N retrial queueing system with time-phased batch arrivals. Problems of Information Transmission 3, 270–281 (2009)
Kim, C., Dudin, A., Klimenok, V., Khramova, V.: Erlang loss queueing system with batch arrivals operating in a random environment. Computers & Operations Research 36, 674–697 (2009)
Pattavina, A., Parini, A.: Modelling voice call inter-arrival and holding time distributions in mobile networks. In: Proceedings of 19th International Teletraffic Congress, Performance Challenges for Efficient Next Generation Networks, pp. 729–738 (2005)
Riska, A., Diev, V., Smirni, E.: Efficient fitting of long-tailed data sets into hyperexponential distributions. In: Proceedings of Global Telecommunications Conference (GLOBALCOM 2002), pp. 2513–2517. IEEE (2002)
Neuts, M.: Matrix-geometric solutions in stochastic models – an algorithmic approach. John Hopkins University Press (1981)
Ramaswami, V.: Independent Markov processes in parallel. Comm. Statist. -Stochastic Models 1, 419–432 (1985)
Ramaswami, V., Lucantoni, D.M.: Algorithms for the multi-server queue with phase-type service. Comm. Statist. -Stochastic Models 1, 393–417 (1985)
Kim, C., Dudin, S., Taramin, O., Baek, J.: Queueing system MAP|PH|N|N + R with impatient heterogeneous customers as a model of call center. Applied Mathematical Modelling 37, 958–976 (2013)
Klimenok, V.I., Kim, C.S., Orlovsky, D.S., Dudin, A.N.: Lack of invariant property of Erlang BMAP/PH/N/0 model. Queueing Systems 49, 187–213 (2005)
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Kim, C., Dudin, A., Dudin, S., Dudina, O. (2013). Queueing System MAP|PH|N|R with Session Arrivals Operating in Random Environment. In: Kwiecień, A., Gaj, P., Stera, P. (eds) Computer Networks. CN 2013. Communications in Computer and Information Science, vol 370. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38865-1_41
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DOI: https://doi.org/10.1007/978-3-642-38865-1_41
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38864-4
Online ISBN: 978-3-642-38865-1
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