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Retrial queueing system of \(MMPP/M/2\) type with impatient calls in the orbit. (English) Zbl 1452.60077
Dudin, Alexander (ed.) et al., Information technologies and mathematical modelling. Queueing theory and applications. 17th international conference, ITMM 2018, named after A.F. Terpugov, and 12th workshop on retrial queues and related topics, WRQ 2018, Tomsk, Russia, September 10–15, 2018. Selected papers. Cham: Springer. Commun. Comput. Inf. Sci. 912, 387-399 (2018).
Summary: In the paper, the retrial queueing system of \(MMPP/M/2\) type with input MMPP-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 orbit 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.
For the entire collection see [Zbl 1403.60002].

MSC:
60K25 Queueing theory (aspects of probability theory)
Software:
MOSEL
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