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A survey of recent results in finite-source retrial queues with collisions. (English) Zbl 1452.60068
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, 1-15 (2018).
Summary: The aim of the present paper is to give a review of recent results on single server finite-source retrial queuing systems with collision of the customers. There are investigations when the server is reliable and there are models when the server is subject to random breakdowns and repairs depending on whether it is idle or busy. Tool supported, numerical, simulation and asymptotic methods are considered under the condition of unlimited growing number of sources. Several cases and examples are treated and the results of different approaches are compared to each other showing the advantages and disadvantages of the given method. In general we could prove that the steady-state distribution of the number of customers in the service facility can be approximated by a normal distribution with given mean and variance. Using asymptotic methods under certain conditions in steady-state the distribution of the sojourn time in the orbit and in the system can be approximated by a generalized exponential one. Furthermore, it is proved that the distribution of the number of retrials until the successful service in the limit is geometrically distributed. By the help of stochastic simulation several systems are analyzed showing directions for further analytic investigations. Tables and Figures are collected to illustrate some special features of these systems.
For the entire collection see [Zbl 1403.60002].
MSC:
60K25 Queueing theory (aspects of probability theory)
Software:
MOSEL
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References:
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