Abstract
The goal of this paper is to investigate the two-way communication by the help of finite source retrial queuing systems. Incoming calls from sources (primary calls) arrive to the server according to a Poisson process. If an incoming call finds the server idle, its service starts. Otherwise, if the server is busy, an arriving (primary or secondary - from the orbit) call moves into the orbit and after some exponentially distributed time it retries to enter to the server. When the server is idle it generates an outgoing call after an exponentially distributed time with different parameters to the calls in the orbit and in the sources, respectively. The service time of the incoming and outgoing calls are exponentially distributed with different rates. Results on two-way communication assume, that after the service an outgoing call (primary or secondary) is sent back to the source. The novelty of this paper is investigating two cases. In Case 1 the secondary outgoing call is sent back to the orbit, thus the pending incoming call will not be lost. In Case 2 after service of the secondary outgoing call its incoming service request will be started immediately. This means a two-phase service. The balance equations are solved by the help of MOSEL-2 tool. Graphical results and comparisons of the cases are presented.
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Acknowledgments
The research work of Attila Kuki, János Sztrik, and Tamás Bérczes was granted by Austrian-Hungarian Bilateral Cooperation in Science and Technology project 2017-2.2.4-TéT-AT-2017-00010.
The research work of Ádám Tóth was supported by the construction EFOP-3.6.3-VEKOP-16-2017-00002. The project was supported by the European Union, co-financed by the European Social Fund.
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Kuki, A., Sztrik, J., Tóth, Á., Bérczes, T. (2018). A Contribution to Modeling Two-Way Communication with Retrial Queueing Systems. In: Dudin, A., Nazarov, A., Moiseev, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM WRQ 2018 2018. Communications in Computer and Information Science, vol 912. Springer, Cham. https://doi.org/10.1007/978-3-319-97595-5_19
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