Abstract
The aim of the present paper is to investigate a retrial queuing system M/M/1 with a finite number of sources and two-way communication. Each source can generate a request after an exponentially distributed time and will not generate another one until the previous call return to the source. If an incoming customer finds the server idle its service starts. Otherwise, if the server is busy an arriving (primary or repeated) customer moves into the orbit and after some exponentially distributed time it retries to enter the server. When the server is idle it generates an outgoing call after an exponentially distributed time with different parameters to the customers in the orbit and to the sources, respectively. The service times of the incoming and outgoing calls are exponentially distributed with different rates. Applying method of asymptotic analysis under the condition of unlimited growing number of sources it is proved that the limiting sojourn/waiting time of the customer in the system follows a generalized exponential distribution with given parameters. In addition, the asymptotic average number of customers in the orbit is obtained.
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The work/publication of A.A. Nazarov is supported by grant RFBR (Russian Foundation for Basic Research), the Agreement number 18_01_00277.
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Nazarov, A., Sztrik, J., Kvach, A. (2018). Asymptotic Sojourn Time Analysis of Finite-Source M/M/1 Retrial Queuing System with Two-Way Communication. 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_14
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