Abstract
In this paper, we consider a single server queueing model \(M^{[n]}|GI|GI|1|L\) with Batch Poisson input flow. Upon arrival, an incoming call from the batch occupies the server, if the server is idle. Other calls from the batch join the orbit and try to occupy the server after an exponentially distributed time. If the server is busy all incoming calls from the batch join the orbit and make a delay for an exponentially distributed time then repeat their request for service. The server makes an outgoing call in its idle time. Our contribution is to derive the stationary probability distribution of the number of incoming calls in the system.
Keywords
The reported study was funded by RFBR according to the research project 18-01-00277.
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Nazarov, A., Phung-Duc, T., Paul, S., Lizura, O. (2019). Single Server Queues with Batch Poisson Input and Multiple Types of Outgoing Calls. In: Dudin, A., Nazarov, A., Moiseev, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2019. Communications in Computer and Information Science, vol 1109. Springer, Cham. https://doi.org/10.1007/978-3-030-33388-1_15
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