Transient Solution for Queueing Delay Distribution in the GI/M/1/K-type Mode with "Queued" Waking up and Balking

Time-dependent behavior of queueing delay distribution in the GI/M/1/K-type model with the “queued” server’s waking up and balking is studied. After each idle period the server is being “queued” woken up, i.e. the processing is being started at the moment the number of packets accumulated in the buffer reaches the fixed level N. Moreover, each incoming packet can balk (resign from service) and leave the system irrevocably, with probability \(1-\beta ,\) and join the queue with probability \(\beta ,\) where \(0< \beta \le 1\).

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