An asymptotic property of output streams in queueing systems with unbounded number of servers and a Markov arrival process

We study the outgoing stream of queueing systems with unbounded number of servers and a Markov arrival process. We consider models with exponential and arbitrary distributions of the service duration. For the case of arbitrary service duration, we propose the sieved stream method that reduces the study of the output stream to studying a sieved stream. We show that for growing service duration, the output stream is asymptotically a simple stream independent of the service duration distribution.

Presented by the member of Editorial Board: A. I. Lyakhov