Systems and Means of Informatics
2015, Volume 25, Issue 2, pp 60-70
A STUDY OF QUEUEING SYSTEMS WITH DISCRETE TIME, AUTOREGRESSIVE ARRIVALS, AND FEEDBACK
- N. D. Leontyev
- V. G. Ushakov
The paper studies two discrete-time single server queueing systems
with infinite capacity and feedback. The arrivals in both systems are driven by
discrete autoregressive models, i. e., the size of each arriving batch may be equal
to the size of one of the previously arrived batches with some fixed probability, or
is a random variable independent of the history with complementary probability.
The main object of the study is the stationary queue length. For the system
with discrete autoregressive arrivals of order 1, expressions for queue length
distribution are derived, and for the system with discrete autoregressive arrivals
of order 2, the expected queue length is found.
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