A study of queueing systems with discrete time, autoregressive arrivals, and feedback

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.