Asymptotic behavior of large discrete-time cyclic queueing networks (Q1333393)

The authors study a discrete-time cyclic network of \(n\) single-server queues with a fixed number of customers circulating clockwise. When being served, a customer moves with probability \(p\) to the next queue in one time unit. The stationary distribution of the vector of queue lengths is computed and yields a formula for the expected number of busy servers. The asymptotic proportion of busy servers for \(n \to \infty\) and \(k/n \to \alpha \in (0,1)\) is found. Further, a variant of the model with queues without waiting room is considered.