Monotonicity and asymptotic queue-length distribution in discrete-time networks (Q1598900)

Monotonicity of performance measures for closed, cyclic, discrete-time networks with one server per node and with independent geometric service times in equilibrium is established. It is observed that the joint distribution of queue-length random variables is negatively associated. The queue-length distribution at any node converges in a strong sense to a distribution that is conditionally geometric and the \(r\)-th moment converges to the corresponding moment of the limiting distribution for any positive \(r\). Some consequences are derived.