The caudal characteristic curve of queues

Many queues and related stochastic models, and in particular those that have a matrix-geometric stationary probability vector, have steady-state queue-length densities that are asymptotically geometric . The graph of the asymptotic rate η of these densities as a function of the traffic intensity ρ is the caudal characteristic curve . This is an informative graph from which a number of qualitative inferences about the behavior of the queue may be drawn.