A Concept of Monotonicity and Its Characterization for Closed Queueing Networks

We define a qualitative property, called monotonicity, for a closed queueing network. This property is defined both for a station in the network and for the network as a whole. Several results in this paper relate monotonic behavior to the known parameters of a network and allow us to state a priori, for many practical systems, whether the monotonicity property will apply for a network or a station. Monotonicity thus ensures that the system is well-behaved with respect to a number of parameters. We present diverse examples that demonstrate how knowledge of this property can be useful in network design and performance evaluation.