\(V\)-uniform ergodicity for state-dependent single class queueing networks
The paper considers single class queueing networks in which arrival and service rates depend on the state of the network. The primary result is concerned with a rate of convergence to the steady-state distribution. Under the uniform (in state) stability condition, it is shown that the queue length process is \(V\)-uniformly ergodic; that is, it has a transition probability kernel which converges to its limit geometrically quickly in the \(V\)-norm sense. As consequences of \(V\)-uniform ergodicity, one can obtain several meaningful asymptotic properties of the process such as a strong form of the large deviation principle and mixing results, a functional central limit theorem and a Strassen-type functional law of the iterated logarithm result. The proofs rely on a critical use of the Lyapunov function methods.
functional law of the iterated logarithm
scientific article; zbMATH DE number 5710664
scientific article