Modeling the Law of the Iterated Logarithm in Open Queueing Networks

A single phase case, where intervals of time between the arrival of customers to queue are independent identically distributed random variables and there is a single device, working independently of the output in heavy traffic, has been completely investigated. But there are only several papers on the theory of open queueing networks in heavy traffic and no proof of the theorems on laws of the iterated logarithm for the main probabilistic characteristics of an open queueing network in heavy traffic (for example, sojourn time of a customer and a virtual waiting time of a customer).