Strong approximations for the open queueing network in heavy traffic (Q1201616)

The authors obtain strong approximations for an open queueing network in heavy traffic. The network consists of \(k\) single server nodes each with infinite capacity, in which at least one node has arrival stream from outside the network. At every node the FIFO service discipline is adopted and after service the customers are either randomly routed to another node or leave the network. The interarrival times and service times are assumed to form mutually independent sequences of i.i.d. random variables. Strong approximations are derived for the queue length, the virtual waiting time, the sojourn time and for the queue length process associated with the embedded arrival epochs.