Recensione dell'articolo: (Minkeviˇcius, Saulius - "On extreme values in open queueing network" - Math.Comput.Modelling 50 (2009), no.7-8, 1058–1066.)

This paper is devoted to the analysis of queuing systems arising in network theory and communication theory. The author presents probability limit theorems for extreme values of the virtual waiting time of a customer in heavy traffic in an open queuing network. He considers open queuing networks with the FCFS service discipline at each station and general distributions of interarrival and service time. The queuing network studied has k single server stations, each of which has an associated infinite capacity waiting buffer. Every station has an arrival stream from outside the network, and the arrival streams are assumed to be mutually independent renewal processes. Customers are served in the order of arrival, and after service they are randomly routed to either another station in the network or out of the network entirely. Service times and routing decisions form mutually independent sequences of independent identically distributed random variables. In this context, as main results, the author proves two functional limit theorems, respectively on the maximum and the minimum of the virtual waiting time of a customer in the network. Leonardo Pasini