On extreme values in open queueing networks

Abstract

This paper presents heavy traffic limit theorems for the extreme virtual waiting time of a customer in an open queueing network. In this paper, functional limit theorems are proved for extreme values of important probability characteristics of the open queueing network investigated as the maximum and minimum of the total virtual waiting time of a customer, and the maximum and minimum of the virtual waiting time of a customer. Also, the paper presents the previous related works for extreme values in queues and the virtual waiting time in heavy traffic.