Abstract
The object of this research in the queueing theory is theorems about the functional strong laws of large numbers (FSLLN) under the conditions of heavy traffic in an open queueing network (OQN). The FSLLN is known as a fluid limit or fluid approximation. In this paper, FSLLN are proved for the values of important probabilistic characteristics of the OQN investigated as well as the virtual waiting time of a customer and the queue length of customers. As applications of the proved theorems laws of Little in OQN are presented.
Highlights
The paper is devoted to the analysis of queueing systems in the context of the network and communications theory
We investigate functional strong laws of large numbers (FSLLN) about the virtual waiting time of a customer and the queue length of customers and theorems on the laws of Little in an open queueing network (OQN) under the conditions of heavy traffic
Reiman [27] proved the heavy traffic limit theorems for the queue length process associated with open queueing networks
Summary
The paper is devoted to the analysis of queueing systems in the context of the network and communications theory. Harrison [10] considered the heavy traffic approximation to the stationary distribution of the waiting times in single server queues in series. His limit process was given as a complicated functional of Brownian motion. Reiman [27] proved the heavy traffic limit theorems for the queue length process associated with open queueing networks. Using a slight modification method, the authors Bramson and Dai of [31] prove heavy traffic limit theorems for six families of multiclass queueing networks (for example, the first three families are singlestation systems operating under first-in-first-out (FIFO) principle, generalized-head-ofthe-line proportional processor sharing (GHLPPS) and static buffer priority (SBP) service disciplines).
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
