Packet Loss Analysis of Load-Balancing Switch with ON/OFF Input Processes

Abstract

Lately, the number of Internet users and, correspondingly, the amount of traversing traffic is growing extremely fast. In spite of the fact that transmission links – mostly optical fibres – have high capacity, the internet routers still remain a point of traffic bottleneck. The construction of highly scalable switches for high-speed transmission still remains a real challenge for designers. In this paper we focus our efforts on the analysis of Load-Balancing Birkhof-von Neumann switch which is lately considered to be a highly efficient distributed switch with simple control and high scalability. Due to the fact that Internet traffic represents an asynchronous traffic which supports a variety of applications, we have introduced the analysis of possible loss inside the load-balanced switch under consideration of variable size packets and finite central stage buffers previously in [1]. Although the analysis has showed some interesting features of the switch, it has exponential complexity of $O\left(N^N\right)$ which makes that model inapplicable for the switches with large number of ports, N. The main goal of this paper is to approximate the switch analysis with lower complexity, i.e., $O\left(2^N\right)$ which can be useful for evaluation of packet loss in the larger load-balanced switches.