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 . Although the analysis has showed some interesting features of the switch, it has exponential complexity of 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 which can be useful for evaluation of packet loss in the larger load-balanced switches.