Abstract: Recent measurement on WAN, LAN, VBR, and ISDN traffic shows that there exist intricately self similar or long range dependence characteristics in the traffic. The queuing analysis with self similar traffic is not complete until now. In this paper, the buffer overflow probability of ATM switches with second order asymptotically self similar input traffic is analyzed. The self similar behavior of traffic has serious influence on the buffer overflow probability of the switches. In contrast to typical ATM traffic models, the buffer overflow probability decreases much more slowly with buffer size.