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It has been reported that Internet Protocol (IP) packet traffic exhibits self-similarity or long range dependence (LRD) and causes the degradation of switch performance. Therefore, it is crucial for an appropriate buffer design of switch. In this paper, we investigate the packet loss behavior of the switch under self-similar variable packet length traffic by modeling it MMPP/M/1/K as queueing system wherein MMPP (Markov-Modulated Poisson Process) is fitted by equating the variance of MMPP and that of self-similar traffic. MMPP model is already validated one to emulate the self-similar characteristics. We investigate the relationship between packet loss probability and system parameters, and parameter of self-similar traffic. Numerical results show that analysis presented here is useful in dimensioning the switch.