The online buffer management problem formulates the problem of queueing policies of network switches supporting QoS (Quality of Service) guarantee. For this problem, several models are considered. In this paper, we focus on shared memory switches with preemption. We prove that the competitive ratio of the Longest Queue Drop (LQD) policy is 4M-4/3M-2 in the case of N=2, where N is the number of output ports in a switch and M is the size of the buffer. This matches the lower bound given by Hahne, Kesselman and Mansour. Also, in the case of arbitrary N, we improve the competitive ratio of LQD from 2 to 2-1/Mmin_k=1,2,…,N{[M/k]+K-1}.