The concept of worst case source and worst case traffic for a policing algorithm is discussed. Emphasis is given to the importance of worst case traffic analysis in performance evaluation of a policing mechanism. Basic leaky bucket and buffered leaky bucket are analysed and compared for worst case traffic. A new algorithm of two stage leaky bucket is proposed. Simulation results show that the algorithm is superior to the buffered leaky bucket in worst case traffic and less cell buffers are needed.