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A message (or a frame) is a group of consecutive packets in high-speed networks. Often a loss of one packet form the message can result in the loss of the whole message. Selective message discarding policies have been proposed to increase goodput and reduce network congestion by discarding the packets which are (or have potentials of being) damaged. In this paper we provide a discrete-time queue for analyzing early message discarding (EMD) policy under bursty fluid. In particular, we obtain exact expressions for the probability distribution of stationary buffer content and the fluid goodput ratio. Our analytical results shall be quite helpful in selecting an optimal discarding threshold and studying the sensitivity of goodput ratio to different parameters. Finally, we give some numerical results.