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This paper analyzes the loss process distribution of a finite buffer queue. In contrast to the previous work that assumed the buffer can merely store finite number of packets, our model adopts the bounded delay policy where only the packet arrival finding its delay not exceeding a preset value is admitted into the buffer. The quantity of interest is the probability distribution of the number of lost packets within a block of n consecutive packet arrivals, which is an important measure for the design of communication networks, e.g., the forward error correction (FEC). We derive a set of recursive equations to compute the above quantity for various packet size distributions. We then focus on the influence of adding redundant packets on loss probability of message block and FEC efficiency. The impacts of bounded delay, packet size distribution and traffic load are also evaluated. We demonstrate a unique property of the finite queue with bounded delay, which is different from that of the conventional finite queue (e.g., M/G/1/K queue).