A discrete and near-uniform arrival (DNA) model is proposed to analyze a statistical voice packet multiplexer. The DNA model assumes that the arrival process of aggregate voice packets from several voice sources in talkspurt be in a discrete mode with near-uniform distribution over a packetization time. Finite queue size for the statistical voice packet multiplexer is also assumed. Results of the probability distribution functions of the queue length and the packet delay are obtained; the optimal packet length is also determined by the 99.9th percentile of delay.