In this paper, we investigate the mean queue length and the mean packet delay of a dynamic bandwidth allocation(DBA) scheme in an Ethernet passive optical network(EPON). We focus on the interleaved polling system with a gated service discipline. We assume that input packets arrive at an optical network unit(ONU) according to Poisson process. We use a continuous time queueing model in order to find the queue length distribution of the gated interleaved polling system with the first stage input queue and the second stage transmission queue. We give some numerical results to investigate the mean queue lengths and mean packet delays for the symmetric polling system with statistically identical stations.