A queueing model suitable for multimedia packets with Poisson and batch Poisson arrivals is studied. In the queueing model, priority is given to the packets with batch Poisson arrival, and the packets with Poisson arrival, accumulated in a buffer, are routed by utilizing intervals of the packets with priority. The queueing performance of the proposed model is evaluated by the mean system delay. We also consider the effect of batch size and the ratio of the traffic with batch Poisson arrival and the one with Poisson arrival on the mean system delay. It is found that the proposed queueing model is useful to reduce the mean system delay of the packets with Poisson arrival, while maintaining the means system delay of the packets with batch Poisson arrival.