The traffic characteristics in recent years have changed considerably having more video and audio traffic with critical real-time constraints. This situation is compounded by the increased number of mobile nodes communicating over Internet. Due to such high data traffic, the access routers are often overloaded with packets with different priority. The access routers have to act quickly enough to avoid loss of connection of mobile nodes' ongoing communication. However, there is a lack of analytical models that focus on the internal queue management access router of IP-mobility protocols. In this paper, we have developed an analytical model using multi-class nonpreemptive priority queues to measure average queuing delay, queue occupancy, and packet drop probability for different classes of data and signaling traffic in the access router. We present numerical results that reflects the impact of node density, service rate and traffic pattern on these measures. The analytical framework presented in this paper will be helpful to better manage access routers with different classes of data and signaling traffic causing least queuing delay and packet loss.