We build and analyze some types of queueing model to discuss capacity dimensioning of access links of a LAN interworking unit connected to the Internet backbone network. We assume that the IWU has a FIFO buffer to transmit IP packets to the Internet through the backbone. In order to analyze the system, we use a Poisson process and an MMPP process as input traffic models of IP packets and we use a general service time distribution as a service time model. But we use both an exponential service time and a deterministic service time in numerical examples for simple and efficient performance comparisons. As performance measures, we obtain the packet loss probability and the mean packet delay. We present some numerical results to show the effect of arrival rate, buffer size and link capacity on packet loss and mean delay.