OpenFlow supports internal buffering of data packets in an SDN switch whereby a fraction of data packet header is sent to the controller instead of an entire data packet. This internal buffering increases the robustness and the utilization of the link between SDN switches and controller by absorbing temporary burst of packets which may overwhelm the controller. Existing queuing models for SDN have focused on the switches that immediately send packets to the controller for decisioning, with no existing models investigating the impact of the internal buffer in an SDN switch and the associated trade-offs of having an internal buffer. In this paper, we propose an analytical model for SDN switch with the internal buffer to investigate the potential benefits, drawbacks and trade-off of internal buffering in SDN switches. It was observed that a switch with internal buffer achieves up to 30% lower average packet transfer delay and 7% lower packet loss rate at the cost of requiring up to 50% more queue capacity than one without the internal buffer. The proposed model is validated with discrete event simulation where the difference between simulation and analytical results was between 0.6% and 2.8% for average packet transfer delay and less than 6% for average packet loss rate. With this investigation, we provide some guidelines to SDN switch designers on the merits, demerits and trade-off of internal buffering in an SDN switch.