The conventional analysis of Delay-Tolerant Network (DTN) routing assumes that the terrain over which nodes move is closed implying that when the nodes hit a boundary, they either wrap around or get reflected. In this work, we study the effect of relaxing this closed terrain assumption on the routing performance, where a continuous stream of nodes enter the terrain and get absorbed upon hitting the boundary. We introduce a realistic framework that models the open terrain as a queue and compares performance with the closed terrain for a variety of routing protocols. With three different mobility scenarios and four different routing protocols, our simulation shows that the routing delays in an open terrain are statistically equivalent to those in closed terrains for all routing protocols. However, in terms of cost some protocols differ widely in two cases while some continue to demonstrate the statistical equivalence. We believe that this could be a new way to classify routing protocols based on the difference in their behavior under churn.