Delay tolerant network (DTN) routing provides a communication primitive in intermittently disconnected networks, such as battlefield communications and human-contact networks. In these applications, the anonymity preserving mechanism, which hides the identities of communicating parties, plays an important role as a defense against cyber and physical attacks. While anonymous routing protocols for DTNs have been proposed in the past, to the best of our knowledge, there is no work that emphasizes analysis of the performance of these protocols. In this paper, we first design an abstract of anonymous routing protocols for DTNs and augment the existing solution with multi-copy message forwarding. Then, we construct simplified mathematical models, which can be used to understand the fundamental performance and security guarantees of onion-based anonymous routing in DTNs. To be specific, the delivery rate, message forwarding cost, traceable rate, and path and node anonymity are defined and analyzed. The numerical and simulation results using randomly generated contact graphs and the real traces demonstrate that our models provide very close approximations to the performance of the anonymous DTN routing protocol.