Internet Topology Modeling—A Review

The paper [CDZ97] presents two related methods of generating artificial, but purportedly realistic, network topologies. Unlike previous methods such as Waxman [3], a hierarchical model of the Internet is assumed based on transit domains, stub domains, and LANs (or equivalently, WANs, MANs, and LANs). Both methods are O(N^2) in time complexity, where N is the number of nodes. Both methods are parameterized by the number of different types of nodes and the number of different types of edges. These methods differ in algorithmic details and implementation. The first, Transit-Stub, generates nodes and edges by a pure probabilistic approach. The second, Tiers, joins nodes by the minimum spanning tree algorithm.

The research topic is worthy since network topology affects network performance and service scalability. The physical topology of the Internet affects the effectiveness of routing protocols. Overlay routing protocols, as seen in many P2P networks, have performance characteristics dependent upon the underlying physical topology. [RD01] [RFI02] As stated, the existing Waxman model appears to be a highly unrealistic in multiple regards, most noticeably in its lack of hierarchy and resemblance to real networks. One question, not addressed, is why artificial topologies should be used instead of real topologies such as in [IMP]?

The paper itself has some substantial problems. Chiefly, no effort is made to justify the realism of the topologies produced by these methods. It would be useful to see some justification that there are generally three and only three levels of hierarchy connected in the prescribed way.

References are thin. Two of the four references are to papers by the authors, and these detail the two discussed network topology generation methods individually. Of the remaining references, only the reference to Waxman is directly related to the research topic.

The general methods appear sound but obvious given the proposed model of the Internet. We are not provided details of the algorithms used, though. For example, is any non-uniform distribution used to assign the positions of stub nodes with respect to their transit nodes (or for LAN nodes with respect to stub nodes)? A main question is how does one parameterize the model to obtain realistic topologies; this is admittedly not attempted in the paper. Therefore, the methods themselves do not appear to be a major contribution from this paper as they result fairly directly from the model

The requirement for the number of links to be (approximately) no less than twice the number of nodes to ensure the possibility of connectivity in a graph might not be obvious, although it is easy to see with a few examples, such in pure linear and star topologies.

It is somewhat odd that no diagrams are shown of Transit-Stub networks, but three diagrams are shown of Tiers networks.

Overall, only a few points can be taken from this paper. What I learned can be summarized as follows: A Waxman method is popular, but limited, for generating artificial network topologies; the author claims there to be three implicit levels of hierarchy with certain topology constraints in the Internet; a number of these network topology generation methods are O(N^2) in complexity; and source code is available for at least two methods.

[CDZ97] Calvert, C., Doar, B., and Zegura, E. “Internet Topology Modeling.” IEEE Communications Magazine, 1997. http://www.cc.gatech.edu/fac/Ellen.Zegura/papers/model.ps.gz

[IMP] Internet Mapping Project. Lumeta Corporation. http://research.lumeta.com/ches/map/

[RD01] Rowstron, A. and Druschel, P. “Pastry: Scalable, distributed object location and routing for large-scale peer-to-peer systems.” In IFIP/ACM International Conference on Distributed Systems Platforms (Middleware), pp. 329-350, Nov. 2001. http://research.microsoft.com/~antr/PAST/pastry.pdf

[RFI02] Ripeanu, M, Foster, I., and Iamnitchi, A. “Mapping the Gnutella Network: Properties of Large-Scale Peer-to-Peer Systems and Implications for System Design.” IEEE Internet Computing, 6(1), 2002. http://citeseer.nj.nec.com/ripeanu02mapping.html