Resilience of the Internet to random breakdowns

A common property of many large networks, including the Internet, is that the connectivity of the various nodes follows a scale-free power-law distribution, P(k)=ck^-a. We study the stability of such networks with respect to crashes, such as random removal of sites. Our approach, based on percolation theory, leads to a general condition for the critical fraction of nodes, p_c, that need to be removed before the network disintegrates. We show that for a<=3 the transition never takes place, unless the network is finite. In the special case of the Internet (a=2.5), we find that it is impressively robust, where p_c is approximately 0.99.Comment: latex, 3 pages, 1 figure (eps), explanations added, Phys. Rev. Lett., in pres

Fault-oriented Test Generation for Multicast Routing Protocol Design

We present a new algorithm for automatic test generation for multicast routing. Our algorithm processes a finite state machine (FSM) model of the protocol and uses a mix of forward and backward search techniques to generate the tests. The output tests include a set of topologies, protocol events and network failures, that lead to violation of protocol correctness and behavioral requirements. We target protocol robustness in specific, and do not attempt to verify other properties in this paper. We apply our method to a multicast routing protocol; PIM-DM, and investigate its behavior in the presence of selective packet loss on LANs and router crashes. Our study unveils several robustness violations in PIM-DM, for which we suggest fixes with the aid of the presented algorithm