Ben Marais (1909-1999): The influences on and heritage of a South African Prophet during two periods of transformation

University of Pretoria / Dissertation / Department of Church History and Church Policy / Advised by Prof J W Hofmeyr

Examples of Network Flow Verification Using TRAFFIC(X)

In our previous work, we developed TRAFFIC(X), a specification language for modeling bi-directional network flows featuring a type system with constrained polymorphism. In this paper, we present two ways to customize the constraint system: (1) when using linear inequality constraints for the constraint system, TRAFFIC(X) can describe flows with numeric properties such as MTU (maximum transmission unit), RTT (round trip time), traversal order, and bandwidth allocation over parallel paths; (2) when using Boolean predicate constraints for the constraint system, TRAFFIC(X) can describe routing policies of an IP network. These examples illustrate how to use the customized type system.

On the Stable Paths Problem and a Restricted Variant

Interdomain routing on the Internet is performed using route preference policies specified independently, and arbitrarily by each Autonomous System in the network. These policies are used in the border gateway protocol (BGP) by each AS when selecting next-hop choices for routes to each destination. Conflicts between policies used by different ASs can lead to routing instabilities that, potentially, cannot be resolved no matter how long BGP is run. The Stable Paths Problem (SPP) is an abstract graph theoretic model of the problem of selecting nexthop routes for a destination. A stable solution to the problem is a set of next-hop choices, one for each AS, that is compatible with the policies of each AS. In a stable solution each AS has selected its best next-hop given that the next-hop choices of all neighbors are fixed. BGP can be viewed as a distributed algorithm for solving SPP. In this report we consider the stable paths problem, as well as a family of restricted variants of the stable paths problem, which we call F stable paths problems. We show that two very simple variants of the stable paths problem are also NP-complete. In addition we show that for networks with a DAG topology, there is an efficient centralized algorithm to solve the stable paths problem, and that BGP always efficiently converges to a stable solution on such networks.