A Moslem seeker after God: showing Islam at its best in the life and teaching of al-Ghazali, mystic and theologian of the eleventh century, by Samuel M. Zwemer ...

http://www.archive.org/details/amoslemseeker00zwemuoft

Foundational Theory for Understanding Policy Routing Dynamics

In this paper we introduce a theory of policy routing dynamics based on fundamental axioms of routing update mechanisms. We develop a dynamic policy routing model (DPR) that extends the static formalism of the stable paths problem (introduced by Griffin et al.) with discrete synchronous time. DPR captures the propagation of path changes in any dynamic network irrespective of its time-varying topology. We introduce several novel structures such as causation chains, dispute fences and policy digraphs that model different aspects of routing dynamics and provide insight into how these dynamics manifest in a network. We exercise the practicality of the theoretical foundation provided by DPR with two fundamental problems: routing dynamics minimization and policy conflict detection. The dynamics minimization problem utilizes policy digraphs, that capture the dependencies in routing policies irrespective of underlying topology dynamics, to solve a graph optimization problem. This optimization problem explicitly minimizes the number of routing update messages in a dynamic network by optimally changing the path preferences of a minimal subset of nodes. The conflict detection problem, on the other hand, utilizes a theoretical result of DPR where the root cause of a causation cycle (i.e., cycle of routing update messages) can be precisely inferred as either a transient route flap or a dispute wheel (i.e., policy conflict). Using this result we develop SafetyPulse, a token-based distributed algorithm to detect policy conflicts in a dynamic network. SafetyPulse is privacy preserving, computationally efficient, and provably correct.

Principles of Safe Policy Routing Dynamics

We introduce the Dynamic Policy Routing (DPR) model that captures the propagation of route updates under arbitrary changes in topology or path preferences. DPR introduces the notion of causation chains where the route flap at one node causes a flap at the next node along the chain. Using DPR, we model the Gao-Rexford (economic) guidelines that guarantee the safety (i.e., convergence) of policy routing. We establish three principles of safe policy routing dynamics. The non-interference principle provides insight into which ASes can directly induce route changes in one another. The single cycle principle and the multi-tiered cycle principle provide insight into how cycles of routing updates can manifest in any network. We develop INTERFERENCEBEAT, a distributed algorithm that propagates a small token along causation chains to check adherence to these principles. To enhance the diagnosis power of INTERFERENCEBEAT, we model four violations of the Gao-Rexford guidelines (e.g., transiting between peers) and characterize the resulting dynamics.