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Advances in Metarouting and Network Optimization: The Future of Dynamic Routing Protocols

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jela
29 diapositives · 492 Views · Aug 07, 2014

This work in progress explores the concepts of metarouting and network optimization using routing algebras. Highlighting the current limitations of existing dynamic routing protocols, it provides insight into the mathematical frameworks that could lead to the development of more efficient routing solutions. By examining algorithms such as the Generalized Dijkstra and Bellman-Ford, the paper identifies the importance of monotonicity and isotonicity for algorithm correctness and loop-freedom. This foundational work paves the way for a new era of customizable and optimal network routing solutions, addressing both theoretical and practical applications.

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Advances in Metarouting and Network Optimization: The Future of Dynamic Routing Protocols
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  1. timothy.griffin@cl.cam.ac.uk Metarouting and Network Optimization (work in progress) alex.gurney@cl.cam.ac.uk CISS 2006

  2. The Current Situation • IP Connectivity is implemented with dynamic routing protocols • These protocols are few in number • Existing protocols tend to get in the way of network optimization, network analysis

  3. Routing Algebras(Sobrinho) 1970s 1980s: Path Algebra = Idempotent semiring. Carre’, Gondran & Minoux 2002: Algebra and Algorithms for QoS Path Computation and Hop-by-Hop Routing in the Internet. 2003: Network Routing and Path Vector Protocols: Theory and Applications. Routing Algebras

  4. Generalized Routing Algebras(Gurney & Griffin, ongoing work) This is a pre-order A semi-group is a semi-group action on S

  5. Big Picture Routing Algebras Path Algebras Generalized Routing Algebras

  6. “Best” Routes For finite, non-empty Total order Partial order Total pre-order Pre-order

  7. Weighted Graph, solution

  8. Generalized Dijkstra for all v in V: d[v]  d[s]  Q  V while Q not empty: choose u in Q with d[u] in min{d[v] | v in Q}; Q  Q - {u}; for all v in V with (u, v) in E: if d[v] > (w(u, v) d[u]) then: d[v]  w(u, v) d[u];

  9. Generalized Bellman-Ford for all v in V: d[v]  d[s]  Q  V for i in {1, 2, ..., |V| - 1} for all (u, v) in E if d[v] > (w(u, v) d[u]]) then d[v]  w(u, v) d[u] -- Negative weight cycle detection for (u, v) in E if d[v] > (w(u, v) d[u]) then: return false -- Found “neg-weight” cycle return true -- No “neg-weight” cycle

  10. Some Important Properties Monotonicity (M) : Strict monotonicity (SM) : Isotonicity (I) : Strict isotonicity (SI) :

  11. What makes these algorithms work (for bounded path algebras)? • Dijkstra • Correctness proof uses monotonicity and isotonicity, • Loop-freedom for hop-by-hop forwarding uses strict monontonicity. • Bellman-Ford • Correctness proof uses monotonicity, • Loop-freedom for hop-by-hop forwarding uses strict monotonicity

  12. Metarouting(Griffin & Sobrinho 2005) • A meta-language for Routing Algebras • Base algebras • Constructors • Property Preservation Rules • Properties of base algebras known, • Preservation rules for each constructor • Can be implemented, standardized

  13. Direct Product

  14. Direct Product M M M I I I SM M M SI I I M SM M I SI I SM SM SM SI SI SI

  15. The corresponding path algebra gives {(300, 30), (571, 70)} = (300, 70) Distance x Bandwidth Prague London Moscow (100, 30) (311, 70) (10, 80) (200, 30) Paris Rome (250, 90) P = Rome  Prague  Moscow = (300, 30) Q = Rome  Paris  London  Moscow = (571, 70) min {w(P), w(Q)} = {(300, 30), (571, 70)}

  16. Lexicographic Product

  17. Property Preservation with Lex Product M M M EQ,SI I I SM SM EQ,SI SI SI M SM SM EQ EQ EQ A design pattern: SM All at least M SM Don’t care!

  18. Local Preference, Origin Preference (Always M)

  19. Disjoint Union

  20. Disjoint Union : Property Preservation M M M I I I SM M M SI I I M SM M I SI I SM SM SM SI SI SI

  21. Scoped Product Q : What is a good mathematical framework for the analysis of routing algebra metalanguages? A : CATEGORY THEORY!

  22. Scoped Product

  23. Scoped Product : Monotonicity Preservation SM M M SM SM SM

  24. Dependent Lexicographic Product

  25. An application… This can be viewed as an instance of

  26. Operations at the Protocol Level B A B A A B A B

  27. …or B A B Adjacencies of B supported by connectivity of provided by A A A B A Think of A = OSPF and B = IBGP …. A

  28. OSPF Revisited Something like Something like where (shortest paths)

  29. Challenge • If you could “roll your own” routing protocols, what would you do? • How does this kind of flexibility change the way you might think about network optimization?