1. New Models and Algorithms for Active Networks

2. 2 The Active Bell-Labs Engine An adjunct active engine to any COTS router Only some packets are diverted to the AE Packet Delay depends on whether it passes thru the AE. Processing time in the AE may depend on –data in the packet. –soft state in the AE. MIB router filter Active Engine (AE) manager session 1session 2

3. 3 Addressing Modes Explicit - sent directly to a known AE. –efficient Oblivious - sent along a path, and intercepted by the first AE en-route. –topology learning –robust

4. 4 What is the right model to analyze algorithmic solutions? How to compare the strength of AN architectures? Are active networks efficient?

5. 5 Standard Asynchronous Model Communication is between neighbors A message arrivals triggers computation at a node A single bound on the delay of a communication + computation cycle –What does O(n log n) mean?

6. 6 The RS Model Two bounds on the delay: –C thru the FF. –P(k) thru the EE. Forwarding is done according to the destination addr. No assumptions on the routing. We use P(k) = P ·k FF Execution Environment (EE) FilterFilter oracle forwarding

7. 7 DARPA Model vs. The RS Model NodeOS EE 1 classclass FF Execution Environment (EE) FilterFilter oracle forwarding EE 2 EE 3 IP

8. 8 Performance Measures Communication (Message) complexity - hops traveled by messages Time complexity - time to mission completion. processing complexity - CPU time used.

9. 9 An Application Example: Route Exploration In the model - a node is only aware of its local neighbors. A node wishes to learn the route to some destination. Abstraction of the traceroute program. 45

10. 10 A naïve Solution The source query nodes sequentially. O(n 2 ) messages. O(n 2 C+nP) time.

11. 11 A naïve Solution The source query nodes sequentially. O(n 2 ) messages. O(n 2 C+nP) time.

12. 12 report-en-route A query process advances sequentially. Reports are sent to the source for each query. O(n 2 ) messages. O(nC+nP) time. send Report(id, c+1) to s if i  d send MSG * (s,d, c+1) to d

13. 13 collect-en-route A query process advances sequentially. Information is collected in the forward direction, and sent by the destination to the source. O(n) messages. O(nC+n 2 P) time.

14. 14 collect-en-route if i==d send Report(list|i) to s else send MSG * (s,d, list|i) to d

15. 15 Route Exploration Can we do better?

16. 16 Report-every- l Obtain the route length. Initiate collect-en-route in n/l segments of length l.

17. 17 Report-every- l Complexities: –message O(n 2 /l) –time O(nC+ ( n+l 2 ) P) alg. at the ith segment starts after (i-1)(C+P)l segment time cmplx: For l=n 2/3 : –message O(n 4/3 ); time O(nC+ n 4/3 P)

18. 18 Collect-rec Optimal up to a log factor ! Obtain the route length. Partition the route to two segments. Send results from the second segment using the FF. Perform recursively. Complexities: –message O(n log n); time O(nC+nP)

19. 19 Collect-rec (2) Time: O(nP+nC) Message: O(nlogn)

20. 20 Collect-rec (2) Time: O(nP+nC) Message: O(nlogn)

21. 21 Collect-rec complexity We can count messages/time per iteration. Alternative approach: –TC(n)  TC(n/2) + 4n(P+C) –MC(n)  2MC(n/2) + 4n

22. 22 Route Exploration (5)

23. 23 A message for a large number of receivers. No notion of group. Ad-hoc. Processing time is linear in the recipient size. Example: a full binary tree Message Dissemination

24. 24 Naïve solution send a message to each recipient Complexity for a full binary tree –time: nP+log n C –message: n log n

25. 25 send a message to each recipient Complexity for a full binary tree –time: nP+log n C –message: n log n Naïve solution Active 2nP+log n C 2n2n Distribute along the tree

26. 26 Mail Distribution (2) 12345678 receivers sender 5,6,7,8,m 7,8,m 8,m 7,m 5,6,m 1,2,3,4,m

27. 27 Multicast We assume a multicast group exist Aim: build the best tree In general: NP -hard We will look at the line case

28. 28 Previous Solutions Unicast: –time complexity: O(nP+C) –message complexity: O(n 2 ) message dissemination: –time complexity: O(n(P+C)) –message complexity: O(n)

29. 29 Better solution Embed a tree in the line What should be its arrity?

30. 30 Complexity of a tree scheme

31. 31 Optimum x / log x achieves optimum at 3 when restricted to integers C=1, P=20 n=32

32. 32 Other Basic Problems Bottleneck detection - computation along a route. Message dissemination to an ad-hoc group. Topology discovery. Computation of a global function.

33. 33 Summary A new model to analyze active network applications. Can be used for Other domains –Peer2Peer –application layer multicast Can be used to compare strength of architectures by comparing lower bounds.