1. 1 Transport BW Allocation, and Review of Network Routing 11/2/2009

2. Recap: Questions r Forward engineering: which allocation objective? r Reverse engineering: what are the objectives of TCP/Reno, TCP/Vegas? 2 ObjectiveAllocation (x1, x2, x3) TCP/Reno0.260.74 TCP/Vegas1/32/3 Max throughput011 Max-min½½½ Max sum log(x)1/32/3 Max sum of -1/(RTT 2 x)0.260.74

3. 3 Recall: Resource Allocation Framework r Maximize aggregate utility, subject to capacity constraints

4. 4 A One-Slide Summary of Optimization Theory g(x) f(x) f(x) concave g(x) linear S is a convex set q1q1 q2q2 S -D(q) is called the dual; q (>= 0) are called prices in economics - Then according to optimization theory: when D(q) achieves minimum over all q (>= 0), then the optimization objective is achieved. -D(q) provides an upper bound on obj.

5. 5 Decomposition r Assume each link l has non-negative congestion signal q l, consider the dual D(q) x1x1 x2x2 x3x3 1 1

6. 6 Distributed Optimization: User Problem r Given price signal per unit rate p f (=sum of q l along the path) flow f chooses rate x f to maximize: r Using the price signals, the optimization problem of each user is independent of each other

7. 7 Distributed Optimization: User Problem At equilibrium (i.e., at optimal), x f satisfies: How should flow f adjust x f locally?

8. 8 Interpreting Congestion Measure x f (t) q l (t) q 2 (t)

9. 9 Distributed Optimization: Network Problem The network (i.e., link l) adjusts the link signals q l (assume after all flows have picked their optimal rates given congestion signal)

10. 10 Distributed Optimization: Network Problem how should link l adjust q l locally?

11. 11 Decomposition r SYSTEM(U): r USER f : r NETWORK:

12. Outline r Bandwidth allocation framework m framework m Nash Bargaining Solution (NBS) m distributed computation m TCP/Reno, TCP/Vegas revisited 12

13. 13 TCP/Reno Dynamics

14. 14 TCP/Vegas Dynamics

15. 15 Summary: TCP/Vegas and TCP/Reno r Pricing signal is queueing delay T queueing r Pricing signal is loss rate p

16. 16 Summary: Global Network Bandwidth Allocation r Understand protocols, m e.g., Reno, Vegas r Design new e2e congestion control and router queue management protocols m e.g., FAST, XCP r Pointer: congestion control through game theory and economics m http://www.statslab.cam.ac.uk/~frank/pf/

17. Exam 1 r Covers lectures 1-16 and the preceding part of today’s lecture r A one-page “cheat” sheet 17

18. 18 Recap: Network Layer: Protocols forwarding Network layer functions: Routing protocols path selection e.g., RIP, OSPF, BGP Network layer protocol (e.g., IP) addressing conventions packet format packet handling conventions Control protocols error reporting e.g. ICMP Transport layer Link layer physical layer Network layer Control protocols - router “signaling” e.g. RSVP

19. 19 Recap: Routing Design Space r Routing has a large design space m who decides routing? m how many paths from source s to destination d? m will routing adapt to network traffic demand? m…m… r We focus mostly on network-based, single- path, static routing - Robustness - Optimality - Simplicity

20. Example: Cisco Proprietary Recommendation on Link Cost r Link metric: By default, k1=k3=1 and k2=k4=k5=0. The default composite metric for EIGRP, adjusted for scaling factors, is as follows: EIGRP : Enhanced Interior Gateway Routing Protocol

21. EIGRP Link Cost r BW min is in kbps and the sum of delays are in 10s of microseconds. r Example r The bandwidth and delay for an Ethernet interface are 10 Mbps and 1ms, respectively. r The calculated EIGRP BW metric is as follows: m 256 × 10 7 /BW = 256 × 10 7 /10,000 m = 256 × 10000 m = 256000

22. 22 Recap: Synchronous Bellman-Ford (SBF) r Nodes update in rounds: m there is a global clock; m at the beginning of each round, each node sends its estimate to all of its neighbors; m at the end of the round, updates its estimation A E D CB 7 8 10 2 1 2 A B E C D

23. 23 Recap: Properties of SBF r Monotonicity: m if d(t)  d’(t) => d(t+1)  d’(t+1) i.e., each node has a higher estimate in one scenario (d) than in another scenario (d’), then each node has a higher estimate in d than in d’ after one round of synchronous update. r SBF/  computes the shortest path costs r Bellman equation has a unique solution r SBF/-1 also computes the shortest path costs

24. Recap: Asynchronous Bellman-Ford (ABF) r No notion of global iterations m each node updates at its own pace r Asynchronously each node i computes using last received value d i j from neighbor j. r Asyncrhonously node j sends its estimate to its neighbor i: m there is an upper bound on the delay of estimate packets (no worry for out of order)

25. Distance Table: Example A E D CB 7 8 1010 2 1 2 d () A B C D E distance tables from neighbors destinations computation E’s distance table distance table E sends to its neighbors A: 10 B: 8 C: 4 D: 2 E: 0 Below is just one step! The protocol repeats forever! 10 15  A B D 0 7  A B D 10 8 2 7 0   1 2   0 A: 10 B: 8 D: 4 D: 2 17 8   9 4   2

26. Recap: Asynchronous Bellman-Ford: Summary r Distributed: each node communicates its routing table to its directly- attached neighbors r Iterative: continues periodically or when link changes, e.g. detects a link failure r Asynchronous: nodes need not exchange info/iterate in lock step! r Convergence in finite steps, independent of initial condition if network is connected

27. Properties of Distance-Vector Algorithms r Good news propagate fast

28. Properties of Distance-Vector Algorithms r Bad news propagate slowly r This is called the counting-to-infinity problem Question: why does counting-to-infinity happen?

29. What is a Routing Loop? r A routing loop is a global state (consisting of the nodes’ local states) at a global moment (observed by an oracle) such that there exist nodes A, B, C, … E such that A (locally) thinks B as down stream, B thinks C as down stream, … E thinks A as down stream 29

30. Backup Slides 30

31. 31 Network problem r As if the network maximizes a logarithmic utility function, but with constants (w f, f  F) chosen by the users

32. 32 Three Optimization Problems r SYSTEM(U f ): r USER f (U f ; p f ) r NETWORK(w f )

33. 33 Decomposition Theorem r There exist vectors p, w and x such that 1. w f = p f x f for f  F 2. w f solves USER f (U f ; p f ) 3. x solves NETWORK(w) r The vector x then also solves SYSTEM(U).

34. 34 Another Decomposition r SYSTEM(U): r USER f (U f ; p f ) r NETWORK(w f )

35. 35 Decomposition Theorem r There exist vectors p, w and x such that 1. w f = p f x f for f  F 2. w f solves USER f (U f ; p f ) 3. x solves NETWORK(w) r The vector x then also solves SYSTEM(U).

36. 36 TCP/Reno: Equilibrium r Pricing signal is aggregated loss rate p

37. 37 TCP/Vegas: Equilibrium r Pricing signal is queueing delay T queueing

38. Summary: Network Bandwidth Allocation r Forward engineering: m how to determine objective functions: “first-principles” approach to derive utility functions m given objective, how to design effective alg (?) r Reverse engineering: understand current protocols r Discussion: problems of the framework 38

39. 39 Using Virtual Circuit to Implement Network Services r In order to provide some functionalities, a network may choose virtual circuit, e.g., Virtual Private Network (VPN)

40. 40 Using Datagram to Implement the Most Basic Network Service r A datagram network generally provides simple services: the forwarding of packets from src to dest. r We will focus on datagram networks which provide best effort service m extensions to provide more services will be discussed in the multimedia networking part of the course

41. EIGRP Neighbor Discovery r EIGRP routers actively establish relationships with their neighbors r EIGRP routers establish adjacencies with neighbor routers by using small hello packets. r The Hello protocol uses a multicast address of 224.0.0.10, and all routers periodically send hellos.

42. EIGRP Neighbor Discovery r On hearing hellos, the router creates a table of its neighbors. r The continued receipt of these packets maintains the neighbor table By forming adjacencies, EIGRP routers do the following: r Dynamically learn of new routes that join their network r Identify routers that become either unreachable or inoperable r Rediscover routers that had previously been unreachable

43. 43 Neighbor Discovery - 3

44. Default Hello Intervals and Hold Time for EIGRP