Building Low-maintenance Expressways for P2P Systems

1. Building Low-maintenance Expressways for P2P Systems Zhichen Xu and Zheng Zhang Presented By Prasetha Panampully

2. Overview • P2P systems can be improved in 3 areas • Maintenance cost • Ability to make discriminative use of nodes • Ability to adapt to network conditions and application needs • Here we try to boost the routing performance of CAN using “Expressways”

3. Agenda • Brief overview of CAN • Definition of an “Expressway” • Building Expressways • Routing with Expressways • Load balance with Expressways • Maintenance • Analysis • Tuning to best performance • Tuning to network conditions • Route around a congested node • Tuning according to application needs

4. P2P Systems Utilize distributed resources and perform critical functions in a de-centralized manner Advantages • Cost sharing • Autonomous • Resource aggregation • Improved scalability/reliability • Increased autonomy • Anonymity/privacy • Dynamism • Ad-hoc communication

5. Content Addressable Network (CAN) • Offers administration-free and fault-tolerant storage utility. • CAN is a distributed infrastructure which provides hash table like functionality. • It is scalable, fault-tolerant and completely self-organizing. • CAN organizes the logical space as a d-dimensional Cartesian coordinate space. • The co-ordinate space is partitioned among existing nodes and each node owns its individual zone.

6. CAN Example • Node n1(1,2) is first node that joins and it covers the entire space. • Then n1 has the authority over all the files present in this space • As we are considering only two dimension, it will be only one copy of particular file in this dimension 7 6 5 4 3 n1 2 1 0 0 2 3 4 6 7 5 1

7. CAN Example • Actions on Node Join • When a new node joins, it joins a node that is close to it in IP distance. • The existing node will split its allocated zone into half. • The neighbors of the split zone must be notified. 7 6 5 4 3 n2 n1 2 1 0 0 2 3 4 6 7 5 1

8. CAN Example If one more node enters the space covered by 1 then the region of 1 is equally divided. 7 6 n3 5 4 3 n2 n1 2 1 0

9. CAN Example More example of the space division. 7 6 n5 n4 n3 5 4 3 n2 n1 2 1 0 0 2 3 4 6 7 5 1

10. CAN Example Here the f1, f2 etc are the id’s of the documents present in this particular network space. 7 6 n5 n4 n3 f4 5 4 f1 3 n2 n1 2 f3 1 f2 0 0 2 3 4 6 7 5 1

11. CAN Example Each item is stored by the node who owns its mapping in the space 7 6 n5 n4 n3 f4 5 4 f1 3 n2 n1 2 f3 1 f2 0 0 2 3 4 6 7 5 1

12. 7 6 n5 n4 n3 f4 5 4 f1 3 n2 n1 2 f3 1 f2 0 0 2 3 4 6 7 5 1 CAN Example • Assume n1 queries for f4,it forwards the query to n3 as it is the nearest neighbor. • n3 forwards it to n4 and n4 to n5. • n5 sends back information to n1 that it has the doc and the file exchange starts if n1 wishes to.

13. Routing in CAN • CAN node maintains a coordinate routing table that holds the IP address and the virtual coordinates of each of its neighboring zones. • A CAN message includes the destination coordinates. Using its neighbor coordinate set, a node routes a message towards its destination by simply forwarding to the neighbor with coordinates closest to the destination coordinates.

14. Routing in CAN Consider a 2-d Cartesian space with 16 equal zones. Each node has maximum of 4 neighbors. So, maximum routing path length is 3 hops. For a d-dimensional space which is partitioned into n equal zones the average routing path length is (d/4)(n^(1/d)) hops.

15. Routing in CAN • No of neighbors for an individual node is 2d. • Thus,for a d-dimensional space, we can grow the number of nodes (zones) without increasing the per node state. • The average routing path length grows in proportion to (n^(1/d)). • Thus the routing performance in CAN is O(n^(1/d)). • Expressways can improve the routing performance to O(log N)

16. Expressway “Expressway” is an auxiliary data structures to deliver high routing performance. Features • Auxiliary mechanisms • Self organized. • Self maintained. • Adaptive to changing network. • High bandwidth.

17. Overview of Expressways • Expressways of CAN’s have routing tables of increasing span. • The entire space is partitioned into zones of different spans with smallest zones correspond to the CAN zones and any other zones are called Expressway zones. • Here CAN zones are at level 3, four of neighboring CAN zones make one level 2 expressway and four such level 2 zones make a level 1 zone.

18. Overview of Expressways • Each node owns a CAN zone and is also a resident of the Expressway zone that encloses its CAN zone. • Expressway zones and CAN zones are recorded in each node in data structure called “Total routing table”. Total routing table of node 1 consists of the default routing table of CAN (plain arcs) and expressway routing tables (thick and long arcs)

19. Expressway Routing • Total routing table RT :< R0, R1, R2, ..RL> where RL corresponds to the node’s default routing table that CAN already builds. • Ri (i=0 to L-1) is called “Expressway routing table” that has larger span. Smaller the i larger the span. • For each neighboring expressway zone, the expressway routing table keeps the address of one or more nodes in that zone.

20. Building an Expressway • The algorithm for building expressway is “Evolving snapshot ”. • According to the algorithm, at regular intervals of system growth, snapshots of current routing table are taken. • Each node takes the snapshot independently by observing its zone size, with which it may infer to what stage the system has grown. • For node x, suppose the current zone size is x.R.Z and the target size is x.R(L-1).Z/K. if the x’s current size shrinks to its target size then it takes a new snapshot by incrementing L. where K is the span of the expressway. • This frozen routing table is then pushed into x’s total routing table.

21. Summary of Notations

22. Expressway Building • CAN can be thought as building a binary tree since each new node splits a random existing node. • When a node y splits with x, it inherits all entries of x’s total routing table other than x’s • current routing table. • Each newly added link of the tree leads to a new node join • Total routing table can be found by walking down the tree from the root towards the node picking up the snapshot routing tables. • Tree rooted by x when it joined system is called x’s expressway tree.

23. Procedure when a node y joins node x y.RT = <x.R0,x.R1,……,x.RL-1,y.RL> repeat the procedure for testing for a new snap shot Procedure for testing for new snapshot: Both nodes test to see if its current zone has shrunken to 1/K th of its last snapshot. If (RL.Z <= RL-1.Z/K) { RL+1 = RL RT=<R0,R1,…..,RL,RL+1> L=L+1 }

24. Routing Route with Expressway If(ptRL.Z) Return; For(i=0;i<=L;i++) If(pt(Ri.Z)) Route using Ri; Route with Ri for(j=0;j<d;j++) if(pt<Ri.Z.Lj||pt>Ri.Z.Uj) { Route to xRi.Nj that is close to pt ; Break }

25. Load Balance For achieving load balance . . . Node z that routes to x in expressway routing, should have the option for replacing x with any node inside the x’s expressway tree. Example: • Let Z.Ri be the routing table used to route to x and X be the x’s expressway zone, then we pick a point pt in X and route to it. Whoever owns that zone now replaces x in Z.Ri. Here the point pt is selected randomly. • No of nodes that replace x is proportional to the size of x’s Expressway tree and therefore is proportional to the no. of residents inside x’s Expressway tree. Thus the algorithm will automatically balance the load among Expressways.

26. Default vs. Random Algorithm This figure shows the simulation results reporting number of messages each node has to forward with default routing table and the routing table constructed using random selection. We see that with random selection, more no of messages are forwarded

27. Dynamic Maintenance Node Joins • When a new node joins the network, it updates its expressway neighbors for the expressway zones recorded in its total routing table. Such maintenance is proportional to the total levels of expressways, which is O(logkN). Node Departs • When a node departs, one of its neighbors will take over departed nodes responsibilities. However the departed node can be the expressway neighbor of multiple nodes and its expressway functions need to be maintained by some other nodes.

28. Dynamic Maintenance • Suppose node x departs from the network, and node y attempts to route to node x, then the request will timeout • Then node y picks up a point in the space of x recorded in the failed routing table, and route to it. This succeeds at node ‘z’ whose zone contains the point. ’z’ is now replacement of x to repair y’s snapshot. • On average the total no. of nodes that will update their routing table entries =Total no. of expressway levels * no. of neighbors in each level = O(d.logkN).

29. Storage The total routing table depth is m and as a result the storage for routing table increases m-folds. m=logkN. Where, m =no of levels of expressways Example : If K=4 and N=2^20 (million nodes), then m =10 and takes only few hundred bytes to store the routing table. Therefore storage is not a concern.

30. Analysis Routing expressways involves at most m levels of CAN like routing. Routing algorithm will iterate through the table to get down to the level where the expressway zone doesn't cover the destination. It will the follow the CAN routing to reach an expressway zone that covers the destination. This process continues until the destination is reached.

31. Analysis Number of levels the routing will travel = logkN The average routing hops in any level = (d/3)K^(1/d) No of hops in the worst case = (logkN)(d/3)K^(1/d) The bigger the K, the less levels of expressways there are but, routing at each level is more expensive, so we need to find the optimal K.

32. Analysis Let f(x)=(d/3).(x^1/d).logxN Taking the derivative and equating it to zero: f(x)’= 0 =>(d/3).(1/d.x^(1/d-1).lnN/lnx = x^(1/d-1).lnN/(lnx)^2 On simplification we get 1/d=1/lnx => x= e^d Thus the optimal K = e^d Optimal routing performance=f(x)=(d/3).((e^d)^1/d).log(e^d)N = d/3.e.lnN/d = e/3 lnN Thus the routing performance of CAN using expressways is O(lnN). And it is independent of choice of d.

33. Expressway Performance Compared With Theoretical Values Comparison of theoretical performance using expressway with results obtained using simulation.

34. Comparison of Expressway with CAN Expressway with lowest dimension outperforms the basic CAN

35. Tuning Towards Best Performance “The representative of each expressway zone can be changed on the fly” • Tuning towards network conditions Locating closest nodes using coordinate maps: Build maps of network coordinates, and utilizing the archival capacity of P2P system itself to store and maintain the maps in various zones in CAN. Any node can find a resident close to it in a given expressway zone Z by consulting the appropriate map

36. Tuning to Network Conditions Devise a hash function that maps positions in N/W co-ordinate space to points in a CAN zone

37. Improving Co-ordinate Maps

38. Ratio of Physical latencies of CAN using co-ordinate maps to those of “ideal” CAN Improvements are close to 50% and stay 2-3 range of the “ideal”

39. Average data latency per hop With expressway physical distance of each logical hop increases whereas for “ideal” case the reverse is true.

40. Route around a congested node Two Steps for handling Congestion Detect and Report Congestion • Explicit congestion notification for congestion avoidance • Active probing for congestion discovery Evaluate alternate routes Additional Method Integrate Congestion control as part of the process of locating most appropriate expressway neighbor.

41. Tuning According to Application Needs • Reducing the per hop distance may not necessarily reduce the total delay. • So, the total routing table of node keeps the addresses of multiple nodes, instead of keeping the address of the node that is physically closest to it. • And while routing to a destination, we attempt to balance the per hop distance and the total number of logical hops to achieve overall small latency. • Routing performance can be further improved by allocating some storage at each node to cache routes based on runtime behavior.

42. Heuristics When choosing a candidate ‘y’ in node x’s total routing table to route from x to destination ‘d’ … Minimize the terms physical_distance(x,y) + ratio_to_ideal * ideal_distance(y,d) Where, physical_distance(x,y) = physical distance between ‘x’ and expressway neighbor y ideal_distance(y,d) = estimates the “ideal” distance between (y,d) ratio_to_ideal = ratio of avg. physical dist. using map to that of “ideal” case

43. Percentage improvement over IP optimization This optimization reduces physical distance up to 19%

44. Contributions • Using expressways the performance of routing in CAN is improved from O(N^1/d) to O(ln N). • Evaluation of the techniques show that • Tuning the expressway to network conditions improve the average physical routing distance by about 50% • Tuning the expressway to application behavior further reduce physical latency up to 19%.