1. 1 PASTRY Partially borrowed from Gabi Kliot ’ s presentation

2. 2 “ Pastry: Scalable, decentralized object location and routing for large-scale peer-to-peer systems ” Antony Rowstron (Microsoft Research) Peter Druschel (Rice University) Sources

3. 3 Pastry Generic p2p location and routing substrate (DHT) Self-organizing overlay network (join, departures, locality repair) Consistent hashing Lookup/insert object in < log 2 b N routing steps (expected) O(log N) per-node state Network locality heuristics Scalable, fault resilient, self-organizing, locality aware, secure

4. 4 Pastry: Object distribution objId/key Consistent hashing 128 bit circular id space nodeIds (uniform random) objIds/keys (uniform random) Invariant: node with numerically closest nodeId maintains object nodeIds O 2 128 - 1

5. 5 Pastry: Object insertion/lookup X Route(X) Msg with key X is routed to live node with nodeId closest to X Problem: complete routing table not feasible O 2 128 - 1

6. 6 Pastry: Routing Tradeoff O(log N) routing table size 2 b * log 2 b N + 2l O(log N) message forwarding steps

7. 7 Pastry: Routing table (# 10233102 ) L nodes in leaf set log 2 b N Rows (actually log 2 b 2 128 = 128/b) 2 b columns L neighbors

8. Pastry: Leaf sets Each node maintains IP addresses of the nodes with the L numerically closest larger and smaller nodeIds, respectively.  routing efficiency/robustness  fault detection (keep-alive)  application-specific local coordination

9. 9 Pastry: Routing procedure If (destination is within range of our leaf set) forward to numerically closest member else let l = length of shared prefix let d = value of l-th digit in D’s address if (R l d exists) forward to R l d else forward to a known node (from ) that (a) shares at least as long a prefix (b) is numerically closer than this node

10. 10 Pastry: Routing Properties log 2 b N steps O(log N) state d46a1c Look for (d46a1c) d462ba d4213f d13da3 65a1fc d467c4 d471f1

11. 11 Pastry: Locality properties Assumption: scalar proximity metric e.g. ping/RTT delay, # IP hops traceroute, subnet masks a node can probe distance to any other node Proximity invariant: Each routing table entry refers to a node close to the local node (in the proximity space), among all nodes with the appropriate nodeId prefix.

12. 12 Pastry: Geometric Routing in proximity space d46a1c Route(d46a1c) d462ba d4213f d13da3 65a1fc d467c4 d471f1 d467c4 65a1f c d13da3 d4213f d462ba Proximity space  The proximity distance traveled by message in each routing step is exponentially increasing (entry in row l is chosen from a set of nodes of size N/2 bl )  The distance traveled by message from its source increases monotonically at each step (message takes larger and larger strides) NodeId space

13. 13 Pastry: Locality properties Each routing step is local, but there is no guarantee of globally shortest path Nevertheless, simulations show: Expected distance traveled by a message in the proximity space is within a small constant of the minimum Among k nodes with nodeIds closest to the key, message likely to reach the node closest to the source node first

14. 14 Pastry: Self-organization Initializing and maintaining routing tables and leaf sets Node addition Node departure (failure) The goal is to maintain all routing table entries to refer to a near node, among all live nodes with appropriate prefix

15. 15 New node X contacts nearby node A A routes “ join ” message to X, which arrives to Z, closest to X X obtains leaf set from Z, i ’ th row for routing table from i ’ th node from A to Z X informs any nodes that need to be aware of its arrival X also improves its table locality by requesting neighborhood sets from all nodes X knows In practice: optimistic approach Pastry: Node addition

16. 16 Pastry: Node addition X=d46a1c Route(d46a1c) d462ba d4213f d13da3 A = 65a1fc Z=d467c4 d471f1 New node: X=d46a1c A is X’s neighbor

17. 17 d467c4 65a1f c d13da3 d4213f d462ba Proximity space Pastry: Node addition New node: d46a1c d46a1c Route(d46a1c) d462ba d4213f d13da3 65a1fc d467c4 d471f1 NodeId space X is close to A, B is close to B1. Why X is close to B1? The expected distance from B to its row one entries (B1) is much larger than the expected distance from A to B (chosen from exponentially decreasing set size) X B1 is first row of B

18. 18 Node departure (failure) Leaf set repair (eager – all the time): Leaf set members exchange keep-alive messages request set from furthest live node in set Routing table repair (lazy – upon failure): get table from peers in the same row, if not found – from higher rows Neighborhood set repair (eager)

19. 19 Pastry: Summary Generic p2p overlay network Scalable, fault resilient, self-organizing, secure O(log N) routing steps (expected) O(log N) routing table size Network locality properties