LECT-10, S-1 FP2P08, Javed I.

Transcription

1 A Course on Foundtions of Peer-to-Peer Systems & Applictions LECT-10, S-1 CS /799 Foundtion of Peer-to-Peer Applictions & Systems Kent Stte University Dept. of Computer Science PASTRY 2 1

2 [mechnics] Updte overview 1 clss strt+routing+node filure LECT-10, S-3 Pstry [updte.. Old] Overview Pstry: Sclble, decentrlized object loction nd routing for lrge-scle peer-to-peer systems, Antony Rowstron nd Peter Druschel, 2001 Topology Consistnt Hshing Key Spce Routing Lef Set Numericlly Closest Set Physiclly Closest Set Node Arrivl Bootstrpping Finding Zone Joining the Routing (Route Tble Updtes) Node Deprture Identifiction of Tkeover Node Recovery Algorithm Performnce Anlysis Evlution Stbility Robustness Lod blncing LECT-10, S-4 2

3 Pstry Topology LECT-10, S- Pstry An overly network tht provides selforgnizing routing nd loction service (like Chord). Seeks to minimize the distnce (sclr proimity metric like routing hops) messges trvel. Epected number of routing steps is O(log N); N=No. of Pstry nodes in the network LECT-10, S- 3

4 Pstry Topology Nodes re orgnized in circulr ID spce, using consistent DHT hshing. NodeId rndomly ssigned from {0,.., } A pstry node cn route to the numericlly closest node to given key in less thn log 2 b N steps. (b, L re configurtion prmeters) Despite concurrent node filures, delivery is gurnteed unless more thn L /2 nodes with djcent NodeIds fil simultneously Ech node join triggers O(log 2 b N) messges LECT-10, S-7 Pstry: Object distribution Consistent hshing O 128 bit circulr id spce nodeids (uniform rndom) objid/key objids/keys (uniform rndom) Invrint: node with numericlly closest nodeid mintins object nodeids LECT-10, S-8 4

5 Pstry: Object insertion/lookup Msg with key X is routed to live node with nodeid closest to X Problem: complete routing tble not fesible O X Route(X) LECT-10, S-9 Pstry Routing LECT-10, S-10

6 Node ID NodeIds re in bse 2 b n b NodId# LECT-10, S-11 Three Concept of Proimity Set of nodes with L /2 smller nd L /2 lrger numericlly closest NodeIds Prefi-bsed routing entries M physiclly closest nodes LECT-10, S-12

7 L nodes in lef set (typicl L= 2 b ) Routing Tble Dimensions log 2b N Rows (ctully log 2 b = 128/b) 2 b columns M neighbors (typicl M= 22 b ) LECT-10, S-13 How to select b? NodeIds re in bse 2 b One row for ech prefi of locl NodeId (Log 2 b N populted on verge) One for ech possible digit in the NodeId representtion 2 b 1 columns b defines the trdeoff: (Log 2 b N) (2 b 1) entries Vs. Log 2 b N routing hops LECT-10, S-14 7

8 8 PEER PEER-TO TO-PEER PEER LECT-10, S-1 Pstry: Prefi Tble (# 1fc Pstry: Prefi Tble (# 1fc) b c d e f b c d e f b c d e f b c d e f log 1 N rows Row 0 Row 1 Row 2 Row 3 PEER PEER-TO TO-PEER PEER LECT-10, S-1 A Hypotheticl Pstry node with ID A Hypotheticl Pstry node with ID Vlues: b = 2, nd l = 8. All numbers re in bse 4. The top row of the routing tble is row zero. The entries re common prefi with net digit - rest of nodeid.

9 Pstry: Lef Sets In lef set ech node mintins IP ddresses of the nodes with the L /2 numericlly closest lrger L /2 L /2 smller numericlly closest nodeids. Routing efficiency/robustness Fult detection (keep-live) Appliction-specific locl coordintion Neighborhood Set The neighborhood set M contins nodeids nd IP ddresses of M nodes those re physiclly closest (or s per some other proimity metric) to the locl node. Its use will be discussed in proimity routing discussion. LECT-10, S-18 9

10 Route Tble of A 1fc Route Tble of B d13d3 Route Tble of C d4213f Find (d41c) 1fc find B (d13d3) d13d3 finds C (d4213f) d4213f finds D(d42b) LECT-10, S-19 Pstry: Routing Route(d41c) d41c d471f1 d47c4 d42b d4213f d13d3 Properties log 1 N steps O(log N) stte 1fc LECT-10, S-20 10

11 Pstry Routing Algorithm (1) Single hop (2) Towrds better prefi-mtch (3) Towrds numericlly closer NodeId D: Messge Key L i : i th closest NodeId in lef set shl(a, B): Length of prefi shred by nodes A nd B R i LECT-10, S-21 j: (j, i) th entry of routing tble Pstry: Routing Procedure if (destintion is within rnge of our lef set) forwrd to numericlly closest member else let l = length of shred prefi let d = vlue of l-th digit in D s ddress if (R l d eists) forwrd to R l d else forwrd to known node tht () shres t lest s long prefi (b) is numericlly closer thn this node LECT-10, S-22 11

12 Routing Performnce: Intuition (1) Single hop, termintion (2) No. of nodes which prefi-mtch the key upto current length reduces by 2 b (3) Low probbility, dds one hop LECT-10, S-23 Pstry Self-Orgniztion LECT-10, S-24 12

13 Pstry: Node Addition d41c d471f1 d47c4 d42b d4213f New node: d41c Route(d41c) d13d3 1fc LECT-10, S-2 Self-orgniztion: Node Arrivl Arriving Node X knows nerby node A. X sks A to route join messge with key = NodeId(X). Messge is routed nd finds Z, whose NodeId is numericlly closest to NodeId(X) All nodes long the pth A, B,, Z send stte tbles to X X initilizes its stte using this informtion. X sends its stte to concerned nodes A Z X LECT-10, S-2 13

14 Stte Initiliztion (1) X borrows A s Neighborhood Set A is geogrphiclly closer to X so it is OK to borrow the set. A B Z X C LECT-10, S-27 Stte Initiliztion (2) Z ID is numericlly closest to X s Therefore: X s lef set is derived from Z s lef set A B Z X C LECT-10, S-28 14

15 Stte Initiliztion (3) X 0 set to A 0 X 1 set to B 1, X 2 set to C 2, Finlly, X trnsmits its lefset, neighborhood set nd routing tble to ech of the nodes in these sets. A B Z X C The totl messge cost is O(log 2b N). The constnt is 32 b. To hndle concurrent rrivl, etensive timestmps re used. LECT-10, S-29 Self-orgniztion: Node Filure (1) Detected when live node tries to contct filed node Updting Lef set get lef set from lrgest inde on the side of the filed node. L - L /2 or L L /2 L /2 bound on filed nodes This set prtilly overlps the present nodes lef set L nd etr nodes not in L. It thus selects the pproprite one. Verifies tht it is live nd dds. LECT-10, S-30 1

16 Self-orgniztion: Node Filure (2) Updting routing tble - To repir R d l, sk ny R i l i d in the sme row for its R d l If the unlikely cse its empty (no live node), with the right prefi then it contcts ny R i l+1 i d. thereby csting wider net. This process is highly unlikely to fil. LECT-10, S-31 Self-orgniztion: Node Filure (3) Updting neighborhood set This is not used in routing generlly. Ask ny live set-members for their neighbors LECT-10, S-32 1

17 Loclity Appliction provides the distnce function Invrint: All routing tble entries refer to node tht is ner the present node, ccording to the proimity metric, mong ll live nodes with n pproprite prefi Invrint mintined on self-orgniztion LECT-10, S-33 Hndling Mlicious Nodes Routing is deterministic Rndomize choice between multiple suitble cndidtes with bis towrds the best one LECT-10, S-34 17

18 Pstry Anlysis LECT-10, S-3 Routing Performnce The epected number of routing steps is log 2b N steps, ssuming ccurte routing tbles nd no recent node filures. Consider the three cses in the routing procedure. If messge is forwrded using the routing tble (lines 8), then the set of nodes whose ids hve longer prefi mtch with the key is reduced by fctor of 2 b in ech step, which mens the destintion is reched in log 2b N steps. If the key is within rnge of the lef set (lines 2 3), then the destintion node is t most one hop wy. The third cse rises when the key is not covered by the lef set (i.e., it is still more thn one hop wy from the destintion), but there is no routing tble entry. Assuming ccurte routing tbles nd no recent node filures, this mens tht node with the pproprite prefi does not eist (lines 11 14). The likelihood of this cse, given the uniform distribution of nodeids, depends on L. Anlysis shows tht with L = 2 b nd L = 22 b, the probbility tht this cse rises during given messge trnsmission is less thn.02 nd 0.00, respectively. When it hppens, no more thn one dditionl routing step results with high probbility. In the event of mny simultneous node filures, the number of routing steps required my be t worst liner in N, while the nodes re updting their stte. This is loose upper bound; in prctice, routing performnce degrdes grdully with the number of recent node filures (shown eperimentlly). Eventul messge delivery is gurnteed unless L /2 nodes with consecutive nodeids fil simultneously. The probbility of such filure cn be mde very low. LECT-10, S-3 18

19 Pstry Etensions: API & Applictions LECT-10, S-37 The Pstry API Opertions eported by Pstry nodeid = pstryinit(credentils,appliction) route(msg,key) Opertions eported by the ppliction working bove Pstry deliver(msg,key) forwrd(msg,key,netid) newlefs(lefset) LECT-10, S-38 19