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CS 525
Advanced Distributed
Systems
Spring 2014
Indranil Gupta (Indy)
Lecture 5
Peer to Peer Systems II
February 4, 2014
1
All Slides © IG
Two types of P2P Systems
Systems used widely in practice but with
no provable properties
• Non-academic P2P systems
e.g., Gnutella, Napster, Grokster,
BitTorrent (previous lecture)
Systems with provable properties
but with less wider usage
• Academic P2P systems
e.g., Chord, Pastry,
Kelips (this lecture)
2
DHT=Distributed Hash Table
• A hash table allows you to insert, lookup and
delete objects with keys
• A distributed hash table allows you to do the same
in a distributed setting (objects=files)
• Performance Concerns:
–
–
–
–
Load balancing
Fault-tolerance
Efficiency of lookups and inserts
Locality
• Napster, Gnutella, FastTrack are all DHTs (sort
of)
• So is Chord, a structured peer to peer system that
we study next
3
Comparative Performance
Memory
Napster
Gnutella
Lookup
Latency
O(1)
O(1)
(O(N)@server)
O(N)
O(N)
#Messages
for a lookup
O(1)
O(N)
4
Comparative Performance
Memory
Napster
Lookup
Latency
O(1)
Gnutella
O(1)
(O(N)@server)
O(N)
O(N)
Chord
O(log(N))
#Messages
for a lookup
O(1)
O(N)
O(log(N)) O(log(N))
5
Chord
• Developers: I. Stoica, D. Karger, F. Kaashoek, H.
Balakrishnan, R. Morris, Berkeley and MIT
• Intelligent choice of neighbors to reduce latency and
message cost of routing (lookups/inserts)
• Uses Consistent Hashing on node’s (peer’s) address
–
–
–
–
–
SHA-1(ip_address,port) 160 bit string
Truncated to m bits
Called peer id (number between 0 and 2m  1 )
Not unique but id conflicts very unlikely
Can then map peers to one of 2m logical points on a circle
6
Ring of peers
Say m=7
6 nodes
0
N112
N16
N96
N32
N80
N45
7
Peer pointers (1): successors
Say m=7
0
N112
N16
N96
N32
N80
N45
(similarly predecessors)8
Peer pointers (2): finger tables
Finger Table at N80
i
0
1
2
3
4
5
6
ft[i]
96
96
96
96
96
112
16
Say m=7
0
N112
80 + 25
N16
80 + 26
N96
80 + 24
N32
80 + 23
80 + 22
80 + 21
80 + 20
N80
N45
ith entry at peer with id n is first peer with id >= n  2i (mod 2m )
9
What about the files?
• Filenames also mapped using same consistent
hash function
– SHA-1(filename) 160 bit string (key)
– File is stored at first peer with id greater than its key
(mod 2 m )
• File cnn.com/index.html that maps to key K42 is stored
at first peer with id greater than 42
– Note that we are considering a different file-sharing
application here : cooperative web caching
– The same discussion applies to any other file sharing
application, including that of mp3 files.
10
Mapping Files
Say m=7
0
N112
N16
N96
N32
N80
N45
File with key K42
stored here11
Search
Say m=7
0
N112
N16
N96
N32
Who has cnn.com/index.html?
(hashes to K42)
N80
N45
File cnn.com/index.html12 with
key K42 stored here
Search
At node n, send query for key k to largest successor/finger entry <= k
if none exist, send query to successor(n)
Say m=7
0
N112
N16
N96
N32
Who has cnn.com/index.html?
(hashes to K42)
N80
N45
File cnn.com/index.html13 with
key K42 stored here
Search
At node n, send query for key k to largest successor/finger entry <= k
if none exist, send query to successor(n)
Say m=7
0
N112
N16
All “arrows” are RPCs
N96
N32
Who has cnn.com/index.html?
(hashes to K42)
N80
N45
File cnn.com/index.html14 with
key K42 stored here
Here
Analysis
Next hop
Search takes O(log(N)) time
Key
Proof
– (intuition): at each step, distance between query and peerwith-file reduces by a factor of at least 2 (why?)
Takes at most m steps: 2m is at most a constant
multiplicative factor above N, lookup is O(log(N))
– (intuition): after log(N) forwardings, distance to key is at
most 2 m / N (why?)
Number of node identifiers in a range of 2 m / N
is O(log(N)) with high probability (why? SHA-1!)
So using successors in that range will be ok
15
Analysis (contd.)
• O(log(N)) search time holds for file insertions too
(in general for routing to any key)
– “Routing” can thus be used as a building block for
• All operations: insert, lookup, delete
• O(log(N)) time true only if finger and successor
entries correct
• When might these entries be wrong?
– When you have failures
16
Search under peer failures
Lookup fails
(N16 does not know N45)
Say m=7
0
N16
N112
X
N96
Who has cnn.com/index.html?
(hashes to K42)
N80
X
N32
X
N45
File cnn.com/index.html17 with
key K42 stored here
Search under peer failures
One solution: maintain r multiple successor entries
In case of failure, use successor entries
Say m=7
0
N112
N16
N96
X
N32
Who has cnn.com/index.html?
(hashes to K42)
N80
N45
File cnn.com/index.html18 with
key K42 stored here
Search under peer failures
• Choosing r=2log(N) suffices to maintain
lookup correctness w.h.p.(i.e., ring connected)
– Say 50% of nodes fail
– Pr(at given node, at least one successor alive)=
1 2 log N
1
1 ( )
 1 2
2
N
– Pr(above is true at all alive nodes)=
1

1 N /2
(1  2 )  e 2 N  1
N
19
Search under peer failures (2)
Lookup fails
(N45 is dead)
Say m=7
0
N16
N112
N96
Who has cnn.com/index.html?
(hashes to K42)
N80
N32
X
X
N45
File cnn.com/index.html20 with
key K42 stored here
Search under peer failures (2)
One solution: replicate file/key at r successors and
predecessors
Say m=7
0
N16
N112
N96
N32
Who has cnn.com/index.html?
(hashes to K42)
K42 replicated
N80
X
N45
K42 replicated
File cnn.com/index.html21 with
key K42 stored here
Need to deal with dynamic
changes
 Peers fail
• New peers join
• Peers leave
– P2P systems have a high rate of churn (node join, leave and
failure)
•
•
•
•
25% per hour in Overnet (eDonkey)
100% per hour in Gnutella
Lower in managed clusters, e.g., CSIL
Common feature in all distributed systems, including wide-area (e.g.,
PlanetLab), clusters (e.g., Emulab), clouds (e.g., Cirrus), etc.
So, all the time, need to:
 Need to update successors and fingers, and copy keys
22
New peers joining
Introducer directs N40 to N45 (and N32)
N32 updates successor to N40
N40 initializes successor to N45, and inits fingers from it
N40 periodically talks to neighbors to update finger table
Say m=7
0
Stabilization
N16
N112
Protocol
(followed by
all nodes)
N96
N32
N40
N80
N45
23
New peers joining (2)
N40 may need to copy some files/keys from N45
(files with fileid between 32 and 40)
Say m=7
0
N112
N16
N96
N32
N40
N80
N45
K34,K3824
New peers joining (3)
• A new peer affects O(log(N)) other finger entries
in the system, on average [Why?]
• Number of messages per peer join=
O(log(N)*log(N))
• Similar set of operations for dealing with peers
leaving
– For dealing with failures, also need failure detectors
(we’ll see these later in the course!)
25
Experimental Results
• Sigcomm 01 paper had results from
simulation of a C++ prototype
• SOSP 01 paper had more results from a 12node Internet testbed deployment
• We’ll touch briefly on the first set
• 10000 peer system
26
Load Balancing
Large
variance
Solution: Each real node pretends to be r multiple virtual nodes
smaller load variation, lookup cost is O(log(N*r)= O(log(N)+log(r))
27
Average Messages per Lookup
Lookups
log, as expected
Number of Nodes
28
Stabilization Protocol
• Concurrent peer joins, leaves, failures might cause
loopiness of pointers, and failure of lookups
– Chord peers periodically run a stabilization algorithm that
checks and updates pointers and keys
– Ensures non-loopiness of fingers, eventual success of
lookups and O(log(N)) lookups w.h.p.
– [TechReport on Chord webpage] defines weak and strong
notions of stability
– Each stabilization round at a peer involves a constant
number of messages
– Strong stability takes O( N 2 ) stabilization rounds (!)
29
Churn
• When nodes are constantly joining, leaving, failing
– Significant effect to consider: traces from the Overnet system
show hourly peer turnover rates (churn) could be 25-100% of
total number of nodes in system
– Leads to excessive (unnecessary) key copying (remember that
keys are replicated)
– Stabilization algorithm may need to consume more bandwidth
to keep up
– Main issue is that files are replicated, while it might be
sufficient to replicate only meta information about files
– Alternatives
• Introduce a level of indirection (any p2p system)
• Replicate metadata more, e.g., Kelips (later in this lecture)
30
Fault-tolerance
500 nodes (avg. path len=5)
Stabilization runs every 30 s
1 joins&fails every 10 s
(3 fails/stabilization round)
=> 6% lookups fail
Numbers look fine here, but
does stabilization scale with N?
What about concurrent joins
&
31
leaves?
Pastry – another DHT
• From Microsoft Research
• Assigns ids to nodes, just like Chord (think
of a ring)
• Leaf Set - Each node knows its successor(s)
and predecessor(s)
• Routing tables based prefix matching
– But select the closest (in network RTT) peers
among those that have the same prefix
• Routing is thus based on prefix matching,
and is thus log(N)
– And hops are short (in the underlying network)
32
33
Wrap-up Notes
• Memory: O(log(N)) successor pointer, m finger/routing
entries
• Indirection: store a pointer instead of the actual file
• Do not handle partitions (can you suggest a possible
solution?)
34
Summary of Chord and Pastry
• Chord and Pastry protocols
–
–
–
–
More structured than Gnutella
Black box lookup algorithms
Churn handling can get complex
O(log(N)) memory and lookup cost
• Can we do better?
35
Kelips – 1 hop Lookup
• K “affinity groups”
• PennyLane.mp3 hashes to k-1
• Everyone in this group stores
<PennyLane.mp3, who-has-file>
– K~√N
• Each node hashed to a group
• Node’s neighbors
15
76
– (Almost) all other nodes in its
own affinity group
– One contact node per foreign
affinity group
• File can be stored at any (few)
node(s)
• Each filename hashed to a
group
– All nodes in the group replicate
<filename, file location>
– Affinity group does not store files
• Lookup = 1 hop (or a few)
• Memory cost O(√ N) low
•
1.93 MB for 100K nodes, 10M files
18
160
129
167
30
…
Affinity
Group # 0 # 1
# k-1
36
Summary – P2P
• Range of tradeoffs available
– Memory vs. lookup cost vs. background
bandwidth (to keep neighbors fresh)
37
Announcements
• No office hours today (talk to me now)
• Next week Thu: Student-led presentations
start
– Please Read instructions on the website!
• Next week Thu: Reviews start
– Please Read instructions on the website!
38
Backup Slides
39
Wrap-up Notes (3)
• Virtual Nodes good for load balancing, but
– Effect on peer traffic?
– Result of churn?
• Current status of project:
–
–
–
–
File systems (CFS,Ivy) built on top of Chord
DNS lookup service built on top of Chord
Internet Indirection Infrastructure (I3) project at UCB
Spawned research on many interesting issues about p2p
systems
http://www.pdos.lcs.mit.edu/chord/
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