Vassilios V. Dimakopoulos and

1
A Peer-to-Peer Approach to Resource Discovery in
Multi-Agent Systems

• Vassilios V. Dimakopoulos and
• Evaggelia Pitoura
• Distributed Data Management Lab
• Dept. of Computer Science,
• Univ. of Ioannina, Greece
• http//softsys.cs.uoi.gr

2
Multi-agent systems (MAS)

• Cooperating agents Each agent offers some
  resources (computation, data, etc)
• To fulfill its goals, an agent requires resources
  provided by other agents
• Closed MAS each agent knows all others and what
  they offer
• vs Open MAS

3
Open MAS

• How does an agent get information about other
  agents/resources?
• Common approach directory-based (e.g. middle
  agent)
• Disadvantage many agents and resources make the
  directory a performance/ reliability bottleneck
• Proposal consider a p2p approach

4
P2P agents

• In P2P,
• Peers (agents) offer resources
• Similar Problem How to locate the peer(s) that
  offer a particular resource
• Structured based on the name or content of the
  resource place it at the appropriate node (Chord,
  CAN etc) vs
• Unstructured no assumption about the location
  of resources (Napster, Gnutella)
• We apply fully decentralized unstructured p2p
  approaches

5
Overview

• Each agent v has a cache with k entries,
  containing information for k resources
• i.e. for each of the k resources, the cache
  holds the contact information for an agent that
  provides it
• If an agent v has contact information for agent
  u then v knows u.
• Network of caches if v knows u there is a link
  from v to u

6
Abstract model
Network of caches (k 2)
Note The network (graph) may be disconnected
7
Search algorithms
Use the distributed network of caches to locate
an agent offering a particular resource

• Flooding-based
• Agent A looks for resource x
• A checks its local cache, if x not in cache, A
  contacts its neighbors,
• Each neighbor check its cache for x, if not
  found contacts its neighbors and so on,
• A number of variations based on contacting
  subsets of the neighbors

8
Results, contributions
Use the distributed network of caches to locate
an agent offering a particular resource

• Algorithms for searching
• Flooding (as in e.g., Gnutella),
• Teeming (randomized flooding),
• Random paths
• Performance Analysis
• Analytical model validated by simulation
• Updates
• Flooding-based propagation,
• Inverted cache

9
Results, contributions
Related work BauerWang92 show that DFS of the
cache network, performs better than flooding for
particular topologies Shehory00 Lattice-like
cache network (each agent knows about exactly
four other agents
10
Talk outline

• Brief presentation of the analytical model
• Performance results related to the search
  procedures
• Updates
• Conclusions and Future Work

11
Performance metrics

• t maximum allowed steps (TTL)
• Qt probability of successful search
• high means other directory mechanisms used
  rarely
• St average steps to find the resource
• Mt average message transmissions
• as few as possible, for speed and small traffic

Note we assume that agents are queried in
parallel (all neighbors are contacted in one
step) but the system is asynchronous
12
Performance model

• N nodes, R resources, k cache size
• Steady state all caches full

• Two cases
• The content of the cache is assumed to be
  completely random
• Hot spots (resources requested frequently)
  appear in a large number of caches
• In a fraction h of all caches (h 1)

13
Performance analysis, preliminaries
PC (1) Probability of finding x in any given
cache Random Requests In Nk total entries, each
resource appears Nk/R times avg., or in a portion
of (Nk/R)/N k/R of the caches. Thus, the
probability of locating a specific resource in a
specific cache is PC(1) k/R PC(1) 1 aR,
with aR 1 k/R Hot Spots Each hot spot
appears in a fraction h of all caches, let rh
portion of hotspots (1-rh)R cold-spots For
hotspots, PC(1) h, PC(1) 1 aH, with aH 1
h For coldspots, PC(1) 1 aC, with aC
14
Performance analysis, preliminaries

• For j caches,
• PC(j) 1 (1 PC(1)) j 1 a j
• If si is the prob. of locating the resource in
  exactly the i-th step, then
• Given the resource is found, the average number
  of steps is

15
Flooding

• Contacts all neigbors (entries in cache)
• Complete k-ary tree
• Exponential messages, relatively small steps

A1
A2
A4
A3
A5
A6
A3
16
Performance of flooding

• In each level of the tree ki caches are queried
• Approximation all these caches are distinct
  (does not introduce significant error)
• Locating resource at exactly step i

17
Performance of flooding, cont.

• Obtained
• Messages if not in roots cache, we get k
  transmissions plus all messages within the k
  subtrees

k
m(t 1)
18
Performance of flooding, cont.

• For each of the k subtrees,
• Solving recursion gives
• Exponential messages, as expected

19
Performance of flooding, cont.
20
Performance of flooding, cont.
21
Performance of flooding, cont.
22
Teeming (randomized flooding)
A1
A2
A4
A3
A6
A3

• Intermediate nodes ask a random subset of their
  neighbors A node asks each neighbor with
  probability f, kf neighbors asked on average
• f 1 is flooding

23
Performance of teeming

• Similarly, obtained
• Exponential slower than flooding, based on f

24
Random paths
A1
p 2 paths

• Inquiring node asks p neighbors
• Intermediate nodes ask 1 neighbor (similar to
  concurrent DFS)
• Fewer messages, more steps

A2
A4
A5
A3
25
Performance of random paths

• Obtained, for p paths

26
Comparison of algorithms, 1 Q
Teeming with f 1/sqrt(k)
Random resource
27
Comparison of algorithms, S
Random resource
28
Comparison of algorithms, M
Random resource
29
Comparison of algorithms, 1 - Q
Hotspots
30
Comparison of algorithms, S
Hotspots
31
Comparison of algorithms, M
Hotspots
32
Comparison, discussion

• Flooding and teeming depend on k, random paths on
  the ratio k/R
• Flooding and teeming yield higher probabilities
  of discovering the resource, and with fewer
  steps However the number of messages, esp. for
  flooding is excessive
• Teeming can balance performance with appropriate
  selection of f
• Few paths are bad for 4 paths probability and
  steps is more than acceptable, messages is
  minimal
• Cache vary efficient for hotspots
• Simple optimizations cycles, periodically
  contact the inquiring agent (else search
  continues even if the resource is found)

33
Simulation

• Simulators for all algorithms constructed
• 200 to 500 resources
• 1000 to 5000 agents/caches
• Initially all caches filled randomly
• Search for a uniformly random resource, 1000
  repetitions
• Analysis confirmed with negligible error (less
  than 0.5 in most cases)

34
Simulation theory
Random resources
35
Simulation theory, cont.
Random resources
36
Simulation theory, cont.
Random resources
37
Simulation theory, cont.
Random resources
38
Simulation theory, cont.
Hotspots
39
Updates

• Type of updates
• (1) Agent offers a new resource or cease to offer
  a resource
• (2) The contact information of an agent changes
  (e.g., it moves)
• Discuss case 2 above decentralized solution

40
Updates, inverted cache

• Each agent maintains which agent know about it
• Use the inverted cache to inform other agents

41
Updates, flooding

• When an agent moves, it informs the agent in its
  cache and so on
• Neighbor relationship is not symmetric, A knows
  B, B may not know A

42
Summary

• A new scheme for open MAS a distributed cache
  network
• Decentralized unstructured p2p resource discovery
• Algorithms proposed classical flooding, teeming
  (randomized flooding), random paths
• Performance study of searching analytical models
  for probability of locating, average steps,
  average messages
• Cache updates

43
Future Work

• Prototype implementation (In progress)
• implementation in the Aglets platform completed
• experimental evaluations under way
• Updates/Mobility (In progress)
• Performance evaluation
• Caches evolve over time
• Cache replacement issues
• Extend performance evaluation
• Random/Hot spots -gt Small world network of
  caches

44
A Peer-to-Peer Approach to Resource Discovery in
Multi-Agent Systems

• QUESTIONS?