A Graph Transformation System Model of Reliable Dynamic Communication Networks for Location Transparent Mobile Agents

1
A Graph Transformation System Model of Reliable
Dynamic Communication Networks for Location
Transparent Mobile Agents

• M. Kurihara (Hokkaido Univ., Japan)
• and
• M. Numazawa (Otaru Univ. Commerce, Japan)

2
Introduction
Mobile agents are software agents that can move
around the network.
Distributed software technologies
Mobile agent technology
research
practice
Future intelligent telecommunication technologies
3
Introduction (2)
mobile agent network
Location transparent
Static reliable
Dynamic sound
4
Structure of this talk

1. Mobile agents location transparency
2. Proxy networks (Reliablity)
3. Graph transformation system(Soundness)

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Mobile Agents

• Software agents that can move around the network

Host 1
Host 2
agent
move
stop
resume
location transparent network
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Location Transparency

• The communications will not fail
• even if agent B has moved to B
• without any notice to A.

move
B
B'
communicating
A
Can communicate?
In the location transparent network, yes.
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Approaches to location transparency(system-level
implementation)

• Logging the agents leave (in the agent server)
  the trail information containing the next
  location
• Brute Force the system searches for the target
  agent by sending a query to every agent server
• Registration the system keeps the locations of
  all agents in a unique directory server, updating
  the information each time an agent makes a move

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Proxy Networks(application-level implementation
of location transparency)
Basic idea simple communication path for
forwarding messages
forward
forward
B'
B
B"
proxy
proxy
target
A

• Problems
• Reliability what if a proxy is abnormal?
• Performance O(the length of the path)

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Reliable and more efficient proxy networks
Normal proxies
Special proxy
Target

• Reliable one abnormal proxy is allowed.
• Performance there is a shorter path.

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Formal Representation(graph-theoretical
definition of proxy networks)
A proxy network is a finite, simple, directed
acyclic graph G(V, E) that satisfy the following
three conditions (in the next slide). (The
vertexes of V are called agents, and the directed
edges of E are called links. By definition, a
simple graph contains no parallel edges, which
connect the same start and end vertexes and an
acyclic graph contains no circuits.)
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Graph-theoretical definition of proxy networks
(Contd.)the three conditions
1. There exists a unique agent (called the
target) with no outgoing links. (The agents
other than the target are called proxies.)
2. There exists a unique proxy (called the
special proxy) with exactly one outgoing link.
The link should be connected to the target.
3. The remaining proxies (called normal proxies)
have exactly two outgoing links.
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Theorem 1 (Reliability)

• For all pairs of distinct proxies v and w, there
  exists a path from v to the target t without
  passing through w.

v
w
t
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Proof of Theorem 1

• Start from v and follow an appropriate path as
  follows.

• At normal proxies, follow a link whose end vertex
  is not w.

normal proxy
w

• Repeat this process while you are at a normal
  proxy.

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Proof of Theorem 1 (Contd.)

• Eventually, you will reach either the special
  proxy or the target.

• If you are at the target, you are done.

• Otherwise, you are at the special proxy.Follow
  the link connected to the target.

t
special proxy
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Graph Transformation Rule
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Graph Transformation System
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The initial network G0
s
t
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Application of graph rewrite rules
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Theorem 2 (Soundness)

• If ,
• then is a proxy network.

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Summary

1. Mobile agents location transparency
2. Proxy networks (Reliablity)
3. Graph transformation system(Soundness)

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Future Work

• Formal theory of more complex mobile agent
  systems

that might allow us (or even agents) to
rigorously (or mechanically) reason about the
dynamic nature of the networks.