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)

Introduction

Distributed software technologies

Mobile agent technology

Future intelligent telecommunication technologies

research practice

Mobile agents are software agents that can move around the

network.

Introduction (2)

mobile agent network

Location transparent

Static: reliable

Dynamic: sound

Structure of this talk

1.Mobile agents & location transparency

2.Proxy networks (Reliablity)

3.Graph transformation system(Soundness)

Mobile Agents

Software agents that can move around the network

agent

stop resumemove

Host 1 Host 2

location transparent network

Location Transparency

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

A

B B'communicatingmove

Can communicate?

In the location transparent network, yes.

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

Proxy Networks(application-level implementation of

location transparency)

Basic idea: simple communication path for forwarding messages

A

B'B B"

proxy

proxy

target

Problems

Reliability: what if a proxy is abnormal?

Performance: O(the length of the path)

forward forward

Reliable and more efficient proxy networks

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

Target

Special proxy

Normal proxies

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.)

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.

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

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.

Repeat this process while you are at a normal proxy.

normal proxyw

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.

special proxy t

Graph Transformation Rule

utts usutEuVEV ,, )}),(),,{(},{(),(

s t s t u

(a) Move to a new host

s t s t u

(a) Move to a new place

s t

(b) Move to the special proxy

s t

u s t

(c) Move to a normal proxy

u s t

u v s t u v s t

(d) Bypass

Graph Transformation System

The initial network G0

)},{(},,{

),(

00

,000

tsEtsV

EVG ts

s t

Application of graph rewrite rules

nGGGG 210

nGG *0

Theorem 2 (Soundness)

If , then is a proxy network.

GG *0

G

Summary

1.Mobile agents

& location transparency2.Proxy networks

(Reliablity)3.Graph transformation system

(Soundness)

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.