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Ferber and Muller develop a consistent formal theory, which is
sucient for dealing with complex interactions between agents and
the environment. A drawback of their original theory is that it
'is limited to synchronous descriptions of the multiagent systems
evolutions' [33]. This is due to the cause that Ferber and Muller
assume that a multi-agent system may be described by repetitive
execution of a
cycle
-function. Each cycle consists of collecting the
influences produced by the agents as well as the dynamics of the
environment and computing the reactions. As pointed out by Ferber
and Muller [33] themselves as well as by Weyns and Holvoet [143],
acting in such a
lock step
manner does not match the autonomous
behavior of agents and limits scalability.
Action model of Weyns and Holvoet
Based on the work of Ferber and Muller, Weyns and Holvoet propose
an alternative to the centralized synchronization model in the form
of an action model based on regional synchronization. With respect
to the approach of Ferber and Muller they point out that 'all agents
of the multi-agent system act at one global pace, i.e., the agents are
globally synchronized' [144]. There are two major diculties with
this: Firstly, global synchronization implies a centralized control of
the multi-agent system (respectively simulation), which is in general
a very undesirable requirement (as it is usually in contrast to the
nature of multi-agent systems, which are often distributed and without
centralized control). Secondly, since the influences of all agents are
treated as if they happen at the same point in time, the total number
of possible interactions is of the order of
O
(
n
2
)foramodelwith
n
agents and thus limits scalability.
The basic idea of Weyns and Holvoet to overcome these diculties
is to constrain simultaneous actions to groups of agents which are only
regionally synchronized. Different groups of agents can therefore act
asynchronously. Figure 2.3 compares the approaches of Ferber and
Muller (F-M) and Weyns and Holvoet (W-H). In the F-M model the
reaction is computed as soon as all influences are collected. This view
