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Fig. 1. Comparison of the cost (left) and comparison of the number of messages in function of
the agent update frequency (right), with p r =0 . 6 and n a = 100
To have the total cost according to the number of messages criteria we have to sum
these costs. Let Cost M = n m (1 + p r n a )+ freq a n a be the total environment cost and
Cost M = n m n a be the total agents cost.
To compare these two costs, we study the sign of the subtraction of the two costs
Cost M = Cost M
Cost M in order to find when the environment mediation is more
costly than the local computation in function of the number of messages and of the
frequency of the update process. The resulting formula is Cost M = n m (1 + n a ( p r
1)) + freq a n a . Figure 1 (left) gives the plan corresponding to this function in the
three dimensional space (message, agent update, cost) if the number of agents ( n a )
and the average proportion of receiver ( p r ) are respectively fixed to 100 and 0.6. These
assessment parameters are unfavourable to the mediation by the environment: 1) the
cost of the update process is not taken into account when the context is computed by
the agents; 2) the agents are interested by more than half the messages. Nevertheless
we can see that there are few cases in which the use of the environment is more costly
than the local matching according to the number of messages criteria.
The function Cost M ( n m ,freq a )=0 enables to find the number of messages ded-
icated to the interaction in the MAS ( m ) that have to be mediated by the environment
to compensate the cost of the update process ( freq a ). The relation between these two
parameters is n m =
freq a ,thevalueof n m is therefore
inversely proportional to the proportion of the agents interested in the messages. Figure
1 (right) illustrates this proposition. The environment area represents the cases where it
is better to use the environment than to mediate the messages in function of the number
of messages. For instance, with freq a =2 , if there is more than 5 messages related
to the interaction in the MAS, then it is better to use the environment to mediate the
communication even if that means that there are freq a n a = 200 messages related to
the update process.
This study has been done in the worst case for the environment because the agents are
not taken into account to evaluate the interaction context ( f c ). If it were the case, there
( n a / (1 + n a (1
p r )))
 
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