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N E
A
tested entities
(1) C 1
n a ∗ C 1
n m =1
(2) n a ∗ C 2
n a ∗ C 2
all the agents in E and each agent individually (A)
(3) p 2 ∗ n a ∗ C 3
p 2 ∗ n a ∗ C 3
p 2 : percentage of agents that have the requested state
(4) n c ∗ C 4
( p 2 ∗p 3 ∗n a ) ∗n c ∗C 4 n c : number of entities that are tested in (4). p 3 :
percentage of agents that are related to the message.
(5) p 4 ∗ n c ∗ C 5
( p 2 ∗p 3 ∗n a ) ( p 4
n c ) ∗ C 5
p 4 : percentage of entities related to the context (4)
(6) ( p 2 ∗ p 3 ∗ n a )
( p 5 ∗p 4 ∗n c )
C 5
( p 2 ∗p 3 ∗n a ) ( p 5
p 4 ∗ n c ) ∗ C 5
p 5 : percentage of entities validating (5)
Moreover, the environment and the agents need the same information to process the
filters and the result has to be balanced by the cost of the access to this information.
Evaluation of the Number of Messages. If the exchange of information is done via
messages, there are two types of messages to take into account: 1) the messages related
to the interaction in the MAS such as the request messages in our example f e ;2)the
messages related to the update process.
Firstly we evaluate the number of messages that are the result of the interaction in
the MAS. Let n m be the number of messages sent by the agents, let p r be the aver-
age percentage of agents that have to receive the messages. If the matching process is
executed by the environment then each message is sent to the environment, and the en-
vironment transmits it to the p r
n a receivers. The total number of messages is therefore
n m (1 + p r
n a ) . If the matching process is executed by the agents, then each message
is sent to all the agents which locally execute the matching process. The total number
of messages is therefore n m
n a . Except if p r is close to 1 which means that the mes-
sage is related to all the agents, the environment mediation is less costly. The more the
selection is important, the more the mediation by the environment is beneficial.
Secondly we evaluate the number of messages that are the result of the update pro-
cess of the MAS. To simplify, we consider only the update process of the descriptions
of the agents and not of the context, although the principle is the same. In our example,
it implies that the state of the victims is not updated (or that its cost is the same if it is
computed by the environment or by the agents). When an agent is updated all its proper-
ties are updated in the environment. Remember that the filter example does not contain
tests on the state of the agents to compute the context ( f c ). Hence, the computation by
the agents does not imply additional costs because we suppose the agents do not need
to access updated information about the other agents, which is an underestimation of
the cost of the local agent solution.
When the communication is mediated by the environment, the agents update their
descriptions by putting in the environment new descriptions that replace the old ones.
This action is associated to the sending of a message. One agent can make between 0
and n updates during a time period. Let freq a be the average frequency of the descrip-
tion update during a time period. There is therefore freq a
n a update messages if the
interaction is mediated by the environment during the reference time period.
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