Biomedical Engineering Reference
In-Depth Information
A Pheromone Mechanism for
Reduction of System Entropy
more operations when the system entropy is high,
whereas operation frequency gradually decreases
as descriptors are properly reorganized. In par-
ticular, at given time intervals, i.e. every 2,000
seconds, each agent counts up the number of times
that it has evaluated the pick and drop probability
functions, and the number of times that it has
actually performed
pick
and
drop
operations, as
the generated random number is lower than the
value of the probability function. At the end of each
time interval, the agent makes a deposit into its
pheromone base, by adding a pheromone amount
equal to the ratio between the number of “unsuc-
cessful” (not actually performed) operations and
the overall number of operation attempts. At the
end of the i-th time interval, the pheromone level
Фi is computed with formula (4).
A spatial entropy function, based on the well
known Shannon's formula for the calculation of
information content, is defined to evaluate the
effectiveness of the ARMAP protocol. For each
peer
p
, the local entropy
Ep
gives an estimation
of the extent to which the descriptors have already
been mapped within the visibility region centered
in
p
.
Ep
has been normalized, so that its value is
comprised between 0 and 1. As shown in formula
(3), the overall entropy
E
is defined as the average
of the entropy values
Ep
computed at all the Grid
hosts. In (3),
fr(i)
is the fraction of descriptors of
class
Ci
that are located in the visibility region
with respect to the overall number of descriptors
located in the same region.
Φ
=
E
⋅
Φ
+
i
v
i
−
1
i
(4)
1
∑
∑
E
fr
(
i
)
⋅
log
2
fr
(
i
)
p
Grid
i
=
1
..
Nc
(3)
In this formula, ϕi is the fraction of unsuc-
cessful operations performed in the last time
interval. An evaporation mechanism is used to
give a higher weigh to recent behavior of the
agent, and the evaporation rate
Ev
is set to 0.9.
With these settings, the value of Фi is always
comprised between 0 and 10. As soon as the
pheromone level exceeds a pheromone threshold
Tf
(whose value is also in the range [0,10]), the
agent realizes that the frequency of
pick
and
drop
operations has remarkably reduced, so it switches
its protocol mode from
copy
to
move
. The value
of
Tf
can be used to tune the number of agents
that work in
copy
mode and are therefore able to
create new descriptor replicas, as discussed in
the next section.
E
=
,
E
=
p
log
Nc
Np
2
In (Forestiero et al., 2005) it was shown that the
overall spatial entropy can be minimized if each
agent exploits both the ARMAP modes, i.e.
copy
and
move
. In the first period of its life, each agent
copies
the descriptors that it picks from a Grid
host, but when it realizes from its own activeness
that the mapping process is at an advanced stage,
it begins simply to
move
descriptors from one host
to another, without creating new replicas.
In fact, agents cannot always operate under the
copy
mode, since eventually every host would be
assigned a very large number of descriptors of all
classes, thus weakening the efficacy of descriptor
mapping. The protocol is effective only if each
agent, after replicating a number of descriptors,
switches from
copy
to
move
. A self-organization
approach based on ants' pheromone mechanism
enables an agent to perform this mode switch only
on the basis of local information. This approach
is inspired by the observation that agents perform
PERFORMANCE EvALUATION
The performance of the ARMAP protocol has
been evaluated with an event-based simulator
written in Java, which will be described in the
chapter section related to the SO-Grid Portal.
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