P. J. IULIANO, L. MARRONE
Copyright © 2013 SciRes. CN
Table 1. Connectivity P/Shannon Entropy Correlation by
Groups.
Sup. N. Grp. 1 C. Pearson
Grp. 1 N. Grp 2 C. Pearson
Grp 2
50 m × 50 m - - [2, 100] −0.993
100 m × 100 m [2, 11] 0.975 [12, 100] −0.965
150 m × 150 m [2, 28] 0.958 [29, 100] −0.971
2) 2
g shows that the relationship between p and s is
inverse (negative) dependence, i.e., for large value s p the
values of s will be small.
Based on these results, we can conclude the following
for MANETs that operate on surfaces of:
1) 50 m × 50 m: uncertainty will decrease as the
amount of network nodes increases, due to greater Con-
nectivity Probability.
2) 100 m × 100 m: first, if the amount of nodes varies
between two and eleven, starting from two and taking
eleven as a maximum, as more nodes are added to the
network, uncertainty and probability will increase together.
Once the twelve node threshold is reached, uncertainty
will begin to decrease, while probability increases.
3) 1 50 m × 150 m: this case is similar to the last, with
the exception that node intervals are displaced—when
the amount of nodes varies between two and twenty-
eight, uncertainty and probability will increase as nodes
increase, and if the amount varies between [29, 100],
uncertainty will decrease while probability still incre as e s .
It is clear that the most interesting results are those
registered in
for all surfaces, as it is there that com-
putations will have the greatest probability to succeed
with less uncertainty. However, the question remains as
to what amount of nodes and Connectivity Probability
will bring a success certainty high enough to begin com-
putation. One valid criterion is to detect value
where Connectivity Probability and uncertainty are equal
or close enough and operate on the uncertainty interval
between
. Values
for the performed simulations
are detailed in Table 2. Therefore, fo r surfaces of 50 m ×
50 m, 100 m × 100 m and 150 m × 150 m, distributed
calculations will begin when 2, 14 and 34 nodes have
been reached, respectively.
4. Conclusion
The development of this work duly evidenced and do-
cumented that the uncertainty existing at the beginning of
a distributed computation on a MANET will depend di-
rectly on the amount of nodes participating in it and on
the surface involved. This statement is based on the re-
sults obtained from the simulations detailed in this doc-
ument, which allowed us to conclude that uncertainty be-
gins to decrease once node density has reached a certain
threshold, and that this threshold takes different values
Table 2. Values of vi.
Sup. Nodes Connectivity Probability Value vi
50 m × 50 m 2 0.779 0.760
100 m × 100 m 14 0.738 0.828
150 m × 150 m 34 0.824 0.671
for differe nt su rfa ce s.
Works oriented towards correctly identifying the amount
of uncertainty existing at the time the results of a distri-
buted calculation on ad-hoc mobile networks are collected
bring the potential benefit that they can be used to de-
velop more intelligent workload distribution strategies
that take into accoun t the amount of uncertainty they w ill
have to deal with, which will necessarily results in more
efficient computations. In this sense and based on the
latest studies oriented towards providing more certain
mechanisms as to the conservation of power in the de-
vices that comprise a MANET [8] or on equally relevant
studies focusing on achieving the greatest cooperation
possible between the nodes of an ad hoc mobile network
[9], thus mitigating their intrinsic egotism, the results of
having an uncertainty measure that would either indicate
that there is no certainty to achieve calculation comple-
tion or ensure its success will be twofold. In the first of
the aforementioned two fields of study, preventing work-
load distribution in situations where calculation concr e-
tion is not ensured will have a direct repercussion in the
conservation of power in devices, which will result in
longer operational periods which unable to identify the
aforementioned scen arios. The secon d research field seeks
to maximize cooperation among the nodes. With this in
mind, in scenarios where completion certainty is medium
or low, one possible distribution strategy oriented toward
collaboration could be assigning workload only to the
most collaborative nodes, to avoid the risk of assigning
load to un-collaborative nodes, which, in the event of
result collection failure, may take a more selfish or con-
servationist attitude tow ard their resources (such as pow-
er) and leave the MANET. In a scheme of mobile distri-
buted calculation where all participants offer their colla-
boration to find the answer to a common interest problem,
such as the SETI@Home program [10], measuring un-
certainty can be used as a function to grant credit to col-
laborators—when a participant is notified that there is a
medium to high level of uncertainty regarding computa-
tion success and they decide to participate nonetheless,
more credits can be granted than in scenarios where total
certainty of success exists. If more credits mean more
benefits for the participant in some way, for example,
publicity of the most committed participant in the calcu-
lation environment, then we would have a psychological
mechanism of positive reinforcement that would promote
node collaboration, which would enable a network con-