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-