![](bg6.png)
Figure 5: Entropy samples prediction with RLS for K=1,
β=0.1, 0.3, 0.5, 0.7 (number of samples on the x-axis and
entropy values on the y-axis).
In order to select the proper value of K, we take
into account the Partial Auto-Correlation Function
(PACF), defined as the autocorrelation between Et(T )
and Et(T − K) with the linear dependence of Et(T )
on Et(T − 1) through Et(T − K + 1) removed (Box
et al., 2015).
After the analysis of different sets of entropy sam-
ples, we can state that the PACF correlogram, like the
one depicted in Figure 4b helps to select the best val-
ues of K, for which the prediction error is minimised.
In our examples, several largest spikes are obtained:
that is, for each combination of simulation parame-
ters (T , avg speed, l, mobility model and other) a set
K
∗
= {K
1
,K
2
,...,K
r
} of lag values can be obtained,
for which the PACF function has a local maximum.
Additional benefit can be seen that regardless of the
chosen combination of simulation parameters, each
correlogram has a spike for K = 1, that is the entropy
process can always be considered also as a K=1-order
Auto Regressive Process (ARP(1)).
In the next step, we chose K = 1 to confirm that
the RLS algorithm can predict the entropy trend with
an acceptable error. Figure 5 shows the results ob-
tained by considering 120 samples of Et(n
T
k
), with
T = 5s, l = 30m, avg speed = 13.9 m/s. It can be
seen how, in general, the RLS can evaluate future
samples with high accuracy.
5 CONCLUSION AND FUTURE
WORKS
In this paper, we presented an in-depth analysis of
the entropy concept related to mobility in MANETs.
In particular, we underlined the key factors that in-
fluence its trend during host mobility inside a geo-
graphical region. A new way of approaching mo-
bility entropy evaluation has been presented, and a
closed form has been obtained for the description of
its average values, in function of several system pa-
rameters. Also, we provided instructions to predict
future entropy values, obtaining beneficial results re-
garding prediction error. Future works will regard the
application of this analysis to forwarding operations
in MANETs, such as packet routing, novel metrics
definition, system stability analysis and predictive re-
laying, and considering the possibility of using novel
routing approaches based on social networks such as
in (Socievole et al., 2013; Socievole et al., 2014).
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