Page 128 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 3 – Internet of Bio-Nano Things for health applications

ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 3

Without loss of generality, we assume that transition be‑ Table 1 – Percent Shapley Values and resource distribution
tween adjacent nodes is a certainty while there is still a
non‑zero chance of the next node receiving the message, Analyic Results Experimental Results
as depicted in Fig. 2. The simulation parameters are also Node Percent Value Percent Value
1 29.72 35.67 21.09 27
chosen to satisfy this assumption. Therefore, we expect
2 27.80 33.36 28.91 37
no drop to occur if all nodes are present, which allows us
to ind (ℛ) = 0. Hence, only the irst term of (5) re‑ 3 28.18 33.82 30.47 39
mains. 5 14.30 17.16 14.84 19
7 0 0 4.69 6
We know that drops occur only if no other node receives 8 0 0 0 0
the message. Otherwise, one of the receiving nodes,
namely, ∈ ℛ relays the message to the sink. Hence,

3.3 Evolutionary solution
+1
( ) = +1 (1 − ∏(1 − )) , (6) In the previous subsection, we used the simplicity of ge‑

=2 ometry to ind an analytic solution to an otherwise com‑
plicated problem. In this section, we allow the parent or‑
where is the activation rate of and is the probabil‑ ganism to continuously evolve as described in Section 2.3.

ity of a successful transmission between node and + .

Note that, 1−∏(1− ) term gives the probability that no We can see in Fig. 6 that expectedly, the resources allo‑

downstream node including the sink receives the message cated to and are reallocated to the and , even
7
2
8
3
coming from +1 and if +1 = 0 if +1 ∉ +ℛ. Here, we after a few iterations. , which only has the burden of
5
also used the fact that the chosen simulation parameters relaying messages originated at , possesses fewer re‑
6
ensures transmission between adjacent nodes, which ren‑ sources than the and , relaying messages originated
2
3
ders drops possible only when one‑step upstream node, at both of the sensor nodes.
i.e., +1 if ( ) is investigated, is transmitting.
Inspecting Fig. 5, we observe that evolution does not
Activation rates depend on the position of the node. guarantee increased performance after each iteration.
While sensor node activation occurs independent of other This observation coincides with the fact that the evolu‑
nodes, relay nodes depend on the activation of sensor tion of species does not guarantee better offspring at ev‑
nodes. For example, , which only has the burden of ery generation. Furthermore, similar to its counterpart in
5
transmitting messages from , is activated less than − biology, evolution may be in luenced by successful organ‑
6
1
. As a result, s can be solved recursively. isms with suboptimal resource distribution. For exam‑
3

For a given node, we can ind +1 as ple, since the sensors are activated randomly, an organ‑
ism with higher sensor activity would require fewer
4
resources overall than an organism with higher sensor
6
activity.
⎛ 1 ⎞
⎟
⎜
⎟
+1 = ∑ ⎜ ∑ ℛ ⎟ Note that there is also a systematic error in our simulation
⎜
⎜
⎟
> +1, ∈ +ℛ 0 , ∉ℛ (ℛ ) (7) method promoting decreased performance in some iter‑
⎝ +1 ∈ℛ ⎠
ations. We force an in initesimal change in all nodes in

+ ∑ +1, +1 , the organism, i.e., nodes do not die off when they do not

∈ have any resources in an iteration. As a result, nodes hav‑
ing no reservoir either stay at no resources or slightly go

where is the Kronecker Delta, is the sensor activa‑ up, causing the organism to approach a distribution just

tion rate of sensor node , is the sink and is the below the optimal.
0

probability of obtaining the particular ℛ . It is calculated
by Table 1 shows the comparison between analytical and
evolutionary results after 200 iterations. Although they
all start at resources enough for 20 transmissions, as ex‑

7
8
ℛ =∏ ∈ℛ 6− ∏ ∉ℛ (1− 6− ).(8) pected, and lose their resources while other nodes
thrive during the evolutionary process. However, as ex‑
≠
plained above, even though it approaches zero, is not
7
Although seemingly complicated, the irst term of (7) de‑ yet quite zero, wasting some resources, which should be
scribes the node acting as a relay probability by summing reallocated to other nodes. The only dramatic discrep‑
over all nodes, which might be relaying a message to node ancy is being lower than the expectations by the analyt‑
1
. The second term describes the node acting as a sen‑ ical solution. We expect that the discrepancy diminishes

sor node. Note that second term becomes non‑zero only with an increasing iteration count.
when ∈ .

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