Advanced Mathematics and Numerical Modeling of IoT

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Figure 3: Experiment topologies: spare and dense models.

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Figure 4: Experiment results of pure DSME beacon scheduling.

SDBitmap. Since the nodes receive the same SDBitmap and
use the same SD selection algorithm, they choose the same
vacant slot and make an attempt to transmit their own
allocation notification message using carrier sense multiple
access/collision avoidance (CSMA/CA). Even though they
transmit their own messages using CSMA/CA, collisions
still occur, as shown inFigure 5(c), and thus the nodes that
are not acknowledged by node 5 retry sending the message
after waiting for random back-off delay. However, since the
random back-off duration is lengthened more whenever
collision occurs, eventually the present superframe duration
being maintained by node 5 is not completed and some
nodes remain unallocated. That is, when the topology is
complex and the number of nodes increases, the collision
possibility for command messages increases. This results in
SD index allocation failure in some nodes. Furthermore, if
acknowledgement of each command frame is disabled, after
transmitting its notification message, each node is convinced
thatitsselectedSDslotisavailableandtransmitsitsbeacon

ontheallocatedSDslot.Inthatcase,thebeaconframesofthe

nodes might collide with each other, as shown inFigure 5(d).

The major reason for these collisions is the hidden node

problem, in which each node cannot identify the presence

of other nodes. Therefore, even though every node per-

forms CSMA before a transmission, allocation notification

messages of others might not be detected. Furthermore, the

back-off effect with respect to the same beacon frame results

in an increased collision possibility among messages. To

observe the effect of hidden node problems in a realistic

environment, we conducted an experiment on successful data

ratios with respect to varying the number of hidden nodes,

as shown inFigure 6. The result shows that a 100% success

ratio is not guaranteed, even among two hidden nodes, and

performance deteriorates drastically as the number of hidden

nodes increases.

4.3. Distributed Permission Notification.The experiment

results revealed that the DSME beacon scheduling algorithm