## 4 Simulation Results
### Hidden Node Problem in IEEE 802.15.4  
In this simulation case, we examine the hidden node problem with IEEE 802.15.4 in low duty cycle multihop networks. As the hidden node problem occurs due to contention based channel access,  
Figure 8: Beacon losses due to packet errors. TUTWSN is presented with synchronization loss after 3 and 4 consecutive beacon misses. ZigBee uses the default 4. Figure 9: Synchronization losses due to several consecutive beacon misses. reservation based protocols, such as TUTWSN, do not suffer from it. Figure 10 shows the goodput with different number of traffic sources. The offered load in the figure is the aggregate offered traffic from all nodes. Thus, the traffic generation interval on a source node is adjusted proportionally to the total number of source nodes, therefore resulting into a comparable aggregate offered load on each case. When the offered load is small, the goodput difference between different amount of source nodes is negligible. As the offered load is increased, the use of several source nodes decreases goodput significantly. Congestion is not an issue, because the network capacity exceeds the offered loads. It is possible that two nodes randomize the same backoff slot, which causes a collision despite of the CCA procedure but such event is rare and is recovered with a retransmission. Thus, the unreliability is caused by the collisions due to the hidden node problem. As more traffic enters the network, the collision probability increases and goodput decreases. The low duty cycle operation increases the effect of the hidden node problem. Without the low duty cycle operation, a node can forward its data immediately which decreases the probability that two nodes transmit at the same time. However, in a low duty cycle network, a node must buffer data received during an idle period and wait until the active period of its next hop neighbor. Consequently, it is likely that several nodes try to transmit data at the beginning of an active period and a collision occurs between hidden nodes. The effect of the access cycle length (beacon interval) to the reliability with 12 sources is shown in Figure 11. The duty cycle and thus the throughput are similar on each case. Because long access cycle length increases the probability that node has data to send during the next active period, the collision probability also increases. Figure 10: Goodput with different number of sources in ZigBee. To evaluate the reason why the goodput drops significantly, lets consider the probability that two transmissions beginning at the same time collide. The length of the random backoff period is \(0..2^{BE}-1\) backoff slots, where \(BE\) is a backoff exponent. \(BE\) ranges between \(macMinBE\) and \(macMacBE\) that have default values of 3 and 5, respectively. At the beginning of the channel access procedure, \(BE\) is initialized to \(macMinBE\). If CCA fails, \(BE\) is increased up to \(macMaxBE\). However, in the hidden node problem, CCA succeeds because the nodes do not hear each other, and therefore \(BE\) is equal to \(macMinBE\). The transmission time of a data frame with 18 B payload and an acknowledgment frame equals to 6 backoff slots. As the default number of backoff slots is \(2^{macMinBE}=8\), there is 75% chance that two hidden node transmissions collide. Since the following retransmission attempts occur also at the same time, the probability that a transmission succeeds is very low. The probability that transmission succeeds in \(i\)th backoff slot when another node has started channel access procedure at the same time (e.g. at the beginning of the active period) can be calculated as  
\[p_{i}=\left\{ \begin{array}{ll}\frac{N-s-i}{N}&i<s\\ \frac{N-2s+1}{N}&s\leq i\leq N-s\\ \frac{i-s}{N}&N-s<i<N\end{array} \right., \tag{2}\]  
where \(N=2^{BE}\) is the total number of backoff slots and \(s\) is the data transmission time in backoff slots.