Network Topologies 3
3.5 Relaying and Cooperation
3.6.3 Collision Probability
In the previous sections, it was assumed that no collisions occurred when packets where transmitted. This assumption was taken to orthogonalize the results from the properties of specific MAC-protocols. When the MAC-protocol is TDMA-based and the slots are well allocated, the results will remain the same. However, problems arise when the slots are not synchronized anymore. For example, con-sider the topology of Figure 3.20. When node A is sending to node B and node C is sending to node D, the packets will collide at node B when the duty cycle is not synchronized.
We can calculate the probability of collision when we know the number of neighbors and the activity level of the nodes. When the node has less neighbors,
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(b) Average maximum network energy. The cooperation graphs coincide and all the graphs for relay devices coincide due to restriction (3.18).
5 6 7 8 9 10 11 12 13 14 15
Figure 3.22: ILP where the reliability is maximized. The restricted relaying is where the number of relaying nodes is minimized.
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the number of nodes that can influence each other is limited. Consequently the interference will drop. We will estimate the probability of a collision at a node i:
Pr[collision i] = 1 − Y
j∈N H(i)
(1 − Pr[Actj]) (3.33)
The product is over all the neighbors of node i, N H(i). Pr[Actj] is the probability of activity of node j1. If we assume that the probability of activity at all nodes in the network is independent and identically distributed, then Pr[Actj] = Pr[Act]
∀ j ∈ N H(i). Consequently, equation (3.33) can be formulated as
Pr[collision i] = 1 − (1 − Pr[Act])N B (3.34) where N B is the number of neighbors (#N H). Plotting the probability, we get the following plot for a varying number of neighbors, Figure 3.23.
Figure 3.23: Probability of collision of node i for a varying number of neighbors. The X-axis shows a varying number of neighbors, the Y-X-axis a varying probability of activity. The lines on the graph show the places with a constant probability of collision.
We see that for a lower number of neighbors, the probability of collision will drop keeping the same probability of activity. Thus, by limiting the number of
1Notice that this model can take into account the difference between the communication range and the interference range of a radio. In regular wireless networks the interference range is about two times the communication range. In this study N H(i) is defined as the set of nodes that can interfere with node i
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neighbors, less interference will be experienced. The number of neighbors can be lowered by decreasing the transmit power Ps,dB. This will lead to a multi-hop network.
The number of neighbors will also influence the reliability and the energy ef-ficiency. When a node has a lot of neighbors, the probability of a collision rises, leading to lower reliability and raising retransmissions. This will also lower the energy efficiency. When the nodes are grouped in a tree network and the tree is built in such a way that neighboring nodes reside in the same branch of the tree, collisions can be avoided by assigning slots. This problem will be the focus of Chapters 5 and 6.
3.7 Conclusion
In this section, we have investigated possible network topologies for a WBAN.
Two important characteristics were considered: energy efficiency and reliability.
For the former, we first defined the lifetime of the network as the time for the first node to die. We started with a very basic comparison between multi-hop and single-hop communication for a line topology and a tree network. It showed that multi-hop communication is better for nodes far away from the personal device, but not for nearer nodes. The effect of aggregation was taken into account and it was demonstrated that aggregation lowers the energy consumption, especially in a tree network. Then cooperation was introduced: sensor nodes cooperate in delivering the data to the personal device. As formal analysis, an ILP formulation was set up. Simulations have shown an increase of 24% on average of the network lifetime when the maximum energy per node is minimized. In a second step, the number of hops per connections was minimized. After minimization, this is about 1.5 hops per connection, indicating that cooperation indeed is beneficial for the lifetime of the network. Next, relay devices were introduced to lower the maxi-mum network energy even further. And finally the concept of cooperation and the use of relay devices was combined and analyzed using an ILP. By letting nodes cooperate and by adding extra relay devices for a better load balancing, even more energy efficient network topologies can be obtained. For larger networks, a life-time increase up to 30% was achieved. For future purposes, it could be interesting to investigate more comprehensively the impact of data aggregation on the lifetime of more general networks by adding it to the ILP.
The reliability was discussed briefly and the loss probability and probability of collision was investigated. We have compared the reliability between a single-hop and multi-hop architecture. Through an example with a line topology, it was clear that a multi-hop architecture is a more reliable choice. In order to evaluate this assumption, we have analyzed the reliability by adding it to the ILP formulation.
It is concluded that the reliability can be increased with only a very limited impact
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on the network lifetime.
Overall, it can be concluded that a multi-hop architecture is the best choice for a WBAN and that one has to deal with a trade-off between energy efficiency and reliability. Adding relay devices is helpful for both the energy efficiency and reliability.
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