Network Topologies 3
3.2 Multi-hop Network Versus a Star Network
3.3.2 Network Model
A wireless Body Area Network can be modeled as a directed graph G where V is the set of nodes including the sink or personal device. The sink is represented as S. A unidirectional link exists between two nodes m and n if n is within the send range of m and m is within the receive range of n. The number of nodes is N . Vsis the set of nodes without the sink S (VS = V \{S}). The distance between nodes i and j is di,j.
The variables of the optimization problem:
yk,li,j =
1, node i relays a packet to node j with origin k and destination l 0, otherwise
(3.10)
As all the data is sent to the sink, the variable is simplified to yki,j. One can argue to even simplify the variable further by not considering the origin of the packet. We choose not to do so, as we can use this information to rapidly determine how the information of node k is forwarded to the sink, e.g. to count the number of traversed hops or to calculate the path probability, as used in Section 3.6.
The total transmission energy of node i ∈ Vscan then be calculated using the radio model of Section 2.3.3.2:
EiT X = X
j∈V
X
k∈VS
yi,jk · [ET Xelec+ Eamp(η) · (di,j)η] (3.11)
The receive energy of node i only accounts for the energy consumed by the cir-cuitry and is given as
ERXi = X
j∈V
X
k∈VS
ykj,i· ERXelec (3.12)
The energy required for sensing is represented as Esense and is the same for all sensing nodes. A typical value is 50nJ/bit [19]. Aggregation of data is not taken into account.
3.3.3 Constraints
The following constraints are used:
64 NETWORKTOPOLOGIES FORWBANS
• Every node has a packet generation rate of 1:
X
j∈V
yi,ji = 1; ∀ i ∈ Vs (3.13)
• Every node forwards all the data it receives:
X
j∈V
yi,jk − X
j∈V
ykj,i = 0; ∀ i, k ∈ Vs; i 6= k (3.14)
The first part accounts for the forwarding of the data originated at node k by node i to all possible nodes. The own generated data is not taken into account (i 6= k), as this is covered by (3.13). The second part reflects the reception of data originating at node k by node i, received from all possible nodes.
• The sink receives all the data:
N − 1 = X
k,j∈Vs
yj,Sk (3.15)
3.3.4 Objectives
We consider different objectives. In the first, the overall energy usage over the network is minimized (total energy):
Obj: minimizeX
i∈Vs
[ERXi + ET Xi + Esense] (3.16)
This objective does not take into account the individual energy usage of the nodes.
It might therefore well happen that one node has a very high energy consump-tion compared to the others. This will lead to a low network lifetime. For the second objective, we will consider the individual energy consumption and as a consequence maximize the lifetime of the network. This can be achieved by find-ing the minimum of the maximum node energy usage. However, this approach only considers the energy consumption of the most consuming node and does not influence the energy usage of the other nodes. Some nodes may thus route their packets inefficiently. Therefore, a low number of hops is still desired and an ILP consisting of 2 phases is used. In the first phase, the maximum node energy usage is minimized (max energy):
Obj: minimize max
i∈Vs[ERXi + ET Xi + Esense] (3.17) In a second phase, this objective value (Emax) is used as a maximum value for the energy consumption and the new objective is to minimize the number of hops (connections):
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ERXi + ET Xi + Esense < Emax; ∀ i ∈ Vs (3.18)
Obj: minimize X
i,j∈V
X
k∈VS
yki,j (3.19)
3.3.5 Analysis
3.3.5.1 Setup
All integer linear programs needed to evaluate the cooperation problem, have been solved using ILOG CPLEX 10.0 [20], running on BEgrid, the computing/data grid infrastructure that results from the Belnet Grid Initiative [21].
The number of nodes is varied from 5 to 15. We have evaluated the average maximum network energy consumption in Joule (J) (Figure 3.12) which is a cri-terion for the network lifetime and the average number of hops per connection (Figure 3.13). The networks are randomly generated in an area of 2m by 2m and the personal device is placed in the middle. Each data point represents an average of 100 runs.
3.3.5.2 Discussion
5 6 7 8 9 10 11 12 13 14 15
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8x 10−4
Number of nodes
Average maximum energy consumption
Total Energy Max Energy Connections
Figure 3.12: The maximum node energy consumption for varying number of nodes for the different objectives: total energy (3.16), max energy (3.17) and connections(3.19). The graphs for max energy and connections coincide due to restriction (3.18). For a higher network lifetime, it is better to consider the maximum node energy.
66 NETWORKTOPOLOGIES FORWBANS
5 6 7 8 9 10 11 12 13 14 15
1 1.5 2 2.5 3 3.5 4
Number of nodes
Number of hops per connection
Total Energy Max Energy Connections
Figure 3.13: The average number of hops per node for a varying number of nodes for the different objectives: total energy (3.16), max energy (3.17) and connections(3.19). It can be seen that the average number of hops is less than 2 when the number of connections is minimized.
The lowest lifetime is achieved when the overall energy usage is minimized (total energy). This is to be expected as the energy usage of the individual nodes is not considered and one node can have a very high load. When the sec-ond objective is used (3.17), the lifetime of the network is improved, but a larger number of hops is used. This was expected as the ILP-solution only looks at the node with the maximum lifetime. Thus, by using the extra condition (3.18) and objective function (3.19), the number of hops is minimized whilst preserving the lifetime, as can be seen in Figure 3.12 (connections). So, the use of these last objectives leads to an optimal network with a minimum number of hops and a maximum lifetime of the network. The lifetime of the network is increased by 24% on average.
The maximum network energy consumption lowers when the network has more nodes. The more nodes available, the more the burden of forwarding data will be distributed, which leads to a decrease of the energy consumption. Further, even when the number of hops per connection is minimized, this is still between 1.5 and 2. This means that forwarding data from other nodes is beneficial for the lifetime of the network. This is in line with (3.2) where dchar is 43 cm and the maximum distance between a node and the personal device is 1 m, giving a Kopt
of 3. As the nodes are uniformly distributed in the area, this is averaged out to 1.5. Moreover, the use of objective (3.19) has the side effect that a node will send his data directly to the personal device as long as its energy consumption is lower than the maximum energy consumption. This also lowers the number of hops per
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connection.
3.4 Relaying
The cooperation from the previous section, proves to be very useful. But the energy consumption can be lowered even more by introducing dedicated relay devices in the network. These are special nodes which only handle traffic relaying and do not do any sensing themselves, thus more energy is available for communication purposes. The main idea is that proper placement of relay nodes can bridge the per-formance gap for the nodes far away from the sink in the case of single-hop traffic and offload the nodes closer to the sink in the case of multi-hop traffic. Further, the relay devices are dedicated devices with no sensing functionality that merely forward data received from other nodes. This means that more of the available energy can be used for forwarding and receiving data. The sensor device handles the received data the same way as a normal node does: the received signal is de-coded, when the signal is not properly received, a retransmission is done. Doing so, propagation of errors in the network is avoided.
For a node relaying traffic from z nodes, energy usage for packets of k bits is similar to a regular node in a multi-hop network (3.4), minus the cost of transmit-ting own packets:
ER(z, d) = z · k · ERXelec+ z · k · φ · (ET Xelec+ Eamp(η) · dη) (3.20) In this formula, d represents the distance to the next relay hop. Further, this equa-tion is independent of the architecture used, i.e. line or tree topology. However, the number of nodes that are relayed, z, depends on the position of the relay node and the architecture used. As in the previous analysis, aggregation with a factor φ can be used.
3.4.1 Line Topology
We will evaluate the use of relay devices for the line topology of Figure 3.3(b).
One extra relay device is used and is placed along the position of node 3 or node 4. Nodes 1 and 2 forward their data to the relay device (Figs. 3.14(a) and 3.14(b)).
The resulting energy usage can be seen in Figure 3.14. Figure 3.14(c) shows for each node the usage when using the single-hop, the multi-hop and the relay sce-nario. It can be seen that the nodes consume the least in the relay node scesce-nario.
The energy consumption of the relay device has also been plotted. It is clear that the relay device will be the limiting factor of the lifetime of the network. By mov-ing the position of the node along node 4, the energy consumption of the relay device decreases, see Figure 3.14(d).
68 NETWORKTOPOLOGIES FORWBANS
Relaydevice
d Central
Device
2 3 4
(a) Relay node at position 3 (topology)
Relaydevice
d Central
Device
2 3 4
1
(b) Relay node at position 4 (topology)
1 2 3 4
(c) Relay node at position 3 vs single-hop and multi-hop
(d) Relay node at position 3 vs position 4
Figure 3.14: Energy usage when relaying in a line topology. No aggregation is used (φ = 1). The energy consumption of the relay devices is also plotted (relay node position)
When aggregation is used by the relay device, the energy consumption will decrease further as less bits need to be sent.
3.4.2 Tree Topology
As an example, consider a binary tree network of 5 levels where the relay devices are placed at level 4, see Figure 3.15. Each node at level 4 has a relay device next to it. The relay devices only forward data from the nodes at levels 1 and 2 and relay it directly to the sink. Figure 3.16(a) shows the result when the distance between the nodes is 20 cm and figure 3.16(b) gives the result for a network with 30 cm between the nodes. The graphs for single-hop and multi-hop communication are plotted. Further, the energy consumption of the relayed network is shown. It can be seen that the lifetime of the nodes at level 1 and 2 improves a lot with respect to the single-hop scenario. In both cases the energy usage at level 1 decreases by a factor 10.
The points at level 4 represent the energy usage of a relay device when it for-wards data from 12 or 6 nodes. When 12 nodes are forwarded, the energy
con-CHAPTER3 69
Figure 3.15: Example of a balanced tree topology with ζ = 2 when a relay device is added on level 4. The communication links are shown on the figure. No aggregation is used (φ = 1)
(a) Inter node distance = 20 cm
1 2 3 4 5
(b) Inter node distance = 30 cm
Figure 3.16: Energy usage when relaying in a tree topology for varying inter-node distances and ζ = 2 (Figure 3.15). No aggregation is used (φ = 1). Relay device 1 forwards data from 12 nodes, relay device 2 forwards data from 6 nodes. The energy consumption of the relay devices is also plotted.
sumption of the relay device is about 6 times higher than the one of the sensor nodes in the relay scenario. When an extra relay device is added, the energy con-sumption of the relay devices is only slightly higher than the maximum energy consumption of the sensor nodes in the relay scenario. When the distance between the nodes is 20 cm (Figure 3.16(a)), we see that the energy needed for relaying data of three nodes is lower than the energy usage of the nodes at level 3. If the distance is larger, i.e. 30 cm, it is even possible to relay 7 nodes while staying under the energy consumption at level 3 (Figure 3.16(b)). The exact number of nodes whose data can be forwarded can be calculated by a formula similar to (3.9). But as the relay device has no data to send, the formula reduces to
#nodes supported =
Elim
ER((L − k + 1) · d)
. (3.21)
70 NETWORKTOPOLOGIES FORWBANS
with L the number of levels of the tree and k the level where the relay device is added and ERis (3.20). Depending on the energy required for sensing, supporting a larger number of nodes should be possible.
It should be noted that the number of nodes in this example network is very high, the number of relay nodes will not have to be that high in realistic WBANs.
Figure 3.17 shows the influence of data aggregation when relaying is used and when the number of relayed nodes varies. The aggregation of data lowers the energy consumption.
0.5 0.6 0.7 0.8 0.9 1
1 2