Performance Analysis

In this section, we present the performance analysis of our proposed protocol. We will address performance issues such as minimum delay, maximum throughput and sleeping time of the nodes.

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5.3.2.1 Maximum Overall Throughput Efficiency

The maximum overall throughput efficiency of the protocol can be seen as the percentage of the useful traffic (or good put) that can be sent over the network. As we are working in a multi hop environment, the maximum throughput efficiency will mostly depend on the number of nodes in the network and the number of levels in the tree. Indeed, the maximum amount of data that can be sent to the sink per WASP-cycle depends on the number of nodes in the first level and the length of the silent period. As mentioned in section 5.3.1.1, the silent period of the sink allows the nodes of level one to receive their data. This means that if we can lower the duration of the silent period, the maximum throughput will rise. Thus by minimizing the number of children of the nodes of level one, the maximum throughput efficiency can be improved. Generally, the throughput efficiency can be found as

T P E = # slots where data is sent to sink

length of a WASP-cycle (5.6)

where the length of the WASP-cycle is expressed in slots and depends on the length of the silent period.

In the example of Figure 5.3, we see that per WASP-cycle 5 packets can be sent to the sink and the total length is 10 timeslots. Thus, we have a maximum throughput efficiency of₁₀⁵ or 50%. This seems to be a low number, but we have to keep in mind that we are working in a multi hop environment and that the medium is shared between multiple nodes.

The following formula determines the length of a WASP-cycle TW C:

T_{W C}= # data children L1 + SP_S + (5.7) forwarding data of L2from L1to L0 + 2

where Lirepresents level i. The two extra time slots added at the end are used for the transmissions of the sink’s WASP-scheme and the contention slot at the end.

The duration of the forwarding period equals the number of timeslots needed to send the data of each node. Using (5.3) we can rewrite this formula as

TW C = X

In order to simplify the formula and to make it more intuitive, we introduce δi. This denotes the number of packets node i generates in one cycle. Using this notation, we can write:

T S_i = X

j ∈ V_i

δ_j + δ_i (5.9)

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Thus, (5.6) can be reformulated as

T P E =

and highly depends on the number of nodes and the structure of the tree. VSrefers to all the nodes in the network except the sink. In order to evaluate this formula, we assume that each node only has 1 packet to send per WASP-cycle. This means that the numerator of (5.10) equals the number of nodes in the network without the sink (N − 1). Further, we limit the maximum number of children a node can have, referred to as ζ. When ζ = 1, all nodes are in different levels and ordered in a line topology and when ζ = N - 1 all nodes can communicate directly with the sink. Of course, ζ can not be higher than N - 1. The second term in the denominator of (5.10) now needs to be written in terms of ζ. For simplicity, we assume a ζ-balanced tree, i.e. each node has exactly ζ children. The second term is the maximum number of nodes below a child of the sink. As the tree is regular by definition, the number of nodes is equally distributed between the children of the sink. Thus, we get

where the right hand of the equation is rounded upwards.

Figure 5.4 shows the throughput efficiency for varying N and ζ. For 50 nodes, an efficiency of 94% is achieved for ζ = 1 and 49% for ζ = 49. When the size of the network is smaller, the efficiency is lower because of the use of the contention slots which is independent of the size of the network. When ζ is lower, the silent period is longer as more data needs to be forwarded in the tree. Thus, in order to increase the throughput efficiency, the silent period should not be too long. From the graph it can be concluded that ζ should be 5 or higher. The more nodes the network has, the higher the throughput efficiency. This is due to the fact that as more slots are used for sending data, the length of the WASP-cycle increases, see (5.8). The fixed part of the WASP-cycle (i.e. a slot for the sink and 2 contention slots) however remains the same. This will lead to a higher throughput efficiency.

5.3.2.2 Delay Limits

The experienced delay depends on the number of levels present in the network.

Indeed, a node can only send his data up one level during each WASP-cycle. The only exception is to be found at level 1, where the sink’s children can first receive the data from their children and then forward the data.

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Figure 5.4: Throughput efficiency of WASP for varying number of nodes and changing tree topology with limited number of children per node.

We can define an upper and lower bound for a node i:

Lower bound = max ((level nodei− 2) · TW C, 1) (5.12) Upper bound = max ((level nodei− 1) · TW C, 1) (5.13) The maximum function is needed as the delay can not be lower than 1 slot.

The maximum delay over the whole network can be expressed as follows, as-suming that the network has at least 2 levels:

maximum delay =



∀i ∈ Vmax(level node_i) − 1



· T_{W C}. (5.14) Summarizing, if we want a high throughput, we should minimize the length of the silent period and for a low delay minimize the number of levels. These two conditions do not contradict, therefore a high throughput can be achieved while preserving the low delay.

5.3.2.3 Sleep Ratio

When the nodes have heard the WASP-scheme of their parent, they can go into a sleep modus in the slots where they are not involved in the communication. This allows for energy saving. For example, the Nordic transceiver has two power sav-ing modes: a standby mode consumsav-ing 12 µA and a power-off mode consumsav-ing 1 µA [33]. Even in standby mode, the power consumption is more than thousand times lower compared to the Rx or Tx mode. An important difference between these two modes is the switching time: switching from the standby mode to the normal mode takes less than 200 µs, from power-off mode to normal mode about 3

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ms. This switching time is important for maintaining the synchronization. Hence, if a node can go to sleep mode for a longer period of time, the power-off mode is the most interesting choice. In the following, we assume that the radio does not consume any energy when it is switched off. This is reasonable as the power con-sumption in either the standby mode or the power-off mode are almost negligible and we are only considering the sleep ratio in one cycle.

In the example scheme of Figure 5.3, the sink can turn its radio off in the silent period as it will not receive data from its child nodes. Thus, the radio can be turned off 3 slots. Node A can also turn its radio off in its silent period, when it knows that its siblings are sending and when none of its children is allowed to send data.

So, node A can sleep 5 slots.

The sleep ratio ρiof node i is defined as:

ρ_i = T_{W C} − Ton,i

TW C

(5.15) The following formula can be used to calculate the number of time slots in which node i has to operate its radio Ton,i:

T_on,i = (X

j∈V_i

δ_j+ 1) + δ_i+X

j∈V_i

δ_j+ 1. (5.16)

The first term refers to receiving the data from its lower layers (including the con-tention slot), the second and third term bring the sending of the data into account and in the last term, the node is listening to the scheme of its parent. This formula gives the upper bound of the number of slots a node can sleep. Indeed, if a node perfectly knows when a slot starts, it could turn on its radio at the beginning of each slot for a very short time. If we divide the formula by the duration of a cycle, we get the time ratio the node can sleep.

In a ζ-balanced tree the most burdened nodes are the nodes right below the sink. If we analyze the formula further assuming a regular ζ-balanced tree and using (5.11) for the node with the most children, the maximum time ratio for the nodes on the level below the sink can be written as

ρ =

Figure 5.5 shows the sleep ratio for varying N and ζ. There is no big difference between large and small networks. When ζ is lower, the sleep ratio ρ is lower as the node will have more nodes below it (more nodes in Vi) and will have to relay more data. This can especially be seen for a ζ = 1 where the sink has only one child that has to forward all the data and the sleep ratio is only 5%. It can be concluded that, also for the energy efficiency, ζ should be 5 or higher.

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0 5 10 15 20 25 30 35 40 45 50

0 10 20 30 40 50 60 70 80 90 100

ζ

ρ (%)

N = 20 N = 30 N = 40 N = 50

Figure 5.5: Sleep ratio of the nodes below the sink in WASP for a ζ-balanced tree.

5.3.2.4 Scalability

The number of nodes in a WBAN is limited by nature of the network. It is expected that the number of nodes will be in the range of 20–50, see Section 2.1. Our address structure, see section 5.3.1.5, supports up to 64 addresses which is most likely sufficient for WBANs. If more addresses need to be supported, the proposed address structure can be altered. Instead of 6 bits, 14 bits can be used. This will however negatively affect the amount of overhead generated by WASP.

Further, the more nodes in the network, the more data will be sent. This will negatively affect the maximum throughput per node.

5.3.2.5 Interference

Although WASP is slotted, interference can arise from nearby subtrees. The re-sulting interference can be minimized by randomizing WASP schemes. This ran-domization is not unlimited, e.g. the position of the contention slot is currently fixed, but it can reduce the interference probability.