**3. Communication, measurements and neighborhoods in WSN**

Communication is one of two (along with measurements made by the nodes) primary forms of WSN network activity. As far measurements are made by the network nodes and can be carried out locally, completely independently, then a communication is a typical collective action in which, besides the transmitter and the receiver, relay nodes actively participate.

The active role of relay results from the limited range of radio communication. Awareness of energy preservation considerations causes that this communication range is much shorter than existing in WSN distances between nodes and BS. Then, in order to make sure that information (a packet) arrives to a destination (BS) from a source of information (a WSN node), an implementation of routing packet based on relays is requisite.

In order to describe mentioned above WSN activities, let us introduce concepts of actions and behavior. *Action* should be considered as the property of each network element such as: a sensor, a Base Station, a cluster head or a regular node. The *behavior*, on the other hand is an external attribute which can be considered either as an outcome of actions performed by the whole WSN or its subset (i.e. cluster, routing tree, group of nodes, neighborhood).

*Action (Act)* is a ternary relation which can be defined as follows:

100 Wireless Sensor Networks – Technology and Protocols

on decision that BS won't be moved.

**2. Related works** 

range with BS, when it is moving away from these nodes.

using both random and deterministic elements.

Another issue to consider is; how often BS should change its position? To minimize BS movement once the intensity of messages is neither changing rapidly nor area of these changes migrating too far, what would the threshold (or any other factor) that has influence

Since it is the common knowledge that migrating BS could help extend WSN lifespan, it is just a question; how this migration should be organized. There are several aspects to be investigated, among others: whether BS should change its position every time a message is received or not (if not how often should it be?), how far BS should move from its previous (original position), how the BS movement affects behavior of all nodes and the BS neighborhood. Another crucial aspect is how to notify the nodes from BS neighborhood that will soon become out of communication

BS movement just a fracture of relay radio link range, seems to be energetically unreasonable, since just this kind of movement involves new distribution of nodes calculation and new relays designation, that consumes a lot of valuable energy resources.

There are a huge number of papers considered communication activity in WSN, related mainly to clustering and routing problems. On the one hand, scientists have discussed sensors' self-configuring [1], self-management [3, 1, 19], adaptive clustering [1, 9, 22] or concept of adjustable autonomy [5]. On the other hand, there are papers which discuss bio-inspired ideas

The WSN communication structure is crucial for BS migration. Authors [4] have shown that the communication topology of some biological, social and technological networks is neither completely regular nor completely random but stays somehow in between these two extreme cases. It is worth to mention papers [22, 19, 3] devoted to self-organizing protocols

In order to effectively manage communication activities, one has to address the problems of sensor network organization and the subsequent reorganization and maintenance [22].

Communication is one of two (along with measurements made by the nodes) primary forms of WSN network activity. As far measurements are made by the network nodes and can be carried out locally, completely independently, then a communication is a typical collective action in which, besides the transmitter and the receiver, relay nodes actively participate.

The active role of relay results from the limited range of radio communication. Awareness of energy preservation considerations causes that this communication range is much shorter than existing in WSN distances between nodes and BS. Then, in order to make sure that information (a packet) arrives to a destination (BS) from a source of information (a WSN

and tend to extract some aspects of the natural world for computer emulation [6].

**3. Communication, measurements and neighborhoods in WSN** 

node), an implementation of routing packet based on relays is requisite.

$$\text{Act:}\,\text{Nodes}\times\text{States}\to\text{States}\tag{1}$$

Therefore, actions that can be taken by nodes of WSN can be represented as a Cartesian product over the sets of nodes (*Nodes*) and their possible states (*States*). Finally, new states are a result of every action taken.

Actions are executed individually by a single node of the network (e.g. measuring the environmental parameter) but some of them require that two or more neighboring nodes cooperate with each other to perform a particular action (e.g. during the message transmission, receiver interact with transmitter). Actions are taken depending on the actual state of the node (different actions will be taken during the network organization or normal operation phase) and lead to new state of the node. Actions may also change the state of the neighboring nodes (e.g. dual actions transmit - receive).

Since nodes are autonomous, each one can execute actions independently of others. Undoubtedly, this is an advantage since WSN as a whole can simultaneously execute a plenty of different tasks. On the other hand, some actions gain in importance only when two or more nodes cooperate with each other taking dual or related actions. For such actions nodes perform their actions in cooperation which means that these actions are related to each other. In such a case we say that actions are related. Routing in WSN is a good example of such related actions.

Let, *R* denotes, routing. We can construct the quotient set called *Behavior*, consist of elements which are called equivalence classes linked to the relation *R* and here denoted as:

$$Beh \colon \mathcal{Act}/R = \{ \mathcal{Act}\_{\mathbf{x}} \in \mathcal{Act} \mid \mathcal{act}\_{\mathbf{x}} R \ge \}\tag{2}$$

So, routing activity is a *behavior* which draws on relations and describes dependencies between actions that are taken by nodes situated on a routing path. In other words, relations refer to actions that depend on each other and are taken together but not necessarily simultaneously – this is the relational way of thinking about the network activity. Detailed explanation of these concepts can be found in [12, 13, 16].

Concerning WSN structure, vicinity *V(k)* of a node *k* describes all what is placed in the radio link range of *k* node. This vicinity consists of various different components that belong to the WSN infrastructure and the other indirect elements that do not belong to WSN, although they play an important role in the behavior of the network. The set of objects from the first group can be called neighborhood *N(k),* and a collection made of objects from the second group is defined as environment *E(k).* The relationship between these three terms can be expressed as:

$$\mathcal{V}(k) = \mathcal{N}(k) \cup \mathcal{E}(k) \tag{3}$$

$$\mathcal{N} \in \left\{ \text{Map}\{\text{Nodes}; \text{Sub}(\text{Nodes})\} \right\} \tag{4}$$

$$\mathcal{N}(k)\_{|k \in \text{Nodes}} = \{ \mathbf{y} \in \text{Nodes} | \, \mathbf{y} \, \mathcal{R}\_{\mathcal{N}} k \}\tag{5}$$

$$\mathcal{N}\{\mathbb{S}\}\_{|\mathbb{S}\subset\mathbb{N}\text{dedes}} = \{\mathbf{y} \in \mathbb{N}\text{dedes} \mid \{\exists k \in \mathbb{S}\} (\mathbf{y} \,\mathcal{R}\_{\mathcal{N}} \, k)\}\tag{6}$$

$$f(\boldsymbol{\chi}) = \begin{cases} \frac{1}{\max\boldsymbol{\chi}}, & 0 \le \boldsymbol{\chi} \le \text{Max}\_{\boldsymbol{\chi}} \\ 0, & 0 > \boldsymbol{\chi} > \text{Max}\_{\boldsymbol{\chi}} \end{cases} \tag{7}$$

structure which yet again is exploited until an energy is depleted, etc. The other algorithms (proactive) determine the routing path, each time when it is needed. Transmission is then carried out closer to the current optimal routing path.

102 Wireless Sensor Networks – Technology and Protocols

all *X* subsets and neighborhood � as a mapping

of set of nodes *S* defined as:

density function

packet creation.

�(�) = �(�) � �(�) (3)

� � ����������� ���(�����)�� (4)

�(�)�������� = {� � ������ � � � �} (5)

�(�)�������� = {� � ������ (�� � �)(� � � �)} (6)

Coming back to mentioned above two crucial WSN activities, communication is a behavior which takes place within a neighborhood while measurements are actions related to environment. Further we will be working on communication aspects within WSN, so now let us come closer to this issue and begin from ���(�� �) expression that can be defined as a collection of mappings of set *X* onto set *Y* (surjection). Next, *Sub(X)* is defined as a family of

Thus, �(�) denotes the the neighborhood of node *k* while, �(�) is the neighborhood

Getting back to the main WSN task, which is the monitoring of selected physical parameters of the given area, let's have look at how it is implemented. A packet containing measurement results is formed in the node that has made this measurement. The sources of packets are all nodes in WSN. We assume a regular frequency of measurements, forming packets and continuous uniform distribution of nodes within WSN area with probability

where � � � � means that nodes *y* and *k* are in relation `*to be neighbors'*.

�(�) = �

communication proximity (neighborhood) of the base station.

� ����

for both X and Y axes. Thus, we consider WSN as a collection of strongly homogenous elements (nodes). During WSN activity we do not affect either the place or the time of new

Then a packet is transmitted to a base station via a routing path. Realization of this communication phase is based on the set of nodes cooperation that relay a packet. Short radio link communication range precludes (for many nodes) sending packet directly to the BS. Only a certain number of nodes can do this because only these are located within

This node's communication phase with the base station has been described repeatedly in the literature [7, 20, 15]. Different criteria for assessing the effectiveness of the retransmission realization are being used. There are many different algorithms for packet routing. Some of these methods (proactive) determine the optimal routing path and exploit them as long as possible. Next, an algorithm strives for finding a new, an optimal path in new patch

� � � � � ���� �� � � � � ����

(7)

**4. Spatial routing and routing chains in WSN** 

At this stage, we propose the following method of spatial route planning which is characterized by two important features:


Using the spatial routing, nodes in the space *S* (Fig.1) can model the routing path collectively realizing inducing cooperation. These features give us a greater flexibility in modeling communication behaviors. Moreover, making a decision collectively (within the neighborhood) increases adaptability to a varied environmental conditions. Note that, if each relay node (in Fig.1) has only *5* choices, so on the way from *s* to BS made up of six relays we have *56 = 15625* choices. It is an impressive number but we must remember that the routing path (*s,t1,t2,…,t6, BS*) makes a chain, whose lifespan is determined by the weakest link.

In our case it is *t6* relay node. Why? Because in a sequence of relay nodes so many (all) choices is being created by *s,t1,t2,…,t5* nodes. The last relay node *t6*, as situated in the vicinity of BS has no choice. Since one possibility is not a choice. Selection starts with two or more possibilities. Consequently, *t6* has to send a packet to BS. A multitude of choices, and thus an ability to spread energy consumption on a certain subset of WSN nodes is not *t6* node merit. Moreover, this node represents a base station neighbors *N(BS).* Thus, whatever the route is, and how many choices for routing (s, ...., BS) we have, each chosen route must end with one of these relay nodes which are neighbors of BS. What does this mean? We can spread an energy consumption for a routing path, forcing the nodes lying on its realization to work, but in the final retransmission phase, all packets, converge in the vicinity of the BS. So, we can offload nodes on a route, but we cannot relieve traffic going across nodes adjacent to the BS, because nothing can replace them.

**Figure 1.** The map of choices during spatial routing from *s* to *BS*

Hence the idea, if we cannot distribute loads of the nodes from BS neighborhood and this results in depletion of energy resources, thereby shortening WSN lifespan, it should ensure a periodic exchange of BS neighbors on other nodes, which have so far not been exploited so intensively or simply have more energy. Such an exchange can take place in two ways, or we will shift nodes in WSN area, or location of BS will be subjected to shift. We prefer the second solution, as more practical in implementation. An octocopter - a flying autonomous agile aerial machine will be used for BS transportation.
