**8.1. Hop zones distributions**

All Wireless Sensor Networks has a circular shape of their close neighbor's communication range. If a Base Station is located in communication proximity of nodes, these nodes are in BS neighborhood, and if messages sent from a node cannot reach directly BS and this action requires relaying nodes - a distance from one node to another closer to BS is called hop, so a message having more than *1* relaying node on route to BS needs to travel through *2* hops. Hop zones gather nodes with the same communication distance to a BS. WSN rules enforcing messages send out to a node located directly within next hop. However, some nodes could potentially have more energy (or located on hop border) to breach the one hop limit and sent message out to another node in next hop. Communication between hop zones is primarily dependent on a node that initiates communication towards sink, because it shapes, by its communication range, entire traffic, deciding to which node in next hop a message is sent. This action is crucial, since a node starts a chain reaction in relaying node. A route will only change once energy of any node on this communication path is drained. Let's assume that we have capability to influence a node where and how far it sends a message. By this feature we may manipulate that messages are being sent as far as communication range extends which ultimately may lead to reduction of regular hops number on a long path. Whether this pays off, yet again, it results from WSN layout and participating nodes. As experiments shows [10] having variable number of hops (based on nodes arrangement) and feasibility to influence message distance send out, a noticeable amount of energy may be preserved.

**Figure 6.** Nodes and hops distribution in a WSN

in the equation (14).

remains on its previous position.

**8. Accompanying issues** 

**8.1. Hop zones distributions** 

amount of energy may be preserved.

However there should be one more observation detected. We select only some of all calculated node's load quotients. One may wonder what and why such a criterion choice is? In our simulations, we were able to choose, building a BS migration vector തݓതത, all the neighbors since we knew their locations. So there was no difficulty in defining direction and sense of all vectors. Selection of neighbors taking part in the shaping of the vector (14) allows for smart elimination of unwanted nodes in this process. For example, if a node transmits the parameter *temperature in my environment*, and this temperature is too high (potentially harmful), then BS should not migrate in that direction. Often in the real world, only some nodes locations are known to BS, then it is apparent to include only those nodes

BS migration shall continue until such location is reached, in which a balanced number of messages reaches BS from all directions in its vicinity. Such a case, in the real world situation may never occur, so in order to stop redundant movements, to prevent further energy drain, we introduce indifference constant *k* (refer to (15)) that decides if any additional movement shall be done or not. If the left part of condition (15) is not fulfilled, BS

All Wireless Sensor Networks has a circular shape of their close neighbor's communication range. If a Base Station is located in communication proximity of nodes, these nodes are in BS neighborhood, and if messages sent from a node cannot reach directly BS and this action requires relaying nodes - a distance from one node to another closer to BS is called hop, so a message having more than *1* relaying node on route to BS needs to travel through *2* hops. Hop zones gather nodes with the same communication distance to a BS. WSN rules enforcing messages send out to a node located directly within next hop. However, some nodes could potentially have more energy (or located on hop border) to breach the one hop limit and sent message out to another node in next hop. Communication between hop zones is primarily dependent on a node that initiates communication towards sink, because it shapes, by its communication range, entire traffic, deciding to which node in next hop a message is sent. This action is crucial, since a node starts a chain reaction in relaying node. A route will only change once energy of any node on this communication path is drained. Let's assume that we have capability to influence a node where and how far it sends a message. By this feature we may manipulate that messages are being sent as far as communication range extends which ultimately may lead to reduction of regular hops number on a long path. Whether this pays off, yet again, it results from WSN layout and participating nodes. As experiments shows [10] having variable number of hops (based on nodes arrangement) and feasibility to influence message distance send out, a noticeable
