An Approach to Construct Weighted Minimum Spanning Tree in Wireless Sensor Networks - Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing - page 70

interest or as requested to its default gateway. Active nodes are default gateways
for other active or sleeping nodes. Active nodes together form the virtual
communication backbone of the network.
Sleeping nodes: In order to conserve the energy of the nodes, the nodes can turn
their radio off instead of actively listening for messages. In addition, the nodes if
they sense any events by themselves will transmit the message concerning the
sensing event; sleeping nodes will not relay messages for other nodes.
Comatose nodes: Comatose nodes may possess sufficient energy to sense and
transmit messages, but due to their location, they are not within the
communication range of any active or sleeping nodes. Since they cannot deliver a
message to the sink due to their unconnected status, they will generally not
contribute sensing or transmitting capability to the network.
Dead nodes: In a WSN, nodes have a finite amount of energy. As the node's
energy is depleted the node will become incapable of sensing events or
transmitting messages. Such nodes are denoted as dead nodes.
Successful Event: A successful event occurs during the operation of the WSN
when a message for a sensing event as determined by either a sleeping or an active
node is delivered and received by the sink node. From the sink node, the message
is transmitted to the Base Station (BS). In this paper, the authors maintain that the
number of successful events is very critical to successful WSN operation since
the main goal of a WSN is to sense events and send the corresponding messages to
the Base Station.
Energy Model: The energy model assumed in this research was adopted from
[4]. The amount of energy consumed in transmission and reception of data can
modeled as:

E t (k,r) = kE elec + kεr 2 (1)
E r (k) = kE elec (2)

where,
E t (k,r) = energy required for transmission
E r (k) = energy required for listening
k = the number of bits in each message
E elec = the energy needed to run the transceiver
ε = energy consumption of the amplifier per unit area
r = distance between parent and child nodes

During testing of the proposed algorithm, the simulations assumed same data
size for each message. In addition the transmission energy dissipated is
proportional to the distance between parent and child nodes as seen in equation 1
and for listening the energy is fixed as in equation 2. As stated before, active
nodes will constantly listen for message delivery request. When a message
delivery request is received, an active node will transmit a message. In addition, if
an event is sensed by an active or sleeping node, it will send a message. Fig. 2
depicts the communication backbone after a random WSN deployment.