## 3 WSAN System Models
### Performance Metrics  
_Communication performance metrics_: The performance measures for evaluating the wireless communication networks are listed as follows: the total number of data packets sent from the source and successfully received at the sink, the jitter duration of data packets, and the total energy consumption of the network. * The total number of data packets sent from the source and successfully received at the sink: These metrics are a total number of sensing data packets which carry a value of measured temperature information sent from node ID 0 and successfully delivered to node ID 1. * The jitter duration: This metric is the time interval between every two consecutive data packets received at the sink node. It indicates the variation in the delay of successfully received data packets. * The total energy consumption of the network: This metric is the sum of all nodes' energy consumptions in all activities during the simulation time. It indicates the energy consumed by a node in the idle listening, transmit and receive states. Note that for the jitter duration and the energy consumption of the network, we also measure these metrics over a predefined interval of time to study their variations. _Control performance metrics_: Three metrics are employed to measure the performance of the building-temperature control system: the system output, the settling time, and the integral of absolute error. \begin{table}
\begin{tabular}{l} \hline
**Parameters Values** \\ \hline Dimension of the Topology (m\({}^{2}\)) 100 m \(\times\) 100 m \\ Simulation time (s) 5,400 s \\ Number of nodes 11 \\ Radio propagation model Two-ray ground \\ Interface queue type FIFO with Drop-tail \\ Interface queue size (packets) 50 \\ Transmission range (m) 15 \\ Initial energy of each node (J) 13000 [36] \\ Transmit power (W) 0.0744 [36] \\ Receive power (W) 0.0648 [36] \\ Idle power (W) 0.00000552 [36] \\ MAC IEEE 802.15.4 \\ Routing AODV \\ \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. The system output: This metric represents the zone temperature value in a room at each the given sampling period. This paper plots this value _versus_ time to study its time response. * The settling time is the time required for the system output to reach and remain within \(\pm 2\%\) of the desired temperature value. At the settling time, the physical system approaches its steady-state response, which is its approximation to the desired response [37]. If the system output does not reach and remain within \(\pm 2\%\) of the desired value during the simulation time, the considered physical system is not controllable. * The integral of absolute error (IAE) [2]: This measure is the sum of the absolute value of the error between the desired and the measured temperature values defined as \[\text{IAE}\!\!=\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! \!\!\!\!\!\!\!\!\!\! traffic flow, the lower path is selected. The number of hops in the path indicates the round-trip time in the case of no traffic flow. The AODV determines a route when the source node wants to send its data to the sink as discussed before. The source node establishes a route in every sampling period for our case. Consequently, there is some chance of route changes during the simulation time due to the interruption of CBR traffic flow on the lower path. Table 3 shows the number of data packets successfully sent from node ID 0 and received by node ID 1 _versus_ the CBR rate. The jitter duration histograms of all successfully received packets are shown in Figure 3.  
From the simulation results, the AODV chooses the lower path for data transmission when there is no background traffic as discussed before. At the CBR rate of 1 Mbps, the AODV often selects the upper path because the CBR traffic flow may interrupts the RREQ message transmission on the lower path occasionally. Due to the hidden node problem, intermediate nodes may not successfully transmit or receive the RREQ or RREP messages.