## 4 Performance Evaluation  
In this section, we will describe our simulation environment for our protocol evaluation. To evaluate the performance of the proposed data forwarding protocol quantitatively, we use NS-2 network simulator [19]. The collection subsystem delivers the power quality data to the substation in a timely and reliable manner. We choose the quality of data delivery in terms of the data delivery ratio and the distribution delay of the power quality data as performance metrics. The collection subsystem is made up of one substation and six feeders. Each feeder collects the power quality data from 300 pole transformers placed in a random pattern. In other words, a total of 1,800 nodes are deployed in the network. The distance between two neighboring pole transformers is set to around 200-300 meters. The transmission radius of a node (a communicating device on the pole transformer) is 500 m. We use the shadowing model in [20] to model a radio propagation environment. IEEE 802.11b is used as the MAC layer in our experiments and its data rate is 11 Mbps. Each node measures the power quality data every one second and transmits the measured data towards the substation at every transmission interval, which ranges from one second to 60 seconds. In our collection subsystem, packets travel along a chain of intermediate nodes towards the substation except for branch nodes. Since radios can interfere with each other beyond the range at which they can communicate successfully, the utilization of a chain of nodes is quite low compared to the maximum throughput [21,22]. As the offered load increases beyond this maximum utilization, the chain throughput drops sharply, so the offered load should be controlled. We vary the offered load to achieve the maximum performance in terms of the quality of data delivery by adjusting the data transmission interval of nodes. The traffic pattern generated by each node is the constant bit rate (CBR). The size of a CBR data packet is set to 1,500 bytes and the total simulation time to 3,600 seconds. Since the RTS/CTS/ACK exchange adds significant overhead in the IEEE 802.11 based network, the data throughput with 1,500-byte data packet is higher than that with 64-byte or 500-byte packet [21]. Thus we employ a 1,500-byte length data packet to forward the aggregated power quality data instead of multiple short packets. Since the packet drop probability in a wireless multi-hop communication environment increases with the number of hops [22], in the simulation we generated three different topologies with 300 nodes: a 30 hops-sized network, a 50 hops-sized network, and a 70 hops-sized network. The 30 hops-sized network represents the longest hop distance between a substation and a node is 30 hops in a feeder. Figure 6 shows the data delivery ratio when the transmission interval of the power quality data is varied from one second to 60 seconds. The data delivery ratio means the average ratio of the number of data messages received by the substation to the total number of data message sent by all data sources. As mentioned earlier, the power quality data is measured every one second and the measured data is aggregated and transmitted every transmission interval. The value of k in each legend of the figure represents the rate of data source in the network. For example, k = 0.5 represents that 900 nodes (50 percent of all 1,800 nodes) measure the power quality data. The power quality data measured at a pole transformer is likely to be similar to the data measured at its geographically adjacent neighboring pole transformer. Thus, we can control the rate k to achieve the maximum performance as well as the transmission interval. In the figure, over 95 percent of the data delivery ratio is obtained for the conditions: the transmission interval is greater than one second in 30 hops-sized network, than 10 seconds in 50 hops-sized network. It is greater than 50 seconds and the value of k is smaller than 0.33 in 70 hops-sized network.