## 5 Simulation Evaluation and Numerical Results
### Numerical Results  
We first study the total energy consumption and data delivery ratio in sensor networks. To evaluate the information retrieval operation with various queries from users, in the simulation we adopt the variable of square areas in which users query sensors for data. The selection of the area being queried is defined by squares of different dimensions. The position of each square in relation to the corresponding nodes is randomly selected among the network. The total energy consumption in a round of data query and collection is the average of 10 cycles of data query and collection. Figures 6 (**A**) and (**B**) present the ratio of energy consumption in the proposed S3 based approaches to the conventional S2 based protocols, which include Flooding and LBM. Most of S3 based approaches, except for LDQD + LSDC Network Random approach, highly reduce the energy consumption compared with S2 approaches, especially when the length of the square being queried is small. In the S3 based approaches, the LDQD + LSCD Center approach that adopts the centre node of the query area as the sink proxy achieves optimised performance when the length of the square being queried is larger than 20, with a ratio of 25-90% energy consumption compared to the flooding-based protocol and 50-90% compared to the LBM-based protocol. The smaller the length of the square being queried, the larger the ratio of energy savings for the proposed approach. The exception is the LDQD + LSDC Network Random, which has greater energy consumption than LBM when the length of square is small because the network-wide random selection of a sink proxy cannot achieve a localised query and data collection for small query areas. In addition to the evaluation of total energy consumption in the network, we studied the distribution of energy consumption at individual sensor nodes. To evaluate the impact of dynamic sink proxy rotation on the energy consumption among individual sensor nodes, we set up a simulation consisting of 40 identical queries with and each query was followed by a data collection operation. The length of  
Figure 5: Simulation topology. query square is set to 40 m and the maximum number of sensing data that can be aggregated in a packet is set to 20. Figures 7 (**A**) and (**B**) shows an example of the distribution of energy consumption at each sensor node in the data collection operation. Flooding-query based data collection and LBM based data collections have high and non-uniform energy consumption with respect to both sending and receiving data. LSDC-center and LSCD-sink based data collections have much lower energy consumption at sensor nodes. LSCD-Random, in which the sink proxy is random selected in every query and rotates among sensor nodes, has the lowest value of the max energy consumption among sensor nodes. Hence, it has most uniform energy distribution among sensor nodes. We also set up a simulation consisting of three query objects, which are selected in the network. Sensor nodes monitoring each object are located within a 20 m \(\times\) 20 m square, in which effective sink proxy can be obtained. For each query object, 40 rounds of queries and data collections are performed. In the simulation S2 approach adopts LDQD + LSDC Limited Random with effective sink proxies. Figure 6: Ratio of energy consumption for approaches using S2 and S3 models. Figure 8 (**A**) illustrates the energy consumption at nodes with respect to their hop-distances to the sink. In the conventional S2 model, nodes of one-hop neighbours of the sink have the largest energy consumption, far larger than that of nodes with a long distance to the sink. In the S3 model, the energy consumption was about 40% of that of the S2 model at nodes of one-hop neighbours of the sink, leading to significant alleviation of the energy bottleneck. Figure 8 (**B**) shows the energy consumption ratio of the S3 model to the S2 model. Energy consumption at nodes near the sink is significantly reduced using the S3 model.