## 4 Advanced SensorNC: In-Network Processing
### Numerical Experiment
#### 4.4.1 Experimental Design  
At first, we create a set of WSN topologies by randomly placing \(n\) sensor nodes on a square field using a uniform random distribution. All nodes have a transmission range of 20 m such that connectivity is likely achieved (if not, the corresponding topologies are discarded). The sink node is in the middle of the sensor field, and the sink tree is built from a shortest path algorithm. For statistical significance, we evaluate 10 topologies for each experiment scenario. In all experiments, we selected \(n=100\) nodes and a sensor field of 100 m\({}^{2}\).  
The parameters relating to the sensor nodes resemble MICAz motes from Crossbow Technology Inc. (Milpitas, CA, USA) [19]. A transmission rate of 250 kbps is used; as MAC, we assumed a TDMA-based scheme that uses a duty cycle of 1% and a TDMA frame length of 100 ms. Thus, the communication service curve is given as \(\beta^{comm}=\beta_{2.5[kbps],0.099[s]}\). As the packet length, 36 B TinyOS packets are assumed. With respect to computational resources, the MICAz has an Atmel ATmega 128 L microcontroller operating at 8 MHz. Assuming an average of four cycles per instruction, its raw capacity amounts to 2 MIPS. Under the realistic assumption that the processor also performs other tasks, for instance network control operations, and that a power management scheme with certain sleep periods in low power modes is applied, we select its capacity for data processing to be 10% of its full capacity with a worst-case latency of 1 ms. Hence, the service curve for computation is given by \(\beta^{comp}=\beta_{0.2[MIPS],0.001[s]}\).  
From the scaling elements, we employ token-bucket functions for the maximum scaling curves and rate-latency functions for the minimum scaling curves. The maximum scaling curve that translates between communication and computation resources is set as \(\overline{S}^{comm2 comp}=\gamma_{5000[Instr./p],b[Instr.]}\), that is a received packet results in 5000 instructions, and deviations from this are captured by the bucket depth \(b\), which varies in the experiments. The minimum scaling curve is set to \(\underline{S}^{comm2 comp}=\beta_{5000[Instr./p],T[p]}\), with the latency parameter \(T\) also being varied in the experiments. Along the same lines, maximum and minimum scaling curves for the translation between sensing and computation resources are set as \(\overline{S}^{sens2 comp}=\gamma_{6000[Instr./p],b[Instr.]}\) and \(\underline{S}^{sens2 comp}=\beta_{6000[Instr./p],T[p]}\); here a higher computational demand for sensing is assumed because raw sensing values are given priority. Rescaling computation into communication resource demand is selected to be roughly inverse to the other scaling elements while also capturing some compression because of, e.g., data aggregation.  
The data arrival from local sensor are modeled by a token bucket \(\gamma_{0.1[p/s],1[p]}\), that is we assume a packet to be created every 10 s with a burst due to an instantaneous packet arrival.  
Clearly, many of these settings seem somewhat arbitrary and differ from scenario to scenario, yet they are from realistic settings and should thus be fairly representative.  
With the aid of the DISCO Deterministic Network Calculator [20; 21], we next present the results from the comparison between holistic and component-wise analysis (the DISCO Deterministic Network Calculator is publicly available under [[https://disco.cs.uni-kl.de/index.php/projects/disco-dnc](https://disco.cs.uni-kl.de/index.php/projects/disco-dnc)]([https://disco.cs.uni-kl.de/index.php/projects/disco-dnc](https://disco.cs.uni-kl.de/index.php/projects/disco-dnc)).)