# Mobile Data-Mule Optimal Path Planning for Wireless Sensor Networks
## 5 Simulation Studies  
### Data Rule for Low Complexity Sparse WSN (\(N=7\))  
A scenario of a sparse WSN with seven deployed static nodes is adopted in order to evaluate the efficiency of the proposed MES scheme along with the formulated optimization MILP problem. This scenario is similar to [32], where only one MoEl was used to accomplish the data harvesting process over a deployment of static nodes.  
In the first (top-left) sub-Figure 2, the static sensor nodes' deployment is presented along with the depot node '1'. The charged MoEls start and end their routes at the depot node, in which the MoEls' stored data are transmitted and stored. Furthermore, in the same Figure, the circular sensing/communicating regions of each static node are designed, resulting in a disconnected network.  
The profit value \(p_{j}\) assigned to each static node depends on its priority; a standard profit value is multiplied by a factor that is proportional to each node's priority (e.g., the highest priority node's profit is multiplied with the greater number of the vector \([1,\ldots,6]\)). The initial value for the profit is given by \(p\_initial=median(c+v)\), where the cost \(c\) is calculated as \(c=dist\_vector/speed\). Specifically, \(dist\_vector\) is a vector that includes the distances per pair of static nodes and per MoEl and uniform \(speed=0.2\) m/s. In addition, \(v\) is a vector of \(v_{t_{j}}\), which is the visiting time of the MoEl at a static node \(j\) and is defined by the static node's storage capacity and the corresponding required data transmission duration experimentally estimated in [33]. The static nodes profits are recalculated in every iteration of the MES scheme algorithm based on the Algorithm 4 and each profit is related to the edge \(x_{ijm}\) that leads to the vertex \(j\).  
The vector \(v_{t_{j}}\) depends on the storage capacity of the static nodes defined in the presented scenario as the vector \([0,3,8,1,2,4,5]\) for the set of static nodes expressed in Kbytes of stored data. The corresponding visiting time vector is \([0,24,68,7,15,34,39]\) s based on [33]. The initial expiration time for the nodes is set as \(e\ initial=[0,1080,1200,900,600,720,720]\) s. This vector denotes the frequency that every node has to be visited by an MoEl and hsa to transmit the stored data, due to these data criticality/storage limitations. Hence, this expiration time vector further determines the priority order of the nodes. It is used in the inequality set (12) and constrains the travel time of an MoEl towards a prioritized static node. This constraint sets an upper limit to the MoEl's travel time starting from the depot and visiting the prioritized node \(j\); this limit is imposed by the dynamically calculated deadline \(e_{j}\), after each iteration of the combined MES scheme. Finally, the time budget \(B\) that is set as a duration limit for the extracted routes is set as 360 s, while the charging duration value is 60 s. The optimization MILP problem was solved using Matlab's \(intlinprog\) routine of the Optimization Toolbox.  
It should be noted that the utilized storage WSN capacity and the download rate in setting the simulation parameters came from our previous work [33], where the communication protocol and data packet transfer were considered for a more realistic simulation study. The objective here is to evaluate the MES scheme efficiency and to investigate the number of data mules/MoEls that could guarantee no data loss within the network.