## 6 Conclusions  
The paper presents two algorithms for slot allocation in a periodic sensor network. Both take advantage of the periodic nature of the data collection process by allocating a subset of nodes to subsequent frames. They can be considered a kind of centralized activity control mechanism coordinating data transmission in subsequent frames. The resulting schedule satisfies two main targets: it reduces power consumption and provides contention-free routing. The communication rate may be relatively low, thanks to data buffering in nodes. Precomputing schedule makes using additional signaling communication channels and synchronization unnecessary. It is important to note that the solution takes into consideration interference (i.e., hidden node problem). As a schedule allows all nodes to send their data, the scheme may be used when periodic data acquisition is necessary. The proposed scheme is restricted to static typologies. In varied environments, decentralized and reactive activity control mechanism provides better performance and reliability. Figure 5: Average values of total energy performance index (left graph) and maximum node energy performance index (right graph) for both algorithms. We conducted numerical experiments to assess the performance of the proposed algorithms. They show that the proposed method of the solution--with the help of branch and bound MIP solver is appropriate for network size in a range of 50 nodes when a maximum node energy consumption performance index is used. Minimization of total energy consumption index results in a much more complicated structure of constraints, so the solution is possible for networks smaller than 20 nodes. However, it is possible (as it was to some extent shown in experiments) that slot allocations found using maximum node energy consumption performance index can provide longer network operation. This is achieved thanks to spreading the load evenly and preventing premature battery exhaustion in nodes of greater centrality. To fully exploit the method using the total energy consumption index, it is necessary to include battery capacity as an additional state variable in the network model. Such modification will further complicate the mathematical programming task so that an effective solution could be possible, probably only using the heuristic method. To enhance method performance and allow finding a solution for more extensive networks, two methods are envisaged. The first may be based on using effective heuristics. Comparing total vs. maximal energy consumption index algorithms shows that they need many branch and bound iterations. One of the reasons may be specific task structure resulting in relatively poor quality of initial upper bounds, especially for more complex initial data locations. So, the heuristic providing any feasible solution may speed up the branch and bound method by providing upper bound and cutting many unnecessary variants. For the same reason, application of any method providing better relaxed solutions like cut and branch or branch and price may be effective. The second approach may be considered complementary to the previous ones. It is important to note that in the experiments, the node to frame allocation was generated randomly. Such a procedure allowed one to test a variety of cases. However, it resulted in very high computation time variance. As it was shown in Section 5, unfavorable initial data locations may cause the increase of computation time in the order of ten times for maximal node energy index variant and even over a thousand times for the total energy index method. Some initial work on classifying initial data location variants was done during the analysis of experiments' results. In the cases which allow binding sending nodes to frames freely, it may be proposed that the allocations should be generated following some rules. At this moment, it is possible to summarize them as dividing the network into several sectors lying in growing distance from the base station and spreading nodes evenly among these sectors.