Impact of Cluster Parameter K on Charging Throughput Per-

We finally study the impact of the cluster parameter K on the performance of al- gorithm Online_K_Clusterby setting K at 1, 5, 10, 20, and 30, while the network size varies from 100 to 1,000 and the time period T is fixed at 1, 800s and 3, 600s, respectively.

From Fig. 5.5, it can be seen that the charging throughput of algorithmOnline_K_Cluster

§5.7 Conclusions 115 100 200 300 400 500 600 700 800 900 1000 0 100 200 300 400 500 600 Network Size C h a rg in g T h ro u g h p u t Online_K_Cluster (K=1) Online_K_Cluster (K=5) Online_K_Cluster (K=10) Online_K_Cluster (K=20) Online_K_Cluster (K=30) (a)T=1, 800s 100 200 300 400 500 600 700 800 900 1000 0 100 200 300 400 500 600 Network Size C h a rg in g T h ro u g h p u t Online_K_Cluster (K=1) Online_K_Cluster (K=5) Online_K_Cluster (K=10) Online_K_Cluster (K=20) Online_K_Cluster (K=30) (b) T=3, 600s

Figure 5.5: The impact of cluster parameter K by varying the network size n and setting the tolerant delay T at 1,800s and 3,600s.

with K = 30 delivers the worst performance. With the network size grows, the per- formance gap becomes smaller. Specifically, in Fig. 5.5(a), the charging through- put of algorithm Online_K_Cluster with K = 5 outperforms that of algorithm

Online_K_Cluster with K = 1 and K = 10 slightly, and is more than at least 25% and 19% compared with that of algorithm Online_K_Cluster with K = 20 and K = 30 when the network size is less than 800, respectively. Fig. 5.5(b) also exhibits the similar performance behavior in which algorithmOnline_K_Clusterwith K=1 outperforms algorithmOnline_K_Clusterwith K=5 and K= 10 slightly, omitted. In general, the charging throughput of algorithmOnline_K_Clusterdecreases when the K value is too large. In order to achieve a best charging throughput, a proper K should be assigned according to the network size and the tour time bound.

5.7

Conclusions

In this chapter we have studied the problem of finding an optimal close trajectory for a mobile charger in renewable sensor networks, subject to the time duration con- straint of the mobile charger per tour. We formulated the problem as a charging throughput maximization problem with an aim of maximizing the number of sen- sors charged per tour. Due to the NP-hardness of the problem, we then proposed an offline approximation algorithm and two online heuristics. Finally, we evaluated the

performance of the proposed algorithms through experimental simulation, and pro- vided numerical results to validate the efficiency of the proposed algorithms. Nev- ertheless, our work mainly focuses on maximizing the number of sensors charged, which may result in biased charging behavior in some edge cases (e.g. some sensors that are far from the base station or sparsely located have few opportunities to be charged). We will extend our work in future by considering fairness issues as well.

Chapter 6

Conclusions and Future Work

This chapter summarizes the contributions we made in this thesis, followed by dis- cussing several potential research topics derived from this work.

6.1

Summary of Contributions

Several key issues of deploying renewable sensor networks for sustainable moni- toring were studied in this thesis. New concepts, models, optimization techniques, and implementations were proposed and evaluated for renewable sensor networks to achieve unattended and continuing quality-aware services. As almost all the formu- lated problems are NP-hard, approximate solutions with guaranteed performance ratios for gathering data from sensor nodes and replenishing energy to sensor nodes efficiently were developed. Fast and scalable algorithms were devised by exploiting the combinatorial property of resource optimization problems (target coverage, mo- bile data collection, and energy replenishment). The main contributions of this thesis are summarized as follows.

• We investigated existing energy harvesting prediction approaches. Specifically, we investigated the accuracy of the energy harvesting prediction approach

VEWMA in comparison with the one of a basic prediction approach EWMA, using the real solar data profiles obtained from The National Solar Radiation Data Base in the States [7], which contain the most comprehensive collection of solar data for public access.

• We dealt with the coverage quality efficiency in renewable sensor networks.

We introduced a new metric that is a weighted linear combination of two sub-modular utility functions to measure the coverage quality within differ- ent time scales. Based on the proposed metric, we devised an offline algorithm

Greedy_Heuristicand its distributed implementationDistributed_Implement

to schedule sensors’ duty-cycles within the given energy budget to maximize the coverage quality. We also proposed an adaptive frameworkAdaptive_Framework

to deal with harvesting energy prediction fluctuations, and showed that under this adaptive framework, the proposed centralized and distributed algorithms are still applicable.

• We addressed the optimization of data collection by sensor networks in two ap- plication scenarios. We first studied the data collection maximization problem in a renewable sensor network with a path-constrained mobile sink, and pro- posed an offline approximation algorithm Offline_Appro and an online dis- tributed algorithm Online_Appro to schedule sensors transmitting their data to the mobile sink, through incorporating time-varying sensor energy budgets and employing multi-rate wireless communications. We also investigated the data quality maximization problem in a renewable sensor network, where a mobile sink with controlled mobility is employed for data gathering, and devel- oped a centralized algorithmMax_Utilityand its distributed implementation

Dis_Max_Utilityfor the problem, which find a close trajectory for the mobile sink and schedule the sojourn time at each sojourn location.

• We studied the energy provisioning for renewable sensor networks, by utilizing wireless energy transfer technology. We formulated the charging throughput maximization problem in a renewable sensor network where a mobile charger travels around the sensing field to replenish sensors with energy. We reduced the problem to the orienteering problem with time windows, and proposed an offline approximation algorithm. We also developed two online heuristics

Online_SPTandOnline_K_Clusterfor it, which construct the tour of the mo- bile charger iteratively.