# Random Walker Coverage Analysis for Information Dissemination in Wireless Sensor Networks
## 5 Conclusions  
The random walker's mechanism is used for information dissemination in order to exploit the probabilistic advantage in the emerging new network environment like energy-harvesting networks. In such environments, approaches like flooding are not suitable since nodes may stop operating from time to time due to energy unavailability resulting in temporarily disconnected networks. In such systems with stochastic behavior, the use of a random walker for the dissemination of information can be quite useful, reducing the number of messages among the nodes. Nevertheless, there is disadvantage with respect to the increased time required for the coverage of the network.  
In this work, a handy analytical tool is given that enables the study of the coverage of a network by a random walker over time. The paper focuses on the study of network coverage achieved by a random walker acting on it, under a novel and original perspective. As the random walker acts on a given network, it inevitably revisits the network's nodes due to the probabilistic nature of the random walker movement. This fact enables the overcoming of the problem of the unavailability of certain nodes from time to time because of a temporary lack of energy. The random walker probabilistically chooses the next neighboring node to visit, without considering any previous visits.  
To sum up the contribution of this study, a novel analytical approach is described, presenting the coverage rate in relation to the number of random walker's steps. In this direction, the probability for the random walker to reach a node for the first time at each step is calculated. Then, this probability value is used to find the number of nodes that had been visited by the random walker, which depends on the number of steps. There are also detailed results on the neighborhood surface in a random geometric graph, as well as some formulas on the average movement of the walker.  
This analysis led to the conclusion that the coverage is independent of the network's connection density (significant time lag is met only in marginally sparse topologies). The analytical findings presented in this work were also evaluated through simulation results in order to be properly verified. As was shown through indicative examples and figures, the presented analytical results were in accordance with the simulation outcomes, even for grid topologies.  
Finally, the results of this work could trigger further investigation of the random walker mechanism in geometric graphs, under different assumptions and functionality modes. For example, one could consider the analytical version of the coverage when multiple walkers are employed, or when each node is weighted according to some metric, e.g., its \"popularity\" (i.e., the number of neighbors); for example, to investigate how the coverage would be affected if a two-hop distance estimation [47] is considered.  
All of the authors have contributed extensively to this study. [PERSON] and [PERSON] conceived of the initial idea. They both developed the initial formulation described in the main part. [PERSON] and [PERSON] thoroughly analyzed the current literature, and they compared it with the described approach. [PERSON] was responsible for supervising the progress and the finishing of this work. [PERSON] and [PERSON] contributed to the proper typing of formal definitions and the math used in the paper. [PERSON] and [PERSON] collaborated in the production of the experimental results. All of the authors contributed to the writing of the paper. All authors have read and approved the final manuscript.  
The authors declare no conflict of interest.