Application of Fiedler Value for Mitigation of Loss of Connectivity in Wireless Mesh Networks

Abstract

This paper proposes a new scheme for very fast detection of a sensor going offline or loss of connectivity of sensor in Wireless Mesh Networks (WMN) in order to avoid any packet loss. A sensor is declared offline by a gateway if it does not receive any packet from the sensor for a specific time interval termed as keep-alive time. In mesh networks, this keep-alive window is kept for a very long duration; sometimes it is as high as 2.5 to 3 hours. The time duration is kept high so that gateway does not declare a sensor that is in deep sleep to conserve battery, as offline. However, keeping a large keep-alive time window leads to the very likely possibility of missing the timely detection of a critical event like a smoke sensor or gas leak sensor going offline. In the proposed method, the gateway maintains its table of neighbourhood matrix in order to facilitate fast and efficient tracking as well as tracing of the nodes for the detection of the loss of connectivity of a sensor. A Laplacian matrix formulation proposed by Fiedler is invoked for tracking and tracing lost nodes of WMN. Through the Fiedler value, this paper substantiates the efficacy of monitoring a large WMN not only for its algebraic connectivity but also to compute the number of disconnected partitions in it. This is achieved through the number of null values of eigenvalues of the Laplacian matrix of the graph of WMN. Through simulation studies, this paper demonstrates achieving an 88 % success rate in the detection of disconnection with an average latency of 39.806 ms. On the contrary, a conventional process for the time duration after which a sensor can be declared offline might be an hour or even more depending upon the pre-set duration of the keep-alive time window.