Hitting time for doubly-weighted graphs with application to robotic surveillance

This article provides analysis results for the weighted hitting time and the pairwise weighted hitting time of a Markov chain. This concepts are useful in many applications from robotics to patrolling, environment monitoring and resources optimization. The aforementioned quantities are a performance indexes which measure the expected time taken by a random walker to travel from an arbitrary node of a graph to a second randomly selected node and the expected time to travel between two chosen nodes. These metrics can be used as objective function in optimization problems. In fact we propose a numerical example applied to robotic surveillance where the weighted hitting time is our cost to minimize with respect to the transition matrix of the agent.