We present a Markov Chain Monte Carlo (MCMC) based stochastic strategy for a robotic surveillance problem. We justify the use of stochastic strategies by showing that deterministic strategies have inherent limitations which make them unsuitable for the posed problem. We also consider the problem of surveillance with multiple agents in both centralized and decentralized setting. The centralized setting suffers from the problem of explosion in the number of states. We show that by incorporating permutation symmetry we can effectively reduce the size of the problem. For the decentralized case we show the issue of conflict resolution among the agents can be cast in the framework of finding a maximum weighted matching in a bipartite graph. We then provide a distributed implementation of the auction algorithm based on message passing which solves the conflict resolution problem.