Providing security for protecting critical infrastructure is a key concern among the world nations, given the rising menace of terrorism. Due to limited security resources, full security coverage of targets (infrastructure) at all times is not possible. Efficient surveillance and allocation of security personnel among targets is an important problem in several real life security scenarios. The adversaries may observe and exploit patterns in selective surveillance of targets. Therefore, there is a need for efficiently allocating security personnel to targets. This calls for randomised strategies for personnel allocation and surveillance. We use a game-theoretic approach for modeling and studying such security problems. The problem is modeled as a security game built upon the Stackelberg game model. The game is played between two players - the Leader (Defender) and the Follower (Attacker). Our model provides an optimal randomized strategy for the leader (security personal), under the assumption that the follower (adversary) will conduct surveillance before launching an attack on the target. Analysing the optimal defender's strategies under a variety of settings helps in optimal resource allocation and planning for surveillance.