The Internet motivated video streaming systems are largely complicated by issues such as a high degree of network resource sharing amongst many flows, which potentially leads to deadlocks. Using concepts of siphons along with their corresponding dangerous markings, we derive an algebraically necessary and sufficient characterization for such a much undesirable situation. The target system is assumed to be described in a Petri net formalism, whose markings provide the information on the current interactions among related network operations and resources. The theoretic materials allow us to introduce the control laws iteratively. At each iteration step, we produce a generalized mutual exclusion constraint which contains only markings for which liveness can be enforced. Since the explicit enumeration of all siphons is avoided, the proposed method can greatly reduce the complexity of off-line computation for the on-line restriction policy. Furthermore, a generalized elementary siphon control investigation is involved such that the final supervisor can be structurally simplified. Examples are demonstrated in this paper to validate the effectiveness and efficiency of the proposed approach.