Distributed Preemption Decisions: Probabilistic Graphical Model, Algorithm and Near-Optimality

Cooperative decision making is a vision of future network management and control. Distributed connection preemption is an important example where nodes can make intelligent decisions on allocating resources and controlling traffic flows for multi-class service networks. A challenge is that nodal decisions are spatially dependent as traffic flows trespass multiple nodes in a network. Hence the performance-complexity trade-off becomes important, i.e., how accurate decisions are versus how much information is exchanged among nodes. Connection preemption is known to be NP-complete. Centralized preemption is optimal but computationally intractable. Decentralized preemption is computationally efficient but may result in a poor performance. This work investigates distributed preemption where nodes decide whether and which flows to preempt using only local information exchange with neighbors. In this work, we first model a large number of distributed preemption-decisions using a probabilistic graphical model. We then define the near-optimality of distributed preemption as its approximation to the optimal centralized preemption within a given error bound. We show that a sufficient condition for distributed preemption to be optimal is that local decisions should constitute a Markov Random Field. The decision variables, however, do not possess an exact spatial Markov dependence in reality due to the flows passing through multiple links. Hence we study traffic patterns of flows, and derive sufficient conditions on flows for the distributed preemption to be near-optimal. We develop, based on the probabilistic graphical models, a near-optimal distributed algorithm. The algorithm is used by each node to make collectively near-optimal preemption decisions. We study trade-offs between near-optimal performance and complexity that corresponds to the amount of information-exchange of the distributed algorithm. The algorithm is validated by both analysis and simulation.