The control of an arbitrary network of signalized intersections is considered. At the beginning of each cycle, a controller selects the duration of every stage at each intersection as a function of all queues in the network. A stage is a set of permissible (non-conflicting) phases along which vehicles may move at pre-specified saturation rates. Demand is modeled by vehicles entering the network at a constant average rate with an arbitrary burst size and moving with pre-specified average turn

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... ios. The movement of vehicles is modeled as a "store and forward" queuing network. A controller is said to stabilize a demand if all queues remain bounded. The max-pressure controller is introduced. It differs from other network controllers analyzed in the literature in three respects. First, max-pressure requires only local information: the stage durations selected at any intersection depends only on queues adjacent to that intersection. Second, max-pressure is provably stable: it stabilizes a demand whenever there exists any stabilizing controller. Third, max-pressure requires no knowledge of the demand, although it needs turn ratios. The analysis is conducted within the framework of "network calculus," which, for fixed-time controllers, gives guaranteed bounds on queue size, delay, and queue clearance times.