Signal control strategies for congested urban road networks designed in a centralized framework require many communication links, serious processing power, and infrastructure for the centralized coordination. As a result, strategies based on a centralized framework are not scalable. The use of decentralized signal control strategies for large-scale urban traffic networks is a solution to this problem, since it allows for the implementation of such strategies on networks whose centralized solution is not easily scalable. This paper addresses the problem of designing a decentralized traffic-responsive signal control solution, proposing two methods based on different formulations of the store-and-forward model: (i) the Decentralized Traffic-responsive Urban Control (DTUC) method; and (ii) the Decentralized Decoupled Traffic-responsive Urban Control (D2TUC). The decentralized configuration is such that each intersection is associated with one computational unit, with limited computational power and memory, which controls the traffic signals of the incoming links. Sufficient conditions for the controllability of the considered store-and-forward models are also presented. Both methods are validated resorting to numerical simulations of the urban traffic network of Chania, Greece, for two demand scenarios, and their performance is compared with the performance of the Traffic-responsive Urban Control (TUC) centralized strategy. One of the proposed decentralized methods, D2TUC, is shown to match the performance of TUC.