This paper proposes a decentralized network-level traffic signal control method addressing the effects of queue spillbacks. The method is traffic-responsive, does not require data communication between intersections' controllers, uses lane-based queue measurements, and is acyclic. Each traffic controller operating at an intersection aims at maximizing the effective outflow rate locally and independently with the goal of maximizing global throughput of the entire network. At each intersection, the signal control method estimates and adopts the maximum possible phase time in which all active movements discharge at their full capacity. This is modeled using a shockwave based queue length estimation model while capturing the spillback at the downstream links. The method demands real-time data including, the queue lengths, the arrival flows, and the downstream queue lengths in all the lanes at the control decision times. The proposed method results in a feasible solution in all conditions in the entire network with any scale within a short amount of time. A stability concept for the traffic network is defined, and asymptotic stability of the controlled traffic network are verified. Moreover, a sufficient condition for the optimality of the proposed control algorithm for maximizing the instantaneous total throughput of the network intersections is demonstrated. Numerical results show that the proposed method outperforms benchmark methods in both isolated intersection and network configurations.