With the attractive feature of guaranteeing maximum network throughput, backpressure routing has been widely used in wireless communication networks. Motivated by the backpressure routing, in this paper, we propose a delay-based traffic signal control algorithm in transportation networks. We prove that this delay-based control achieves optimal throughput performance, same to the queue-based traffic signal control in literature. However, a vehicle at a lane whose queue length remains very small

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... ay be excessively delayed under queuebased signal control. Our delay-based backpressure control can deal with the excessive delays, and achieve better fairness with respect to delay, while still guaranteeing throughput optimality. Moreover, a general weighted control scheme combining the queue-based and delay-based schemes is also investigated, to provide a more flexible control according to the quality of service requirements. Numerical results explore their performance under both homogeneous and heterogeneous traffic scenarios.