We present and analyze a new aggregate model of urban traffic. The objective is to analytically capture the correlation between the different components of the network while maintaining a tractable model that can be used in an optimization framework. Existing analytical queueing models for urban networks are formulated for a single intersection, and thus do no take into account the interactions among upstream and downstream roads. We formulate a model that considers a set of intersections and captures the correlation structure between consecutive roads based on finite capacity queueing theory. It therefore provides a detailed description of congestion. It identifies the sources of congestion (e.g. bottlenecks), describes how congestion propagates and dissipates; and quantifies the impact on the network performance. We use the model in the context of fixed-time traffic signal optimization. Although there is a great variety of signal control methodologies in the literature, there is still a need for solutions that are appropriate and efficient under saturated conditions, where the performance of signal control strategies and the formation and propagation of queues are strongly related. To the best of our knowledge, the existing signal control strategies based on analytical network models have not taken spillbacks into account. We formulate a fixed-time signal control problem where the network model is included as a set of constraints. We apply this methodology to a subnetwork of the Lausanne city center and use a microscopic traffic simulator to analyze its performance. We compare its performance to that of several other methods. The results show the importance of taking the correlation between consecutive roads into account.