With the increase in the urban population witnessed in all major cities worldwide, efficient urban traffic planning, modeling and control are indispensable. In this paper we propose a novel macro-model for urban networks based on queuing theory and cast in a state-space representation. The model for each junction incorporates a switching mechanism capturing both the nonlinear dynamics of normal traffic conditions and the linear evolution of vehicle queues during junction block-back scenarios. Moreover, while competing models suffer a quadratic increase in computational cost with every added junction, our model exhibits only a linear increase in dimensionality and thus significantly lowers its computational demands. The simulation results from the proposed model are validated against a standard micro-modelling simulation package. These results will demonstrate through a Monte Carlo simulation that given correct model parameters, the proposed macro-model can well capture the complex vehicle dynamics of an urban region, thus paving the way for an accurate analysis of the network and for the development of efficient urban traffic control strategies.