This study explores the limiting properties of network-wide traffic flow relations under heavily congested conditions in a large-scale complex urban street network; these limiting conditions are emulated in the context of dynamic traffic assignment (DTA) experiments on an actual large network. The primary objectives are to characterize gridlock and understand its dynamics. This study addresses a gap in the literature with regard to the existence of exit flow and recovery period. The one- dimensional theoretical Network Fundamental Diagram (NFD) only represents steady-state behavior and holds only when the inputs change slowly in time and traffic is distributed homogenously in space. Also, it does not describe the hysteretic behavior of the network traffic when a gridlock forms or when network recovers. Thus, a model is proposed to reproduce hysteresis and gridlock when homogeneity and steady-state conditions do not hold. It is conjectured that the network average flow can be approximated as a non-linear function of network average density and variation in link densities. The proposed model is calibrated for the Chicago Central Business District (CBD) network. We also show that complex urban networks with multiple route choices, similar to the idealized network tested previously in the literature, tend to jam at a range of densities that are smaller than the theoretical average network jam density. Also it is demonstrated that networks tend to gridlock in many different ways with different configurations. This study examines how mobility of urban street networks could be improved by managing vehicle accumulation and re-distributing network traffic via strategies such as demand management and disseminating real-time traveler information (adaptive driving). This study thus defines and explores some key characteristics and dynamics of urban street network gridlocks including gridlock formation, propagation, recovery, size, etc.