Road traffic models allow understanding the properties of the traffic and improving traffic control. To do so, the models must be realistic and also understandable (i.e. with few parameters that can be interpreted and calibrated). Macroscopic models are in particular useful for the simulation of large traffic networks. Yet intersection models are under-represented compared to traffic models on links in the literature (especially urban regulated intersection models). In this contribution, we analyse and compare four minimal regulated and unregulated macroscopic intersection models of the first-order. The two unregulated models are the FIFO model (first-in-first-out, i.e. roundabout-type intersection) and an optimal non-FIFO model for which the flow by direction are independent (i.e. highway-type intersection). The control (i.e. traffic light) operates upstream on the flows going-in for the first regulated intersection model while the control takes place downstream on the directions for the second regulated model. We demonstrate mathematical relationships between the intersection models and analyze the performances using Monte-Carlo simulation. The numerical simulations are performed by assuming random demand upstream and supply downstream, and also random direction distributions. This approach allows us to account for average performances but also for standard deviations and more generally for the distributions of the performances. Indeed, reliable intersections should describe ”regular” performances with small variations. We observe that the optimal regulated intersection models overcome the performances of the FIFO model, on average but also in terms of variability (i.e. reliability). Furthermore, bounds for the four intersection models are provided.