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This paper highlights several properties of large urban networks that can have an impact on machine learning methods applied to traffic signal control. In particular, we show that the average network flow tends to be independent of the signal control policy as density increases. This property, which so far has remained under the radar, implies that deep reinforcement learning (DRL) methods becomes ineffective when trained under congested conditions, and might explain DRL's limited success for traffic signal control. Our results apply to all possible grid networks thanks to a parametrization based on two network parameters: the ratio of the expected distance between consecutive traffic lights to the expected green time, and the turning probability at intersections. Networks with different parameters exhibit very different responses to traffic signal control. Notably, we found that no control (i.e. random policy) can be an effective control strategy for a surprisingly large family of networks. The impact of the turning probability turned out to be very significant both for baseline and for DRL policies. It also explains the loss of symmetry observed for these policies, which is not captured by existing theories that rely on corridor approximations without turns. Our findings also suggest that supervised learning methods have enormous potential as they require very little examples to produce excellent policies.