  Scramble intersections stand as compelling examples of complex systems,
shedding light on the pressing challenge of urban mobility. In this paper, we
introduce a model aimed at unraveling the statistical intricacies of pedestrian
crossing times and their fluctuations in scenarios commonly encountered in
major urban centers. Our findings offer snapshots that faithfully mirror
real-world situations. Significantly, our results underscore the importance of
two key factors: pedestrian flexibility and population density. These factors
play a pivotal role in triggering the transition between mobile and immobile
behavior in the steady state, a concept expounded upon within this paper
through a straightforward order parameter known as directed mobility.
