We model and analyze a futuristic intersection that serves only connected, autonomous andcentrally managed vehicles. Under consideration are three control strategies that aim tominimize the total system delay by choosing an optimal trajectory for each vehicle. The firsttwo abandon the concept of signal timing all together whereas the third strategy keeps it. Thedifference between the two signal-free strategies has to do with a fail-safe buffer requirementintroduced to provide redundancy. Each control strategy leads to a unique version of atrajectory-based autonomous intersection management (T-AIM) problem, which is formulatedas a mixed integer linear program and solved using both a commercial solver and a specializedheuristic algorithm. We find the signal-free strategy holds an overwhelming advantage over thesignal-based strategy in terms of efficiency. However, its success is fragile and dependent onthe faith in the safety and reliability of the system. When the fail-safe buffer is introduced,the efficiency of the signal-free strategy degrades to a level comparable to that of a properlyoptimized signal-based strategy. Surprisingly, the signal-free strategy with redundancy tends toarrange vehicles in groups that take turns to cross the intersection together. This ''signal-likebehavior" manifests itself whenever congestion rises to a certain threshold. In addition, solvingthe T-AIM problem based on signal timing enjoys significant computational benefits, because iteliminates many conflicts. Thus, the basic logic of signal timing - if not the physical equipment- may survive even after humans are no longer allowed to drive.