  We consider a perimeter surveillance problem introduced by Kingston, Beard,
and Holt in 2008 and studied by Davis, Humphrey, and Kingston in 2019. In this
problem, $n$ drones surveil a finite interval, moving at uniform speed and
exchanging information only when they meet another drone. Kingston et al.
described a particular online algorithm for coordinating their behavior and
asked for an upper bound on how long it can take before the drones are fully
synchronized. They divided the algorithm's behavior into two phases, and
presented upper bounds on the length of each phase based on conjectured
worst-case configurations. Davis et al. presented counterexamples to the
conjecture for phase 1.
  We present sharp upper bounds on phase 2 which show that in this case the
conjectured worst case is correct. We also present new lower bounds on phase 1
and the total time to synchronization, and report partial progress towards
obtaining an upper bound.
