Overflow of integer counter in distributed systems
In general:


  Paxos algorithm uses unbounded integers to tag data. In practice,
  however, every integer handled by the processors is bounded by some
  constant $2^b$ where $b$ is the integer memory size. Yet, if every integer
  variable is initialized to a very low value, the time needed for
  any such variable to reach the maximum value $2^b$ is actually way
  larger than any reasonable system’s timescale. For instance,
  counting from $0$ to $2^{64}$ by incrementing every nanosecond takes roughly
  500 years to complete. Such a long sequence is said to be practically
  infinite.


Self-stabilizing systems:


  One particular aspect of self-stabilizing systems is the need to
  re-examine the assumption concerning the use of (practically)
  unbounded time-stamps. While in practice it is reasonable for Paxos to
  assume that a bounded value, represented by 64 bits, is a natural
  (unbounded) number, for all practical considerations, in the scope of
  self-stabilization the 64 bits value may be corrupted by a transient
  fault to its maximal value at once, and still recovery following such
  a transient fault must be guaranteed.


Source: Self-Stabilizing Paxos