An Overview of Transience Bounds in Max-Plus Algebra
  We survey and discuss upper bounds on the length of the transient phase of max-plus linear systems and sequences of max-plus matrix powers. In particular, we explain how to extend a result by Nachtigall to yield a new approach for proving such bounds and we state an asymptotic tightness result by using an example given by Hartmann and Arguelles. 
Thomas Nowak and Bernadette Charron-Bost
math.CO cs.DM