Discounting in Time

This paper deals with the issue of discounting in weighted timed transition systems. Discounting provides a way to model optimal-cost problems for infinite runs and has applications in optimal scheduling and other areas.We show that when postulating a certain natural additivity property for the discounted weights of runs, there is essentially only one possible way to introduce a discounting semantics. Our proof relies on the fact that a certain functional equation essentially only has one solution, for which we provide an elementary proof.