Actor programs give rise to computation structures that evolve dynamically and unpredictably both in shape and size. Therefore, their execution times cannot be statically determined. This paper describes an approach to the problem of estimating time costs of actor programs. The approach takes into account the constraints imposed both by the semantics and implementation of the model. In particular, implementation constraints can be captured and exploited to drastically reduce the number of computations generable by the program, thus simplifying the execution time evaluation. Moreover, execution times are expressed in a parametric form by using a variant of the LogP model able to synthetically characterize the target hardware/software platform.