Running an algorithm for fixed amount of time on RAM model machine Suppose there is a deterministic algorithm of size $O(1)$ that operates on an input of size $N$ on a RAM model machine. I want to run the algorithm for $O(\sqrt{N})$ time, pause the algorithm, print "Hello", and then resume its execution, run it again for $O(\sqrt{N})$ time and repeat this cycle until the algorithm execution terminates. If the algorithm takes time $T$, then there would be $O(T/\sqrt{N})$ print statements.

It is obvious that an algorithm can be paused/resumed in constant time by storing/loading the content of all registers of the CPU in the memory. However, how is it possible to measure elapsed time in the RAM model and stop the algorithm after $O(\sqrt{N})$ steps? Does the RAM model support such an operation (a Turing machine definitely does)? Any reference or a simple argument is welcome!
One approach is to implement an interpreter for the RAM model, and then instrument the interpreter with a counter that keeps track of the number of instructions executed.  I suspect it should be possible to build an interpreter that incurs at most a $O(1)$-factor slowdown, but I haven't checked the details (the instruction set is so primitive that the programming is ugly) -- you should be able to check whether the obvious approach works.