Past research in theoretical computer science has focused mainly on static computation problems, where the input is known before the start of the computation and the goal is to minimize the number of steps till termination with a correct output. Many important processes in today’s computing are dynamic processes, whereby input is continuously injected to the system, and the algorithm is measured by its long term, steady state, performance. Examples of dynamic processes include communication protocols, memory management tools, and time sharing policies. Our goal is to develop new tools for the design and analyzing the performance of dynamic processes, in particular through modeling the dynamic process as an infinite stochastic processes.