Modeling Timed Systems

This chapter is devoted to modeling timing in complex systems. We begin with a discussion of clocks, with particular emphasis on multiform time. We then illustrate how to use multiform time in three particular modeling problems. First, we consider clock synchronization, where network protocols are used to correct clocks in distributed systems to ensure that the clocks progress at approximately the same rates. Second, we consider the problem of assessing the effect of communication delays on the behavior of systems. And third, we consider the problem of assessing the effect of execution time on the behavior of systems. We then conclude the chapter with an introduction to a programming model called Ptides that makes possible systems whose behavior is unaffected by variations in the timing of computation and networking, up to a point of failure. The Ptides model of computation enables much more deterministic cyber-physical systems