  Efficient and faithful parallel simulation of large asynchronous systems is a
challenging computational problem. It requires using the concept of local
simulated times and a synchronization scheme. We study the scalability of
massively parallel algorithms for discrete-event simulations which employ
conservative synchronization to enforce causality. We do this by looking at the
simulated time horizon as a complex evolving system, and we identify its
universal characteristics. We find that the time horizon for the conservative
parallel discrete-event simulation scheme exhibits Kardar-Parisi-Zhang-like
kinetic roughening. This implies that the algorithm is asymptotically scalable
in the sense that the average progress rate of the simulation approaches a
non-zero constant. It also implies, however, that there are diverging memory
requirements associated with such schemes.
