  The scalability of massively parallel algorithms is a fundamental question in
computer science. We study the scalability and the efficiency of a conservative
massively parallel algorithm for discrete-event simulations where the discrete
events are Poisson arrivals. The parallel algorithm is applicable to a wide
range of problems, including dynamic Monte Carlo simulations for large
asynchronous systems with short-range interactions. The evolution of the
simulated time horizon is analogous to a growing and fluctuating surface, and
the efficiency of the algorithm corresponds to the density of local minima of
this surface. In one dimension we find that the steady state of the macroscopic
landscape is governed by the Edwards-Wilkinson Hamiltonian, which implies that
the algorithm is scalable. Preliminary results for higher-dimensional logical
topologies are discussed.
