  A computer simulation has to be fast to be helpful, if it is employed to
study the behavior of a multicomponent dynamic system. This paper discusses
modeling concepts and algorithmic techniques useful for creating such fast
simulations. Concrete examples of simulations that range from econometric
modeling to communications to material science are used to illustrate these
techniques and concepts. The algorithmic and modeling methods discussed include
event-driven processing, ``anticipating'' data structures, and ``lazy''
evaluation, Poisson dispenser, parallel processing by cautious advancements and
by synchronous relaxations. The paper gives examples of how these techniques
and models are employed in assessing efficiency of capacity management methods
in wireless and wired networks, in studies of magnetization, crystalline
structure, and sediment formation in material science, in studies of
competition in economics.
