This study shows how the performance of a parallel simulation may be affected by the structure of the system being simulated. We consider a wide class of “linearly synchronous” simulations consisting of asynchronous and synchronous parallel simulations (or other distributed-processing systems), with conservative or optimistic protocols, in which the differences in the virtual times of the logical processes being simulated in real time t are of the order o(t) as t tends to infinity. Using a random time transformation idea, we show how a simulation's processing rate in real time is related to the throughput rates in virtual time of the system being simulated. This relation is the basis for establishing upper bounds on simulation processing rates. The bounds for the rates are tight and are close to the actual rates as numerical experiments indicate. We use the bounds to determine the maximum number of processors that a simulation can effectively use. The bounds also give insight into efficient assignment of processors to the logical processes in a simulation.