The authors study the adaptation of an optimistic Time Warp kernel to cross-cluster computing on the Grid. Wide-area communication, the primary source of overhead, is offloaded onto dedicated routing processes. This allows the simulation processes to run at full speed and thus significantly decreases the performance gap caused by the wide-area distribution. Further improvements are obtained by employing message aggregation on the wide-area links and using a distributed global virtual time algorithm. The authors achieve many of their objectives for a cellular automaton simulation with lazy cancellation and moderate communication. High communication rates, especially with aggressive cancellation, present a challenge. This is confirmed by the experiments with synthetic loads. Even then, a satisfactory speedup can be achieved, provided that the computational grain of events is large enough.