Abstract: Data processing apparatus comprises distributed processors for the parallel discrete event simulation of physical processes by the parallel execution of virtual-time-stamped logical processes scheduled by the transmission of virtual-time-stamped messages on logical channels between the processors. Each processor has a clock representing virtual time and ordering forward processing, and a memory for storing a state queue, representative of the physical state at different times of the system upon which the physical processes operate. Each processor is programmed with an operating system supporting optimistic time warp management of the message scheduling and message transmission and of the state queue, allowing interruption of forward processing for local rollback to an earlier virtual time and to earlier states and allowing cancellation of messages upon recognition by the processor of a sequence error in messages received at that or another processor.