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Event simulation allows the design to contain simple timing information - the delay needed for a signal to travel from one point to another. During simulation, signal changes are tracked in the form of events. A change at a certain time triggers an event after a certain delay. Events are sorted by time when they will occur, and when all events for a particular time have been handled, the simulated time is advanced to the time of the next scheduled event. How fast an event simulation runs depends on the number of events to be processed (the amount of activity in the model).
In cycle simulation, it is not possible to specify delays. A cycle-accurate model is used, and every gate is evaluated in every cycle. Cycle simulation therefore runs at a constant speed, regardless of activity in the model. Optimized implementations may make take advantage of low model activity to speed up simulation by skipping evaluation of gates whos inputs didn't change.
While event simulation can provide some feedback regarding signal timing, it is not a replacement for static timing analysis.
In comparison to event simulation, cycle simulation tends to be faster, to scale better, and to be better suited for hardware acceleration / emulation.