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Please shed some light on me.
How real-time system defines that events happened simultaneously?
1. By the time they occurred?
2. By the time range they occurred?
Thanks in advance.
You should take a look on Operational Transformation algorithms, they deal perfectly with concurrent events with continuous integration.
An OT enabled system is able to accept time-concurrent events and transform these events, if necessary, so State in server and all clients Converge.
Or to say in other way is able to manage client “divergence” due network latency and make all client and server to finish in same state with “operations” applied in a well-defined order.
Google Wave was an example of a system using OT for Concurrent Editing, here you can see a rude explanation on how Google Wave deal with OT. and here you have a very well develop explanation.