In use case modelling, if I have functions that have to be done by the system itself (without actors), how can I represent them?
For example, sending SMS message, compute bus route, or notify someone when a change occur.
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A function performed by the system is not a use case. It is an action which is part of a use case. A use case is some added value it's primary actor gets when applying the use case.
You can represent them as use cases of sub-function level and performed by the system as primary actor.