Since the release update of 2016-11-18 we can now mark a Logic App trigger as “Singleton”.
Which results in a Logic App that will run as only one instance at a time. To be more precise: it is the trigger who will not fire unless the previous instance of the Logic App has fully completed.
A trigger which was skipped because of a running instance will result in a “WorkflowRunInProgress” code.
Marking a trigger as singleton
Currently there is no possibility to mark a trigger as singleton in the designer. You need to switch to codeview and add the following at the same level as the recurrence property.
As soon as you save, the setting will become active and your Logic App will run as a singleton.