Pause model execution may take several seconds before displaying the stack

When running a model a relatively high number of steps (several thousands logical steps), then pause the execution (for example using the UI)
then the debug stack view may take time before being filled and available. (it may last several seconds)

I experimented that using the JavaEngine but I suspect that all engines could be impacted.

Other symptoms:
in the language workbench, in the debug view, some threads blink (very quickly). The debug UI in the modeling workbench becomes available when the blinking in the language workbench stops.

I succeed to pause on one of those "blink":

Apparently, a big bunch of "Check Debug Command" are queued and processed when pausing.
(related to org.eclipse.debug.core.commands.AbstractDebugCommand.UpdateJob)

Need further investigation in order to find out why.