I'm computing tasks from Asteroids@home and ClimatePrediction.net having a resource share ratio of 1:10 000, respectively. I want BOINC to prefer ClimatePrediction.net over Asteroids@home always when there are tasks available for ClimatePrediction.net. But still BOINC suspends ClimatePrediction.net tasks over Asteroids@home even with the huge resource share ratio. Is there a way to fix this? Only reason I have Asteroids@home tasks is to avoid unused processing time going to waste when there are not enough tasks for ClimatePrediction.net.

I actually tried that but it didn't change anything.

I'm computing tasks from Asteroids@home and ClimatePrediction.net having a resource share ratio of 1:10 000, respectively. I want BOINC to prefer ClimatePrediction.net over Asteroids@home always when there are tasks available for ClimatePrediction.net. But still BOINC suspends ClimatePrediction.net tasks over Asteroids@home even with the huge resource share ratio. Is there a way to fix this? Only reason I have Asteroids@home tasks is to avoid unused processing time going to waste when there are not enough tasks for ClimatePrediction.net.

Set Asteroids@home to share 0 zero. That way BOINC will only look to get a task when CPDN fails to send one and the cache is getting empty. HOWEVER once that task is sent, it will compute to completion in such a manner as it does not miss deadline no matter what the resource share percent you have set. The larger the difference the more the priority will be backwards to what you expect. This because of EDF (Earliest Deadline First) mode being forced on. EDF gets set because there isn't enough regular compute time with the large ratio to finish before deadline.

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The BOINC "resource share" is a long time base average effort share, not (as one might expect) a fixed time per project. Thus, over time, the effort per project will tend to the ratios of the shares you assign to each project.
The exception to this is "zero share" projects, which will only get work when there is no work available from projects with non-zero shares.