Does livy support concurrency for centain spark session?

To use spark sql concurrency for internal fair schedule
in [post] /sessions/

{id}

/statements use param "conf":

{"spark.scheduler.mode":"FAIR","spark.scheduler.allocation.file":"/home/.../spark-schedule.xml"}

spark-schedule.xml is as follows:
<allocations>
<pool name="FAIR">
<schedulingMode>FAIR</schedulingMode>
</pool>
</allocations>

Log shows tow jobs surely be added into fair pool:
INFO scheduler.FairSchedulableBuilder: Added task set TaskSet_10.0 tasks to pool FAIR
...
INFO scheduler.FairSchedulableBuilder: Added task set TaskSet_11.0 tasks to pool FAIR

But from spark web console the second job starts only when the first finished.
I also tried with zeppelin, which concurrency works well with spark but not work in livy.
Did I miss some configuration? Thanks.