DB performance issue

Hi,
I am seeing performance issue in our 2 node RAC 10.2.0.3 DB between 10:00 PM and 11:00 PM. Statspack report shows latch: library cache among Top 5 Timed Events. Node 1 alert log has "WARNING: inbound connection timed out (ORA-3136)" . We have RMAN backup running during this period. My initial suspicion for the performance issue is DEFAULT_MAINTENANCE_PLAN window and RMAN backup window falling during the same period. Could this be causing issues here?

Statspack Profile
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Load Profile                            Per Second       Per Transaction
~~~~~~~~~~~~                       ---------------       ---------------
                  Redo size:             73,581.41                298.65
              Logical reads:            230,650.73                936.17
              Block changes:                458.20                  1.86
             Physical reads:                 73.43                  0.30
            Physical writes:                 40.18                  0.16
                 User calls:              7,070.54                 28.70
                     Parses:              1,529.13                  6.21
                Hard parses:                  1.03                  0.00
                      Sorts:                201.37                  0.82
                     Logons:                  1.14                  0.00
                   Executes:              2,113.61                  8.58
               Transactions:                246.38