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i would start with testing each of them independently (queue, processor and logger) for all possible scenarios. For example; for a queue i would test the push, pop, isempty and other such functions for different states of the queue. Same for the processor and logger by creating a stub queue for processor and a stub processor for logger.

like muhammd said

start by testing all possible scenarios for each of the parts in the system
queues, processor, and logger

for queues check enqueue dequeue operations,case of empty queues,
for processor, cases like read failure write failure, what happens if the power is lost during reading, during writing, what back up mechanism?? make sure the processor reads and writes at exactly hour apart.

a logger can have several scenarios since it connects to the database. what happens when there are no files, what does it write to database, power failures, back up mechanisms, database failures, connection failures,


Then go to the interface testing. what will the processor do if the queue is empty.
if it fails to read data, then what happens to the logger, what would it write to the database.

Individual testing of queue, processor and logger
Intra module tests bw q&p, p&l and q,p&l
End to end tests (postive test)
Integration tests
Negative End-2-End tests
Exception handling
Failure recovery

-- Queue has provided so much data that file that is being created by processor has crossed file size limit( say a file greater than 4 GB),, Will it create new file for the same hour