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Could you further define what you mean by providing minimum bandwidth?
If you mean last to get bandwidth, use a bandwidth statement rather than the priority statement. Setting to 8, I recall, will provide the lowest possible dequeuing priority.
Then match the traffic you want to provide this low priority to.
You might also consider a generic policy such as:
policy-map generic
class LLQ
priority percent 33
class HiPriority
bandwidth remaining percent 81
fair-queue
class LoPriority
bandwidth remaining percent 1
fair-queue
class class-default
bandwidth remaining percent 9
fair-queue
The above (as a model) often addresses about 99% of any QoS needs (for congestion management), just direct traffic to the "correct" class.
