I have been working as a software consultant for more than 11 years. Because of that I am an eager supporter of lean principles and agile methods.
How do we approach the problem with overwhelmingly large backlogs? The answer is simple. Make sure the backlog is prioritized first and then simply throw away the lower half. It sounds controversial but it’s all about limiting work to capacity. Having too large backlogs means that you are building inventory and inventory is waste that eventually degrades and becomes obsolete.
Instead adapt your backlog to your output capacity. If you are afraid of loosing important features in this process you need not worry, if they are important they will eventually reappear. Having a smaller backlog also makes you more responsive to new features and it consumes less resources.
These conclusions can be drawn by studying Lean Manufacturing Principles, which partially originates from queuing theory.