The idea behind the miller cycle concept is to run a boosted engine using a higher nominal compression ratio then is conducive (for typical Otto-cycle valve events) in terms of full load knock (eg.11:1 vs 9:1). It has been used successfully in production by Mazda on their Millennium and Xedos 9 ranges.
The Miller cycle theory uses the fact that thermal efficiency is connected more with a high expansion ratio (or Nominal Compression Ratio) then it is to the dynamic compression ratio. With this in mind a Miller cycle engine typically uses a late intake valve closing event to lower the effective compression ratio and not be severely knock limited at WOT. In addition during tests I found that knock limit is raised by the later IVC point allowing the ignition to be further advanced because the initial compression cycle temperature is lowered. However despite the lower overlap, combustion stability is adversely effected due to late start of compression (not really a great bother at full load)
Part load fuel economy benefits not only from the raised compression ratio but also from the lowered pumping loss from the late intake valve closing (collectively estimated at 6 % plus)
Unfortunately these valve events are far from optimum for full load performance and this is where an efficient supercharger is required to work hard to get the performance back to optimal. A Roots blower is not wholly appropriate as it becomes inefficient at pressure ratios above 2 and a Turbo charger typically has lag/response issues. A Lysholm compressor is more efficient and can operate at pressure ratios in excess of 2. On the one hand the intercoolers would have to very efficient because the supercharger would be made to work harder, however the Lysholm compressor is inherently more efficient then the Roots blower so some of this is offset. It is was found that the compromise depended on the intake valve timing chosen for the engine to operate knock free at the nominal CR chosen and the level of the lysholm was required to operate at to achieve the desired performance. It seems obvious that the Miller cycle route should only be pursued if, when using typical conventional otto cycle valve events and a 9:1 CR, a lot of performance reserve is in hand in terms of the Lysholm compressor not exceeding its maximum recommended speed or efficient pressure ratio.
The issues with using a Lysholm compressor arise from needing to de clutch it at part load to realise fuel economy benefit. This is because, unlike a Roots blower which can simply be bypassed/recircuated post charger with minimal impact on part load fuel economy, a Lysholm Compressor does internal compression work. Clutching the supercharger has adverse implications on transient driveability which is unacceptable for cars in most market segments. Not clutching the Lysholm compressor at part load was deemed to have a fuel economy defecit of the order of about 5%. This invalidates the estimated gains from running miller cycle.