The cube you mentioned is very heavy as per my experience..even to see small data you need to put enough filters in LISTCUBE.
Step -1 )
For performance tuning kindly analyze how much old data is there by giving hit n trial period selections.
Confirm with business if you need that much old data. After taking confirmation ,delete unnecessary old data from cube.
Step -2 )
Use the aggregates to improve the performance of the cube/report.
Step -3)
Compression of infocube requests would help to improve the reporting.
Let us know if this helps.
Best Regards,
Arpit