For SSAS, it is sometimes good to separate deployment into multiple database servers, depending on sizing, availability and performance requirements (and budget of course).
The primary reasons for splitting up the servers is that both SQL Server relational database instance and Analysis Services multidimensional instance utilize large amounts of memory and also have different disk usage patterns. Performance may be impacted
if both are on same server. Same goes for Tabular instance and Sharepoint services.
Not sure what application server you are referring to...
If you can give further details on your scenario please do.
Andrew Sears, T4G Limited, http://www.performancepointing.com