The reason to use 3 tier architecture is typically not the performance, at least not the only reason. The benefits lie elsewhere. Have a look at for example
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Multitier architecture[
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N-Tier Architecture and Tips[
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Regarding your comment on business logic and database residing on different systems, this is often true also in 2 tier applications. Having this said, the speed of executing the database commands can be the same in both architectures. The overall execution time from end to end may be different but again this probably wouldn't be the reason to use or abandon n-tier architecture. Cosider for example that if the application and the database originally resided on the same computer the performance may get better if they are separated into different tiers, especially in a situation where they both are consuming heavily a bottleneck resource such as CPU or disk