Big data processing is driven by new types of in-memory database systems. In this paper we apply performance modeling to efficiently optimize workload placement for such systems. In particular, we propose novel response time approximations for in-memory databases based on fork-join queuing models and contention probabilities to model variable threading levels and per-class memory occupation under analytical work-loads. We combine these approximations with a non-linear optimization methodology that seeks for optimal
load dispatching probabilities in order to minimize memory swapping and resource utilization. We compare our approach with state-of-the-art response time approximations using real data from an SAP HANA in-memory system and show that our models markedly improve accuracy over existing approaches, at similar computational costs.