This paper proposes the derivation of a physics- based model of an analog memristive device realized as a bi-layer Al2O3/Nb2O5 stack. Memristive crossbar arrays implementing matrix-vector multiplications are a central building block of novel computing-in-memory architectures for artificial neural network and neuromorphic computing applications. The presented memristor shows analog, multi-level switching at high resistances without electroforming and is suitable for crossbar operations with low energy consumption. By including a graphical analysis method of the I-V curves obtained in a quasi-static approach, the dynamic behavior is analyzed with regard to ohmic and Poole- Frenkel behavior. Finally, a compact model, represented by an algebraic differential equation, is proposed and verified by fitting calculated solutions to experimental data.