A comprehensive model is presented of erbium-doped integrated optical waveguide amplifiers that include high concentration dissipative ion-ion interactions. Calculations based on actual waveguide parameters closely reproduce measured gains for different pump powers and different erbium concentrations up to 60 x 10(24) m-3. The quenching concentration for erbium-doped phosphate glass is found to be 20-30 x 10(24) m-3.