Even given today’s rich hardware platforms, computation-intensive algorithms and applications, such as large-scale simulations, are still challenging to run with acceptable response times. One way to increase the performance of these algorithms and applications is by using the computing power of Graphics Processing Units (GPU). However, effectively mapping distributed software models to GPU is a non-trivial endeavor. In this paper, we investigate ways of improving execution performance of multi-agent systems (MAS) models by means of relevant task allocation mechanisms, which are suitable for GPU execution. Several task allocation architecture variants for MAS using GPU are identified and their properties analyzed. In particular, we study three cases: Agents and their runtime environment can be (i) completely on the host (CPU); (ii) partly on host and device (GPU); (iii) completely on the device. For each of these architecture variants, we propose task allocation models that take GPU restrictions into account.