Multi-robot task allocation (MRTA) problems require that robots take complex choices based on their understanding of a dynamic and uncertain environment. As a distributed computing system, the Multi-Robot System (MRS) must handle and distribute processing tasks (MRpTA). Each robot must contribute to the overall efficiency of the system based solely on a limited knowledge of its environment. Market-based methods are a natural candidate to deal processing tasks over a MRS but recent and numerous developments in reinforcement learning and especially Deep Q-Networks (DQN) provide new opportunities to solve the problem. In this paper we propose a new DQN-based method so that robots can learn directly from experience, and compare it with Market-based approaches as well with centralized and purely local solutions. Our study shows the relevancy of learning-based methods and also highlight research challenges to solve the processing load-balancing problem in MRS.