Reconfigurable Intelligent Surfaces (RIS) have recently emerged as a hot research topic, being widely advocated as a candidate technology for next generation wireless communications. These surfaces passively alter the behavior of propagation environments enhancing the performance of wireless communication systems. In this paper, we study the use of RIS in cell-free multiple-input multiple-output (MIMO) setting where distributed service antennas, called Access Points (APs), simultaneously serve the users in the network. While most existing works focus on the physical layer improvements RIS carry, less attention has been paid to the impact of dynamic arrivals and departures of the users. In such a case, ensuring the stability of the network is the main goal. For that, we propose an optimization framework of the phase shifts, for which we derived a low-complexity solution. We then provide a theoretical analysis of the network stability and show that our framework stabilizes the network whenever it is possible. We also prove that a low complexity solution of our framework stabilizes a guaranteed fraction (higher than 78.5%) of the stability region. We provide also numerical results that corroborate the theoretical claims.

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