  We study the convergence in expectation of the Random Coordinate Descent
algorithm (RCD) for solving optimal resource allocations problems in open
multi-agent systems, i.e., multi-agent systems that are subject to arrivals and
departures of agents. Assuming all local functions are strongly-convex and
smooth, and their minimizers lie in a given ball, we analyse the evolution of
the distance to the minimizer in expectation when the system is occasionally
subject to replacements in addition to the usual iterations of the RCD
algorithm. We focus on complete graphs where all agents interact with each
other with the same probability, and provide conditions to guarantee
convergence in open system. Finally, a discussion around the tightness of our
results is provided.
