  Bertrand et al. introduced a model of parameterised systems, where each agent
is represented by a finite state system, and studied the following control
problem: for any number of agents, does there exist a controller able to bring
all agents to a target state? They showed that the problem is decidable and
EXPTIME-complete in the adversarial setting, and posed as an open problem the
stochastic setting, where the agent is represented by a Markov decision
process. In this paper, we show that the stochastic control problem is
decidable. Our solution makes significant uses of well quasi orders, of the
max-flow min-cut theorem, and of the theory of regular cost functions. We
introduce an intermediate problem of independence interest called the
sequential flow problem and study its complexity.
