  Service federation in 5G/B5G networks enables service providers to
orchestrate network services across multiple domains where admission control is
a key issue. For each demand, without knowing the future ones, the admission
controller either determines the domain to deploy the demand or rejects it in
order to maximize the long-term average profit. In this paper, at first, under
the assumption of knowing the arrival and departure rates of demands, we obtain
the optimal admission control policy by formulating the problem as a Markov
decision process that is solved by the policy iteration method. As a practical
solution, where the rates are not known, we apply the Q-Learning and R-Learning
algorithms to approximate the optimal policy. The extensive simulation results
show the learning approaches outperform the greedy policy, and while the
performance of Q-Learning depends on the discount factor, the optimality gap of
the R-Learning algorithm is at most 3-5% independent of the system
configuration.
