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Quick diagnosis is critical to stroke patients, but it relies on expensive and heavily used imaging equipment. This results in long waiting times with potential threats to the patient's life. It is important for neurovascular departments treating stroke patients to reduce waiting times for diagnosis. This paper proposes a reservation process of magnetic resonance imaging (MRI) examinations for stroke patients. The neurovascular department reserves a certain number of appropriately distributed contracted time slots (CTS) to ensure quick diagnosis of stroke patients. Additional MRI time slots can also be reserved by regular reservations (RTS). The problem consists in determining the contract and the control policy to assign patients to either CTS or RTS in order to reach the best compromise between the waiting times and unused CTS. Structural properties of the optimal control policy are proved by an average-cost Markov decision process (MDP) approach. The contract is determined by combining a Monte Carlo approximation approach and local search. Extensive numerical experiments are performed to show the efficiency of the proposed approach and to investigate the impact of different parameters.