Whether or Not to Allow Preoccupation of Seats in Cafeteria Queues

Our queueing model is motivated by cafeterias where food and seats are provided. Cafeterias vary according to the policy they impose on the preoccupation of seats: customers are either allowed to secure the seats before the food or they should first obtain the food and next take the seats. We analyze the problem of selecting the policy that results in higher social welfare using a stylized fluid model. First, the dynamics of the system are identified in both of the policies. These results are used to construct stationary states of the system. Finally, the social welfares in the stationary states from both of the policies are compared and it turns out that the social welfares are identical and the choice of the policy is irrelevant of the efficiency.