Bounding the price of anarchy, which quantifies the damage to social welfare due to selfish behavior of the participants, has been an important area of research in algorithmic game theory. In this paper, we study this phenomenon in the context of a game modeling queuing systems: routers compete for servers, where packets that do not get service will be resent at future rounds, resulting in a system where the number of packets at each round depends on the success of the routers in the previous rounds. We model this as an (infinitely) repeated game, where the system holds a state (number of packets held by each queue) that arises from the results of the previous rounds. We assume that routers satisfy the no-regret condition, e.g. they use learning strategies to identify the server where their packets get the best service.