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We study a noncooperative game problem for queueing control in the Cognitive Radio (CR) system where selfish Secondary User's (SU) data packets (a.k.a. "customers" in this work) are served by a CR base station (a.k.a. "server"). The scenario is modeled as an M/M/1 queueing game with server breakdowns where each customer wants to optimize their benefit in a selfish distributed manner. We first show that the game has an inefficient unique Nash Equilibrium (NE). In order to improve the outcome efficiency, we propose an appropriate admission fee that can be easily implemented at the server. We then show that the social welfare at the equilibrium point can be coincided the social welfare of the socially optimal strategy.