Abstract-In this paper, we study sleeping control and power matching for a single cell in cellular networks with bursty traffic. The base station (BS) sleeps whenever the system is empty, and wakes up when N users are assembled during the sleep period. The service capacity of the BS in the active mode is controlled through adjusting its transmit power. The total power consumption and average delay are analyzed, based on which the impact of parameter N and transmit power on the energy-delay tradeoff is studied. It is shown that given the average traffic load, the more bursty the traffic is, the less the total power is consumed, while the delay performance of more bursty traffic is better only under certain circumstances. The optimal energy-delay tradeoff is then obtained through joint sleeping control and power matching optimization. The relationship between the optimal control parameters and the asymptotic performance are also provided. Moreover, the influence of the traffic autocorrelation is explored, which shows less impact on the system performance compared with that of the burstiness. Numerical results show the energy saving gain of the joint sleeping control and power matching scheme, as well as the impact of burstiness on the optimal energy-delay tradeoff.