The surging mobile traffic poses serious challenges for mobile operators and the advancement of information and communication technologies (ICT). The cost and energy consumption cannot support affordable mobile services and sustainable growth. As a new architecture, cloud-based radio access network (C-RAN) is proposed to confront these challenges. C-RAN is a deployment paradigm that seeks to isolate baseband unit (BBU) from its remote radio unit (RRU) in base station (BS), consolidating the BBUs into a common place (i.e. BBU pool). In the BBU pool, the computing resources provided by the BBUs can be dynamically assigned to RRUs on demand by the BBU controller. Thus, with the fluctuation of data traffic from RRUs, a part of BBUs can be dynamically turned on or off. As a result, the energy consumption of the BBU pool can be reduced correspondingly. In this paper, we design a Markov chain-based calculation model to formulate the energy-saving operation of the BBU pool with an active/sleep mode under dynamic RRU traffic load. On this basis, we propose two different BBU state transition strategies for the BBU pool, i.e., “Cautious ON, Bold OFF (CO-BF)” strategy and “Bold ON, Cautious OFF (BO-CF)” strategy. We formulate the key performance indicators in terms of the energy saving efficiency (ESE), the consequent packet queuing delay (PQD) and the normalized tradeoff cost as well. In extensive simulations, we investigate the effect of these key parameter indicators on the system performances of the BBU pool. Achieving the minimum normalized cost, an optimal operating strategy for the BBU pool can be determined by adjusting the parameter values of the ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> ). The simulation results show when RRU traffic load is light (e.g., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda =0.1$ </tex-math></inline-formula> ), the proposed BO-CF strategy can lead to the minimum normalized cost, which corresponds to ESE of up to 75.4% and PQD of 0.0097ms. For heavier load (e.g., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda =0.4$ </tex-math></inline-formula> ), the minimum normalized cost can be obtained along with ESE of up to 74.1% and PQD of 0.1241ms, when the CO-BF strategy is adopted. Hence, we observe that the BO-CF strategy is slightly better than the CO-BF for the light traffic load of the BBU pool, while the CO-BF strategy would be more suitable for the BBU pool with the heavier traffic load. It proves the efficacy of our proposed Markov chain-based calculation model to pursuit an optimal operating strategy for the delay-aware and energy-efficient BBU pool.