In the Cloud Radio Access Network (C-RAN) architecture, the baseband signals from multiple remote radio heads are processed in a centralized baseband unit (BBU) pool. This architecture allows network operators to adapt the BBU's computational resources to the aggregate access load experienced at the BBU, which can change in every air-interface access frame. The degree of savings that can be achieved by adapting the resources is a tradeoff between savings, adaptation frequency, and increased queuing time. If the time scale for adaptation of the resource multiplexing is greater than the access frame duration, then this may result in additional access latency and limit the energy savings. In this paper we investigate the tradeoff by considering two extreme time-scales for the resource multiplexing: (i) long-term, where the computational resources are adapted over periods much larger than the access frame durations; (ii) short-term, where the adaption is below the access frame duration. We develop a general C-RAN queuing model that describes the access latency and show, for Poisson arrivals, that long-term multiplexing achieves savings comparable to short-term multiplexing, while offering low implementation complexity.