Cloud-based Radio Access Network (C-RAN) is a centralized cloud com- puting architecture for radio access networks (RANs) that provides large-scale deployment, joint support for radio technologies, and real-time virtualization capabilities. By moving signal processing functions to a data center, C-RAN significantly reduces power consumption and deployment cost. The architecture of the cloud radio access network consists of three main components: a pool of base-band units (BBU pool), remote radio heads (RRHs), and a transport network. In C-RAN, base stations are replaced by remote radio heads: data blocks are digitized, transmitted through the fiber-optical infrastructure, and remotely processed in BBU pool. One of the main issues is to control the round- trip delay between the remote radio heads and the BBU pool. In the paper, we describe a C-RAN in terms of queuing network and accurately evaluate all delay components. Besides, we analyze the required computational resources of the BBU pool required to satisfy the strict round-trip delay budget in C-RAN.