Functional splitting and packetized fronthaul (FH) are two approaches to realize cloud radio access networks in a cost-effective manner. In the former, some baseband functionalities are offloaded to remote radio units (RRUs) instead of centralizing all of them at a baseband unit pool. This reduces the capacity and latency requirements on FH when massive multiple-input-massive-output RRUs are used. The latter approach aims to use the ubiquitous Ethernet networks for FH. However, this leads to random packet delays due to queuing at switching/aggregating gateways. In this letter, we present a novel analytical framework to characterize the distribution of queuing delays at an aggregation gateway in the uplink. This framework incorporates random user activity, the uplink spectral efficiencies of users, the slotted nature of uplink transmissions, and FH capacity. We study the impact of packet arrival rates, average packet sizes, and FH capacity on queue length and queuing delay distributions. We show that significant statistical multiplexing gains are possible by aggregating traffic from multiple RRUs. © 1997-2012 IEEE.