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The Next Generation 5G Networks can greatly benefit from the synergy between virtualization paradigms, such as the Network Function Virtualization (NFV), and service provisioning platforms such as the IP Multimedia Subsystem (IMS). The NFV concept is evolving towards a lightweight solution based on containers that, by contrast to classic virtual machines, do not carry a whole operating system and result in more efficient and scalable deployments. On the other hand, IMS has become an integral part of the 5G core network, for instance, to provide advanced services like Voice over LTE (VoLTE). In this paper we combine these virtualization and service provisioning concepts, deriving a containerized IMS infrastructure, dubbed cIMS, providing its assessment through statistical characterization and experimental measurements. Specifically, we: i) model cIMS through the queueing networks methodology to characterize the utilization of virtual resources under constrained conditions; ii) draw an extended version of the Pollaczek-Khinchin formula, which is useful to deal with bulk arrivals; iii) afford an optimization problem focused at maximizing the whole cIMS performance in the presence of capacity constraints, thus providing new means for the service provider to manage service level agreements (SLAs); $iv)$ evaluate a range of cIMS scenarios, considering different queuing disciplines including also multiple job classes. An experimental testbed based on the open source platform Clearwater has been deployed to derive some realistic values of key parameters (e.g. arrival and service times).