In modern telecommunication networks, services are provided through Service Function Chains (SFC), where network resources are implemented by leveraging virtualization and containerization technologies. In particular, the possibility of easily adding or removing network resources has prompted service providers to redefine some concepts including performance and availability. In line with this new trend, we propose a performability study of a multi-provider containerized IP Multimedia Subsystem (cIMS), an SFC-like infrastructure used in the core part of 4G/5G networks to handle multimedia sessions. On the one hand, performance issues are tackled by modeling each cIMS node in terms of a G/G/m queueing system to derive the Call Setup Delay (CSD), a performance metric related to the user-end experience in multimedia communications. On the other hand, availability issues are addressed through the Multi-State System (MSS) formalism, to take into account different performance rates of the system. Then, we devise an algorithm called PE-MUGF (Performability Evaluation through Multidimensional Universal Generating Function) to identify the minimum-redundancy cIMS configuration which meets given performance and availability targets at the same time. Finally, an extensive experimental analysis based on Clearwater, a containerized IMS testbed, allows us to estimate most of system parameters whose robustness is evaluated through a sensitivity analysis.