This paper aims to use analytical modeling technique to quantitatively study the dependability of Vehicle Platooning Application, which consists of Multiple Sub-Services (VPP-MSS) to achieve its functionality. Each sub-service (SS), based on network function virtualization technology, is executed in a container. Both SSes and OSes which SSes run on can suffer from software aging after a long and continuous running, reducing VPP-MSS dependability. Rejuvenation techniques are usually used to combat software aging, but they require the support of backup components. Quantitative study of VPP-MSS dependability enables in-depth understanding of the effectiveness of rejuvenation techniques based on analytical models. In contrast to the existing studies, we develop a semi-Markov process (SMP) model to jointly analyze the impact of rejuvenation technique trigger intervals (RTTIs), backup components’ behaviors, time-dependent interactions between various behaviors and the number of active SSes deployed on an OS on the effectiveness of rejuvenation technique. Sensitivity analysis helps identify key parameters for improving the dependability of VPP-MSS. Extensive numerical experiments demonstrate the necessity of considering backup components’ behaviors and investigating non-exponentially distributed failure times. We also determine both the optimal RTTI combination and the optimal combination of SSes and OSes, which can maximize VPP-MSS dependability.