Availability modeling of a virtualized IP multimedia subsystem using non-Markovian stochastic reward nets

A significant fraction of current research in telecommunications is investigating new paradigms to guarantee high flexibility in deploying network infrastructures. Network Function Virtualization (NFV) is probably the most effective paradigm: it adapts tothe telecommunication networks the virtualization concepts originally conceived in the computer world. According to NFV specifications, network elements as switches or routers can be implemented as virtual machines called Virtual Network Functions (VNFs), and deployed in field by timely and cost-effective operations. Some Telco operators are already taking advantage of these virtualized resources, by aggregating more VNFs in order to provide new services. One example is IP Multimedia Subsystem (IMS), providing multimedia delivery services, that can be suitably deployed by means of interconnected VNFs. We consider a virtualized implementation of an IMS system (vIMS) that we characterize by an availability standpoint. First, we describe a vIMS system as a chain of virtualized network elements modeled by three components: hardware, hypervisor, and application. Subsequently, we model the probabilistic behavior of the network nodes by Stochastic Reward Nets, that account for failure and repair events characterizing each node. Innovating on previous formulations, part of the analysis is carried out by adopting non-Markovian models, thus allowing for more realistic (non-exponentially distributed) times between some state transitions. As final results, we determine the optimal redundant vIMS configuration able to guarantee a steady-state availability not less than 0.99999, and we provide a sensitivity analysis useful to evaluate the system robustness to variation of parameters from their nominal values.