Reliability Analysis of a Multipath Transport System in Fog Computing

We consider a fog computing approach with function virtualization in an IoT scenario that uses an SDN/NFV protocol stack and multipath communication between its clients and servers at the transport and session layers. We analyze the reliability of the associated redundant transport system comprising two logical channels that are susceptible to random failures. We model the error-prone system with a single repair unit and independent phase-type distributed repair times by a Marshall-Olkin failure model. The failure processes of both channels are described by general Markov-modulated Poisson processes (MMPPs) that are associated with the corresponding failure times and that are driven by the transitions of a common random environment. First we identify the generator matrix of the associated continuous-time Markov chain that is determined by the interarrival times of the Markov-modulated failure processes and the independent phase-type distributed repair times and the Kronecker-product structures of their associated parameter matrices. Then we show that the steady-state distribution of the restoration model can be effectively calculated by a semiconvergent iterative aggregation-disaggregation method for block matrices. Finally, we compute the associated reliability function and hazard rate of the multipath transport system.