Analytical Model of Middlebox Unavailability under Shared Protection Allowing Multiple Backups

Abstract

This paper presents an analytical model that yields the unavailability of a network function when each backup server can protect two functions and can recover one of them. Previous work describes a model to deal with the case that each function can be protected only by one server. In our model, we allow each function to be protected by multiple servers to ensure function availability. This requires us to know the feasible states of a connected component and its state transitions. By adopting the divide-and-conquer method, we enumerate the feasible states of a connected component. We then classify its state transitions. Based on the obtained feasible states and the classification of the state transitions, we enumerate the feasible states incoming to and outgoing from a general state, the transfer rates, and the conditions. With those informations, we generate multiple equations about the state transitions. Finally, by solving them, we obtain the probabilities that a connected component is in each state and calculate the unavailability of a function. Numerical results show that the average unavailability of a function is reduced by 18% and 5.7% in our two examined cases by allowing each function to be protected by multiple servers.