FAVE: A fast and efficient network Flow AVailability Estimation method with bounded relative error

Abstract: This paper focuses on helping network providers to carry out network capacity planning and sales projection by answering the question: For a given topology and capacity, whether the network can serve current flow demands with high probabilities? We name such probability as "{\it flow availability}", and present the \underline{f}low \underline{av}ailability \underline{e}stimation (FAVE) problem, which is a generalisation of network connectivity or maximum flow reliability estimations. Realistic networks are often large and dynamic, so flow availabilities cannot be evaluated analytically and simulation is often used. However, naive Monte Carlo (MC) or importance sampling (IS) techniques take an excessive amount of time. To quickly estimate flow availabilities, we utilize the correlations among link and flow failures to figure out the importance of roles played by different links in flow failures, and design three "sequential importance sampling" (SIS) methods which achieve "bounded or even vanishing relative error" with linear computational complexities. When applying to a realistic network, our method reduces the flow availability estimation cost by 900 and 130 times compared with MC and baseline IS methods, respectively. Our method can also facilitate capacity planning by providing better flow availability guarantees, compared with traditional methods.