Quantitative Network Analysis

Network Verification is emerging as a critical enabler to manage large complex networks. So far attention has been focused on functional correctness – in particular, reachability properties for large networks that forward packets modeled as header spaces (bit-vectors). This line of work ignores performance-related questions regarding, for example, bandwidth, latency and link loads. To address such queries we introduce Quantitative Network Analysis (QNA) that works in the context of large header spaces and quantities. We propose a modular approach where header spaces are reduced to equivalence classes and quantities are propogated using an algebraic framework inspired by tropical algebras and network calculus. In order to scale to data-center networks found in Microsoft Azure we developed a new data structure called ddNF, disjoint difference normal form, that serves as an efficient container for a small set of equivalence classes over header spaces. Our experiments show that ddNFs outperform representations proposed in previous work, in particular representations based on BDDs, and is especially suited for incremental verification. We then introduce our general framework to do quantitative analysis on the resulting equivalence classes, and show how it instantiates in a scalable way to checking properties of latency inflation, flow rates, and link loads.