The IEEE 802.11ax standard, which realizes multi-user transmission based on orthogonal frequency division multiple access (OFDMA), has been highlighted as a key technology to meet high future demand for Wi-Fi systems. Since this standard is still being developed, performance analysis through mathematical modeling is of paramount importance; however, existing studies have several limitations. Firstly, most of these consider only the saturation network throughput, whereas for 802.11ax in particular, the access delay of the nodes needs to be studied carefully, since they no longer acquire the medium independently but depend solely on the access point’s (AP’s) schedule. Secondly, since the network performance may be affected to a greater extent by legacy nodes than by 802.11ax nodes, it is desirable to consider various heterogeneous cases of networks with existing legacy nodes. In this paper, a new analytical framework for the 802.11ax MAC protocol is provided. Markov-chain-based models are developed to represent the behavior of the 802.11ax nodes, and both non-saturated traffic conditions and co-existence with the legacy nodes are considered. Through both analysis and MATLAB simulations, it is shown that the proposed model accurately evaluates the throughput and the delay performance under various network conditions.