Non-saturated IEEE 802.11 networks. A hierarchical 3D Markov model

One of the most widely adopted IEEE 802.11 DCF modeling paradigms is the mean-field Markov model approach. It has its foundations on the analytical two-dimensional Markov model presented by Bianchi, which characterizes the basic access mechanism of DCF under a saturated traffic assumption. This basic approach has been refined by a series of follow-up models that take into account important practical issues not considered in the original model, such as non-saturated traffic load and error-prone channels. However, two-dimensional models are either based on bufferless or infinite buffer network assumptions and thus, they are unable to properly model QoS performance metrics related to finite queues. In this paper, a hierarchical three-dimensional Markov model able to fully capture the Quality of Service (QoS) performance and queueing behavior of non-saturated IEEE 802.11 DCF-based networks is proposed. The third dimension in the hierarchical three-dimensional Markov chain is used to model the queue length and the hierarchy is used to efficiently capture, on one hand, the freezing rules of backoff counters when the broadcast channel is sensed busy and, on the other hand, the error-prone channel conditions. The issue of computational complexity is addressed by devising a computationally efficient method to solve for the steady-state transition probabilities of the 3D Markov chain. The solution for the Markov chain is then exploited to obtain analytical expressions for the whole set of QoS performance metrics of the system, allowing the evaluation/prediction of the impact of buffer size, block error probability and backoff freezing rules on all relevant QoS metrics of a DCF-based IEEE 802.11 network. A close match between analytical and simulation results confirms the validity and effectiveness of the proposed approach.