Characterizing the Stability Region of IEEE 802 . 11 Distributed Coordination Function-Part I : Single Channel Analysis

In this paper we model and characterize the stability region of IEEE 802.11 Distributed Coordination Function (DCF) bot h qualitatively and quantitatively. We also provide an intui tive explanation and verification by comparing it to the know stability region of slotted Aloha. We show that the size of backoff wind ow plays a decisive role in shaping the corresponding stabil ity region. Specifically, when the backoff window is sufficientl y large, the stability region is convex, and it evolves into a concave region as the window size decreases. In addition, for given p arameterization, there exists a unique stable region when t window size is sufficiently large, whereas smaller window sizes may le d to a collection of stability regions. I. I NTRODUCTION As a widely deployed WLAN multiple access solution, the IEEE 802.11 Distributed Coordination Function (DCF) has been extensively studied, particularly in terms of its throughp ut erformance. Such exercises provide insights in our unde rstanding of the potential and limitation of 802.11 DCF. Generally spe aking, the modeling of the throughput performance of 802.11 may be categorized into two classes, namely, one that focuse s on thesaturatedregime and one on the non-saturatedregime. Under the saturated case where each node is an infinite source , a m an field Markov model with great intuitive appeal was firs t proposed by Bianchi in his seminar work [1]. This model was sh own to produce accurate prediction on the system throughput of a singleclique, where all nodes interfere with each other. It has since moti vated a large body of work on models of a similar nature, see e.g., [2] for a more general framework ba sed on a simplified fixed point analysis using renewal theory. There has also been work studying the unsaturated case, whic h is often done by adding extra states to the original Markov chain proposed by Bianchi in [1], see e.g., [3], [4], [5]. In t he unsaturated case the service processes across all nodes b ecome coupled, thus characterizing the system throughput become s much harder, and determining the queue stability region ha s been regarded as an open problem [6]. In this paper, we seek to characterize the stability regionof 802.11 DCF for a clique of a finite number of users operating on a single channel. It is defined as the set of all arrival rate s that can be stabilized by 802.11 DCF. We present a system of equations with feasibility constraints to describe this stability region. We then investigate the existence and uni queness of its solutions. In particular, we show that there exists a u niq e solution to this system of equations when the size of th e backoff window is sufficiently large. We further show that th e size of the backoff window plays a decisive role in shaping the corresponding stability region. In particular, when th e backoff window is sufficiently large, the corresponding st ability region is convex; as the window size decreases it evolves int o a concave region. We provide an intuitive explanation for t his phenomenon, and connect this result to known results on slot ted Aloha [7]. We note that while our discussion is focused on 802.11, our analytical framework is more generally applica ble. It is worth noting that results on the rate or throughput capacityregion of 802.11 DCF are available in the literature [8], [9]. Technically, rate region and stability region are two d ifferent concepts: the former may be analyzed assuming all u sers are saturated while the latter by definition is a notion that is on ly applicable to a set of non-saturated users. In practice, s tudies have shown that in the case of slotted Aloha, its stability re gion is the same as the Shannon capacity region [7]. This migh t suggest that in the case of 802.11 DCF the two regions are also geometrically more similar than not. Results obtained in th s paper seem to support this statement (more is discussed in Se ction IV), though fully validating it is out of the scope of th e present paper and will be addressed in a future study. The rest of this paper is organized as follows. In Section II w e present our model and state definitions and assumptions. In Section III the aforementioned constrained system of equ ations termed(Σ, C, λ) is presented to quantitatively describe the stability region, followed by an analysis on its solutions. Analytical results generated by the model are then compared to that from simulation in Section IV. We provide an intuitive expla nation in Section V on the shape of the stability region by dra wing results from slotted Aloha, and we conclude the paper in Sect ion VI.