The worldwide popularity of IEEE 802.11 wireless local area networks (WLANs) is mainly attributed to the medium access control (MAC) protocol of distributed coordination function (DCF). DCF is based on the Carrier Sense Multiple Access (CSMA) protocol with two access mechanisms including the basic access mechanism and the request-to-send/clear-to-send (RTS/CTS) mechanism. As a random access protocol, DCF inherits the merits of minimum coordination and distributed control, which, on the other hand, also renders difficulty in modeling and performance evaluation.

A widely adopted model of IEEE 802.11 DCF networks was proposed in [Bianchi'00], where a two-dimensional Markov chain was established to characterize the backoff behavior of each single node. It is well supported by simulation results and shown to be a powerful, yet simple, analytical tool to evaluate the throughput performance when the network becomes saturated, i.e., each node always has a packet to transmit. Bianchi¡¯s model has been refined by a series of follow-up papers and extended to unsaturated networks. Little consensus is, nevertheless, reached on the characterization of the network steady-state operating point in unsaturated scenarios due to differences in assumptions and models. Moreover, in the above studies, the steady-state point is usually obtained by numerically solving a set of nonlinear equations, which becomes increasingly complicated when advanced features are further introduced. The implicit nature of the solution also makes it difficult to search for the optimal network configuration.

In [Dai-Sun'13], the unified analytical framework proposed for CSMA networks [Dai'13] was applied to IEEE 802.11 DCF networks. Different from [Bianchi'00] where only the backoff process of each saturated node was characterized, the complete behavior of each HOL packet, including backoff, collision and successful transmission, was modeled in [Dai-Sun'13] as a discrete-time Markov renewal process. Given that the network is in unsaturated or saturated conditions, two network steady-state points, i.e., the desired stable point pL and the undesired stable point pA, were derived as explicit functions of system parameters. Fundamental performance limits, such as the maximum network throughput, the minimum mean access delay and the stable regions, were characterized, and the optimal values of key system parameters to achieve the performance limits were obtained.

The analysis was further generalized to heterogeneous IEEE 802.11 DCF networks in [Gao-Sun-Dai'13] and IEEE 802.11e EDCA networks in [Gao-Sun-Dai'14]. The effect of backoff design was studied in [Sun-Dai'15], and the optimal downlink/uplink throughput allocation was presented in [Gao-Dai'13]. All the above studies assumed a single basic service set (BSS) with one access point (AP). The analytical framework was further extended in [Gao-Dai-Hei'17] to a universal-frequency-reuse based multi-BSS IEEE 802.11 DCF network where all the BSSs share the frequency band.

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G. Bianchi, ¡°Performance analysis of the IEEE 802.11 distributed coordination
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Lin Dai and Xinghua Sun, "A Unified Analysis of IEEE 802.11 DCF Networks: Stability, Throughput and Delay," *IEEE Trans. Mobile Computing***,** vol. 12, no. 8, pp. 1558-1572, Aug. 2013.

Lin Dai, "Toward a Coherent Theory of CSMA and Aloha," *IEEE Trans. Wireless Commun*., vol. 12, no. 7, pp. 3428-3444, July 2013.

Yayu Gao, Xinghua Sun and Lin Dai, "Throughput Optimization of Heterogeneous IEEE 802.11 DCF Networks," *IEEE Trans. Wireless Commun*., vol. 12, no. 1, pp. 398-411, Jan. 2013.

Yayu Gao, Xinghua Sun and Lin Dai, "IEEE 802.11e EDCA Networks: Modeling, Differentiation and Optimization,"* IEEE Trans. Wireless Commun.*, vol. 13, no. 7, pp. 3863-3879, July 2014.

Xinghua Sun and Lin Dai, "Backoff Design for IEEE 802.11 DCF Networks: Fundamental Tradeoff and Design Criterion,"* IEEE/ACM Trans. Networking*, vol. 23, no. 1, pp. 300-316, Feb. 2015.

Yayu Gao and Lin Dai, "Optimal Downlink/Uplink Throughput Allocation for IEEE 802.11 DCF Networks," *IEEE Wireless Commun. Letters ***,** vol. 2, no. 6, pp. 627-630, Dec. 2013.

Yayu Gao, Lin Dai and Xiaojun Hei, "Throughput Optimization of Multi-BSS IEEE 802.11 Networks With Universal Frequency Reuse," *IEEE Trans. Commun*.,
vol. 65, no. 8, pp. 3399-3414, Aug. 2017.