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Abstract-In wireless LANs (WLANs), the medium access control (MAC) protocol is the main element that determines the efficiency in sharing the limited communication bandwidth of the wireless channel. In this paper we focus on the efficiency of the IEEE 802.11 standard for WLANs. Specifically, we analytically derive the average size of the contention window that maximizes the throughput, hereafter theoretical throughput limit, and we show that: 1) depending on the network configuration, the standard can operate very far from the theoretical throughput limit; and 2) an appropriate tuning of the backoff algorithm can drive the IEEE 802.11 protocol close to the theoretical throughput limit. Hence we propose a distributed algorithm that enables each station to tune its backoff algorithm at run-time. The performances of the IEEE 802.11 protocol, enhanced with our algorithm, are extensively investigated by simulation. Specifically, we investigate the sensitiveness of our algorithm to some network configuration parameters (number of active stations, presence of hidden terminals). Our results indicate that the capacity of the enhanced protocol is very close to the theoretical upper bound in all the configurations analyzed. Index Terms-Multiple access protocol (MAC), performance analysis, protocol capacity, wireless LAN (WLAN).

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a b s t r a c tWe use data on frequencies of bi-directional posts to define edges (or relationships) in two Facebook datasets and a Twitter dataset and use these to create ego-centric social networks. We explore the internal structure of these networks to determine whether they have the same kind of layered structure as has been found in offline face-to-face networks (which have a distinctively scaled structure with successively inclusive layers at 5, 15, 50 and 150 alters). The two Facebook datasets are best described by a four-layer structure and the Twitter dataset by a five-layer structure. The absolute sizes of these layers and the mean frequencies of contact with alters within each layer match very closely the observed values from offline networks. In addition, all three datasets reveal the existence of an innermost network layer at ∼1.5 alters. Our analyses thus confirm the existence of the layered structure of ego-centric social networks with a very much larger sample (in total, >185,000 egos) than those previously used to describe them, as well as identifying the existence of an additional network layer whose existence was only hypothesised in offline social networks. In addition, our analyses indicate that online communities have very similar structural characteristics to offline face-to-face networks.Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).

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Abstract-In WLANs, the medium access control (MAC) protocol is the main element that determines the efficiency of sharing the limited communication bandwidth of the wireless channel. The fraction of channel bandwidth used by successfully transmitted messages gives a good indication of the protocol efficiency, and its maximum value is referred to as protocol capacity. In a previous paper we have derived the theoretical limit of the IEEE 802.11 MAC protocol capacity. In addition, we showed that if a station has an exact knowledge of the network status, it is possible to tune its backoff algorithm to achieve a protocol capacity very close to its theoretical bound. Unfortunately, in a real case, a station does not have an exact knowledge of the network and load configurations (i.e., number of active stations and length of the message transmitted on the channel) but it can only estimate it. In this work we analytically study the performance of the IEEE 802.11 protocol with a dynamically tuned backoff based on the estimation of the network status. Results obtained indicate that under stationary traffic and network configurations (i.e., constant average message length and fixed number of active stations), the capacity of the enhanced protocol approaches the theoretical limits in all the configurations analyzed. In addition, by exploiting the analytical model, we investigate the protocol performance in transient conditions (i.e., when the number of active stations sharply changes).Index Terms-Markov chain, multiple access protocol (MAC), performance analysis, protocol capacity, wireless LAN (WLAN).

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