Many studies have tried to evaluate wireless networks and especially the IEEE 802.15.4 standard. Hence, several papers have aimed to describe the functionalities of the physical (PHY) and medium access control (MAC) layers. They have highlighted some characteristics with experimental results and or have attempted to reproduce them using theoretical models. In this paper, we use the first way to better understand IEEE 802.15.4 standard. Indeed, we provide a comprehensive model, able more faithfully to mimic the functionalities of this standard at the PHY and MAC layers. We propose a combination of two relevant models for the two layers. The PHY layer behavior is reproduced by a mathematical framework, which is based on radio and channel models, in order to quantify link reliability. On the other hand, the MAC layer is mimed by an enhanced Markov chain. The results show the pertinence of our approach compared to the model based on a Markov chain for IEEE 802.15.4 MAC layer. This contribution allows us fully and more precisely to estimate the network performance with different network sizes, as well as different metrics such as node reliability and delay. Our contribution enables us to catch possible failures at both layers.
In another context, numerous works focus on the physical layer modeling. For instance, Zuniga and Krishnamachari @cite_6 @cite_15 have analyzed the major causes behind unreliability @cite_6 @cite_15 and the negative impact of asymmetry on link efficiency @cite_15 in low power wireless links. Instead of the binary disc-shaped model these models reproduce the called @math @math @cite_4 @cite_8 @cite_12 in order to model the transmission range. The packet reception rate and the upper-layer protocol reliability are highly instable when a neighbor is located in this region. To understand it, two models have been proposed: a channel model that is based on the log-normal path loss propagation model @cite_10 and a radio reception model closely tied to the determination of packet reception ratio. Through these models, it is possible to derive the expected distribution and the variance of the packet reception ratio according to the distance.
@cite_4 @cite_8 @cite_6 @cite_15 @cite_10 @cite_12
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Experimental studies have demonstrated that the behavior of real links in low-power wireless networks (such as wireless sensor networks) deviates to a large extent from the ideal binary model used in several simulation studies. In particular, there is a large transitional region in wireless link quality that is characterized by significant levels of unreliability and asymmetry, significantly impacting the performance of higher-layer protocols. We provide a comprehensive analysis of the root causes of unreliability and asymmetry. In particular, we derive expressions for the distribution, expectation, and variance of the packet reception rate as a function of distance, as well as for the location and extent of the transitional region. These expressions incorporate important environmental and radio parameters such as the path loss exponent and shadowing variance of the channel, and the modulation, encoding, and hardware variance of the radios. The wireless sensor networks community, has now an increased understanding of the need for realistic link layer models. Recent experimental studies have shown that real deployments have a "transitional region" with highly unreliable links, and that therefore the idealized perfect-reception-within-range models used in common network simulation tools can be very misleading. In this paper, we use mathematical techniques from communication theory to model and analyze the low power wireless links. The primary contribution of this work is the identification of the causes of the transitional region, and a quantification of their influence. Specifically, we derive expressions for the packet reception rate as a function of distance, and for the width of the transitional region. These expressions incorporate important channel and radio parameters such as the path loss exponent and shadowing variance of the channel; and the modulation and encoding of the radio. A key finding is that for radios using narrow-band modulation, the transitional region is not an artifact of the radio non-ideality, as it would exist even with perfect-threshold receivers because of multi-path fading. However, we hypothesize that radios with mechanisms to combat multi-path effects, such as spread-spectrum and diversity techniques, can reduce the transitional region. In this paper we propose the following approach to the dimensioning of the radio part of the downlink in OFDMA networks. First, we use information theory to characterize the bit-rate in the channel from a base station to its mobile. It depends on the power and bandwidth allocated to this mobile. Then, we describe the resource (power and bandwidth) allocation problem and characterise feasible configurations of bit-rates of all users. As the key element, we propose some particular sufficient condition (in a multi-Erlang form) for a given configuration of bit-rates to be feasible. Finally, we consider an Erlang's loss model, in which streaming arrivals whose admission would lead to the violation of this sufficient condition are blocked and lost. In this model, the blocking probabilities can be calculated using Kaufman-Roberts algorithm. We propose it to evaluate the minimal density of base stations assuring acceptable blocking probabilities for a streaming traffic of a given load per surface unit. We validate this approach by comparison of the blocking probabilities to these simulated in the similar model in which the admission control is based on the original feasibility property (instead of its sufficient condition). Our sufficient bit-rate feasibility condition can also be used to dimension the network with respect to the elastic traffic. We investigate the secure connectivity of wireless sensor networks under the random key distribution scheme of Eschenauer and Gligor. Unlike recent work which was carried out under the assumption of full visibility, here we assume a (simplified) communication model where unreliable wireless links are represented as on off channels. We present conditions on how to scale the model parameters so that the network: 1) has no secure node which is isolated and 2) is securely connected, both with high probability when the number of sensor nodes becomes large. The results are given in the form of full zero-one laws, and constitute the first complete analysis of the EG scheme under non-full visibility. Through simulations, these zero-one laws are shown to be valid also under a more realistic communication model (i.e., the disk model). The relations to the Gupta and Kumar's conjecture on the connectivity of geometric random graphs with randomly deleted edges are also discussed.