The end-to-end throughput of multi-hop communication in wireless ad hoc networks is affected by the conflict between forwarding nodes. It has been shown that sending more packets than maximum achievable end-to-end throughput not only fails to increase throughput but also decreases throughput owing to high contention and collision. Accordingly, it is of crucial importance for a source node to know the maximum end-to-end throughput. The end-to-end throughput depends on multiple factors, such as physical layer limitations, medium access control (MAC) protocol properties, routing policy, and nodes’ distribution. There have been many studies on analytical modeling of end-to-end throughput but none of them has taken routing policy and nodes’ distribution as well as MAC layer altogether into account. In this paper, the end-to-end throughput with perfect MAC layer is obtained based on routing policy and nodes’ distribution in 1-D and 2-D networks. Then, imperfections of IEEE 802.11 protocol are added to the model to obtain precise value. An exhaustive simulation is also made to validate the proposed models using ns-2 simulator. Results show that if the distribution to the next hop for a particular routing policy is known, our methodology can obtain the maximum end-to-end throughput precisely.
Assuming that all nodes are placed equi-distance apart, the authors in @cite_40 obtained the maximum end-to-end throughput of chain-topology. Many research @cite_5 @cite_41 @cite_43 @cite_20 @cite_8 @cite_29 @cite_13 @cite_36 @cite_6 used the same idea to obtain a slightly better formula for maximum end-to-end throughput in chain-topology. However, none of those works took node distribution and routing policy into account. Furthermore, it is not clear how one can extend the models to 2 dimensional networks. In @cite_35 , however, the author generalized the method used in @cite_40 to any chain-topology when the location of nodes are known. By running a backward iterative process which is relatively complicated for a computationally limited wireless node, a source node can obtain the maximum end-to-end throughput. In @cite_6 , the model is extended to support heterogeneous networks in which nodes transmit different length frames with various loads when all nodes reside in carrier sense range of all other nodes. The model, however, cannot be extended to multi-hop networks.
@cite_35 @cite_8 @cite_41 @cite_36 @cite_29 @cite_6 @cite_43 @cite_40 @cite_5 @cite_13 @cite_20
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Understanding the maximum end-to-end throughput available with any given wireless multi-hop network is an important, but very challenging task. It may be approximated up to certain degree for several simplified topologies such as chain, cross, and others. Typically, in case of chain-topology wireless multi-hop networks employing IEEE 802.11 DCF (distributed coordination function), the maximum throughput can be derived by calculating 1-hop average throughput considering the so-called bottleneck region. However, this approximation method that utilizes only the 1-hop average throughput is limited in terms of accuracy. Thus, in this paper, after verifying the limitation of 1-hop average approximation for the throughput calculation of chain-topology multi-hop wireless networks, a refined calculation scheme is proposed by additionally considering the deviation of throughput. Especially, we focus on the fact that the throughput deviation could lead to collisions, and the throughput deviation happens due to the summation of uniformly distributed backoff times of IEEE 802.11 DCF. With several ns-2-based network simulations, we verify the impact of selected temporal variations to the throughput calculation and thus validate the improved accuracy of proposed calculation scheme. In this paper, we present a methodology to analytically compute the throughput capacity, or the maximum end-to-end throughput of a given source and destination pair in a multi-hop wireless network. The end-to-end throughput capacity is computed by considering the interference due to neighboring nodes, as well as various modes of hidden node interference. Knowing the throughput capacity is important because it facilitates the design of routing policy, admission control for realtime traffic, as well as load control for wireless networks. We model location-dependent neighboring interference and we use a contention graph to represent these interference relationships. Based on the contention graph, we formulate the individual link capacity as a set of fixed point equations. The end-to-end throughput capacity can then be determined once these link capacities are obtained. To illustrate the utility of our proposed methodology, we present two important applications: (a) route optimization to determine the path with the maximum end-to-end throughput capacity and, (b) optimal offered load control for a given path so that the maximum end-to-end capacity can be achieved. Extensive simulations are carried out to verify and validate the proposed analytical methodology. It is important to obtain analytical expressions of the maximum throughput in IEEE 802.11 Distributed Coordination Function multi-hop networks. In the previous works, the analytical expressions of the maximum throughput for one-way string multi-hop networks taking into account the signal capture effect were obtained. In other researches, the analytical expressions of the maximum throughput for one-way string multi-hop networks were also obtained, which are, however, valid only for short-frame communications. There is no analytical expression for maximum throughput, which is valid for long-frame communications. This paper presents an analytical expression of the maximum throughput for long-frame communications. For the long-frame-communication analysis, we make different assumptions from those in the previous-analyses. In the short-frame-communication analyses, it is assumed that all nodes always have frames. In the long-frame-communication analysis, however, it should be assumed that every equal to or more than three nodes in a string-topology network have frames. The comprehension of this behavior is the most important progression in this paper. The assumptions and the analytical expression are validated by the simulation results. We consider the problem of determining rates of growth for the maximum stable throughput achievable in dense wireless networks. We formulate this problem as one of finding maximum flows on random unit-disk graphs. Equipped with the max-flow min-cut theorem as our basic analysis tool, we obtain rates of growth under three models of communication: (a) omnidirectional transmissions; (b) "simple" directional transmissions, in which sending nodes generate a single beam aimed at a particular receiver; and (c) "complex" directional transmissions, in which sending nodes generate multiple beams aimed at multiple receivers. Our main finding is that an increase of Θlog2n in maximum stable throughput is all that can be achieved by allowing arbitrarily complex signal processing (in the form of generation of directed beams) at the transmitters and receivers. We conclude therefore that neither directional antennas, nor the ability to communicate simultaneously with multiple nodes, can be expected in practice to effectively circumvent the constriction on capacity in dense networks that results from the geometric layout of nodes in space.