Carrier-sense multiple access collision avoidance networks have often been analyzed using a stylized model that is fully characterized by a vector of back-off rates and a conflict graph. Furthermore, for any achievable throughput vector @math , the existence of a unique vector @math of back-off rates that achieves this throughput vector was proven. Although this unique vector can in principle be computed iteratively, the required time complexity grows exponentially in the network size, making this only feasible for small networks. In this paper, we present an explicit formula for the unique vector of back-off rates @math needed to achieve any achievable throughput vector @math provided that the network has a chordal conflict graph. This class of networks contains a number of special cases of interest such as (inhomogeneous) line networks and networks with an acyclic conflict graph. Moreover, these back-off rates are such that the back-off rate of a node only depends on its own target throughput and the target throughput of its neighbors and can be determined in a distributed manner. We further indicate that back-off rates of this form cannot be obtained in general for networks with non-chordal conflict graphs. For general conflict graphs, we nevertheless show how to adapt the back-off rates when a node is added to the network when its interfering nodes form a clique in the conflict graph. Finally, we introduce a distributed chordal approximation algorithm for general conflict graphs, which is shown (using numerical examples) to be more accurate than the Bethe approximation.
Several generalization of the ideal CSMA CA model have been studied. These include linear networks with hidden and exposed nodes @cite_2 , single and multihop networks with unsaturated users @cite_25 and networks relying on multiple channels @cite_11 @cite_15 , where it should be noted that the stability conditions for the unsaturated network presented in @cite_25 are not valid in general @cite_32 .
@cite_32 @cite_2 @cite_15 @cite_25 @cite_11
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We present a novel modeling approach to derive closed-form throughput expressions for CSMA networks with hidden terminals. The key modeling principle is to break the interdependence of events in a wireless network using conditional expressions that capture the effect of a specific factor each, yet preserve the required dependences when combined together. Different from existing models that use numerical aggregation techniques, our approach is the first to jointly characterize the three main critical factors affecting flow throughput (referred to as hidden terminals, information asymmetry and flow-in-the-middle) within a single analytical expression. We have developed a symbolic implementation of the model, that we use for validation against realistic simulations and experiments with real wireless hardware, observing high model accuracy in the evaluated scenarios. The derived closed-form expressions enable new analytical studies of capacity and protocol performance that would not be possible with prior models. We illustrate this through an application of network utility maximization in complex networks with collisions, hidden terminals, asymmetric interference and flow-in-the-middle instances. Despite that such problematic scenarios make utility maximization a challenging problem, the model-based optimization yields vast fairness gains and an average per-flow throughput gain higher than 500 with respect to 802.11 in the evaluated networks. Due to a poor understanding of the interactions among transmitters, wireless networks using carrier sense multiple access with collision avoidance (CSMA CA) have been commonly stigmatized as unpredictable in nature. Even elementary questions regarding the throughput limitations of these networks cannot be answered in general. In this paper, we investigate the behavior of wireless CSMA CA networks to understand how the transmissions of a particular node affect the medium access, and ultimately the throughput, of other nodes in the network. We introduce a theory which accurately models the behavior of these networks and show that, contrary to popular belief, their performance is predictable and can be described by a system of equations. Using the proposed theory, we provide the analytical expressions necessary to fully characterize the capacity region of any wireless CSMA CA network. We show that this region is nonconvex in general and agnostic to the probability distributions of all network parameters, depending only on their expected values. Our theory is also shown to extend naturally to time division multiple access (TDMA) networks and to predict how the network responds to infeasible input rates. Due to a poor understanding of the interactions among transmitters, wireless multihop networks have commonly been stigmatized as unpredictable in nature. Even elementary questions regarding the throughput limitations of these networks cannot be answered in general. In this paper we investigate the behavior of wireless multihop networks using carrier sense multiple access with collision avoidance (CSMA CA). Our goal is to understand how the transmissions of a particular node affect the medium access, and ultimately the throughput, of other nodes in the network. We introduce a theory which accurately models the behavior of these networks and show that, contrary to popular belief, their performance is easily predictable and can be described by a system of equations. Using the proposed theory, we provide the analytical expressions necessary to fully characterize the capacity region of any wireless CSMA CA multihop network. We show that this region is nonconvex in general and entirely agnostic to the probability distributions of all network parameters, depending only on their expected values. CSMA CA is a popular random-access algorithm for wireless networks, but its stability properties are poorly understood. We consider a linear multi-hop network of three nodes where the neighbouring nodes interfere with each other and medium access is governed by the CSMA CA algorithm. We assume that the source node is saturated and packets are forwarded through the network, each node transmitting towards its neighbour on the right. We demonstrate that the queue of the second node is saturated (unstable) and the queue of the third node is stable; this confirms heuristic arguments and simulation results found in the research literature. Providing a rigorous proof for the (in)stability of these nodes is complicated by the fact that neither queue is Markovian when considered in isolation, and the two queues are dependent. We then compute the limiting behavior of node 3, and use this to determine the end-to-end throughput of the network. Finally, we vary the access probabilities of the nodes, and evaluate how this affects the stability and throughput of the system.