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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Abstract Random-access algorithms such as the Carrier-Sense Multiple-Access (CSMA) protocol provide a popular mechanism for distributed medium access control in large-scale wireless networks. In recent years fairly tractable models have been shown to yield remarkably accurate throughput estimates in scenarios with saturated buffers. In contrast, in non-saturated scenarios, where nodes refrain from competition for the medium when their buffers are empty, a complex two-way interaction arises between the activity states and the buffer contents of the various nodes. As a result, the throughput characteristics in such scenarios have largely remained elusive so far. In the present paper we provide a generic structural characterization of the throughput performance and corresponding stability region in terms of the individual saturation throughputs of the various nodes. While the saturation throughputs are difficult to explicitly determine in general, we identify certain cases where these values can be expressed in closed form. In addition, we demonstrate that various lower-dimensional facets of the stability region can be explicitly calculated as well, depending on the neighborhood structure of the interference graph. Illustrative examples and numerical results are presented to illuminate the main analytical findings. Wireless networks equipped with the CSMA protocol are subject to collisions due to interference. For a given interference range, we investigate the tradeoff between collisions (hidden nodes) and unused capacity (exposed nodes). We show that the sensing range that maximizes throughput critically depends on the activation rate of nodes. For infinite line networks, we prove the existence of a threshold: When the activation rate is below this threshold, the optimal sensing range is small (to maximize spatial reuse). When the activation rate is above the threshold, the optimal sensing range is just large enough to preclude all collisions. Simulations suggest that this threshold policy extends to more complex linear and nonlinear topologies. This paper proposes and analyzes the performance of a simple frequency-agile CSMA MAC protocol. In this MAC, a node carrier-senses multiple frequency channels simultaneously, and it takes the first opportunity to transmit on any one of the channels when allowed by the CSMA backoff mechanism. We show that the frequency-agile MAC can effectively 1) boost throughput and 2) remove temporal starvation. Furthermore, the MAC can be implemented on the existing multiple-frequency setup in Wi-Fi using multi-radio technology, and it can co-exist with the legacy MAC using single radio. This paper provides exact stationary throughput analysis for regular 1D and thin-strip 2D CSMA networks using a "transfer-matrix" approach. In addition, accurate approximations are given for 2D grid networks. Our closed-form formulas accurately quantify the throughput gain of frequency-agile CSMA. To characterize temporal starvation, we use the metric of "mean residual access time" (MRAT). Our simulations and closed-form approximations indicate that the frequency-agile MAC can totally eliminate temporal starvation in 2D grid networks, reducing its MRAT by orders of magnitude. Finally, this paper presents a "coloring theorem" to justify the use of the frequency-agile MAC in general network topologies. Our analysis and theorem suggest that with enough frequency channels, the frequency-agile MAC can effectively decouple the detrimental interactions between neighboring links responsible for low throughput and starvation. 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. We analyze the performance of CSMA in multi-channel wireless networks, accounting for the random nature of traffic. Specifically, we assess the ability of CSMA to fully utilize the radio resources and in turn to stabilize the network in a dynamic setting with flow arrivals and departures. We prove that CSMA is optimal in the ad-hoc mode, when each flow goes through a unique dedicated wireless link from a transmitter to a receiver. It is generally suboptimal in infrastructure mode, when all data flows originate from or are destined to the same set of access points, due to the inherent bias of CSMA against downlink traffic. We propose a slight modification of CSMA that we refer to as flow-aware CSMA, which corrects this bias and makes the algorithm optimal in all cases. The analysis is based on some time-scale separation assumption which is proved valid in the limit of large flow sizes.