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.
Another line of related work, inspired by maximum weight scheduling @cite_23 , considers adapting the transmission lengths based on the current queue length of a node @cite_27 @cite_28 , that is, backoff periods and packets have mean length @math and after a backoff period or packet transmission a node transmits a packet with some probability that depends on a weight function of its queue length (provided that its neighbors are sensed silent). The main observation was that a slowly changing weight function is necessary for stability and among such functions a slower function leads to a more stable network at the cost of increased queue-sizes (and delay). Other queue-length based CSMA CA algorithms that were shown to be throughput-optimal in some setting include @cite_7 @cite_18 .
@cite_18 @cite_7 @cite_28 @cite_27 @cite_23
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In this paper, we consider the CSMA CA multihop networks where the two end-nodes transmit their packets to each other and each intermediate node adopts network coding for delivering bidirectional flows. In addition, the neighbor nodes are randomly uniformly deployed with the Poisson Point Process. By varying the combination of the physical carrier-sensing range of the transmitter node and the target signal-to-interference ratio (SIR) set by the receiver node, we can control the interference level in the network and the degree of spatial reuse of a frequency band. The larger the carrier-sensing range is, the smaller the interference level, while the smaller the opportunity of getting a channel by a node. Similarly, the higher the target SIR value is, the more probable the retransmission (by the exponential random backoff) is, while the better the link quality on successful transmission is getting. Under this tradeoff context, we find the optimal combinations of these two factors that make the end-to-end throughput of the flow maximal for three different retransmission schemes. It was shown recently that carrier sense multiple access (CSMA)-like distributed algorithms can achieve the maximal throughput in wireless networks (and task processing networks) under certain assumptions. One important but idealized assumption is that the sensing time is negligible, so that there is no collision. In this paper, we study more practical CSMA-based scheduling algorithms with collisions. First, we provide a Markov chain model and give an explicit throughput formula that takes into account the cost of collisions and overhead. The formula has a simple form since the Markov chain is "almost" time-reversible. Second, we propose transmission-length control algorithms to approach throughput-optimality in this case. Sufficient conditions are given to ensure the convergence and stability of the proposed algorithms. Finally, we characterize the relationship between the CSMA parameters (such as the maximum packet lengths) and the achievable capacity region. In this paper, we consider a source node that operates over a time varying channel with energy harvesting capability. The goal of the source is to maximize the average number of successfully delivered packets per time slot. The source is able to choose whether to transmit a packet or defer the transmission in each time slot. The decision which is chosen by the source depends on the channel information available and the length of the energy queue. We formulate the problem of finding the optimal policy as a Markovian decision problem. We show some properties of the value function that represents the discounted number of successfully delivered packets per time slot. We prove that the optimal policy is a threshold type policy depending on the state of the channel and the length of the energy queue. We also derive an upper bound for the average number of packets per time slots successfully received by the destination. We show using numerical results that this bound is a tight bound on the performance of the optimal policy. And we consider the case of time varying channel but without channel state information (CSI). Then, we study the impact of channel time varying nature and the availability of CSI. In this case, we show that the optimal policy is a greedy policy. The performance of this greedy policy is also calculated. This paper provides proofs of the rate stability, Harris recurrence, and e-optimality of carrier sense multiple access (CSMA) algorithms where the random access (or backoff) parameter of each node is adjusted dynamically. These algorithms require only local information and they are easy to implement. The setup is a network of wireless nodes with a fixed conflict graph that identifies pairs of nodes whose simultaneous transmissions conflict. The paper studies two algorithms. The first algorithm schedules transmissions to keep up with given arrival rates of packets. The second algorithm controls the arrivals in addition to the scheduling and attempts to maximize the sum of the utilities, in terms of the rates, of the packet flows at different nodes. For the first algorithm, the paper proves rate stability for strictly feasible arrival rates and also Harris recurrence of the queues. For the second algorithm, the paper proves the e-optimality in terms of the utilities of the allocated rates. Both algorithms are iterative and we study two versions of each of them. In the first version, both operate with strictly local information but have relatively weaker performance guarantees; under the second version, both provide stronger performance guarantees by utilizing the additional information of the number of nodes in the network.