This book chapter introduces the use of Continuous Time Markov Networks (CTMN) to analytically capture the operation of Carrier Sense Multiple Access with Collision Avoidance (CSMA CA) networks. It is of tutorial nature, and it aims to be an introduction on this topic, providing a clear and easy-to-follow description. To illustrate how CTMN can be used, we introduce a set of representative and cutting-edge scenarios, such as Vehicular Ad-hoc Networks (VANETs), Power Line Communication networks and multiple overlapping Wireless Local Area Networks (WLANs). For each scenario, we describe the specific CTMN, obtain its stationary distribution and compute the throughput achieved by each node in the network. Taking the per-node throughput as reference, we discuss how the complex interactions between nodes using CSMA CA have an impact on system performance.
In this paper, we use a Markov model to develop a product form solution to efficiently analyze the throughput of arbitrary topology multihop packet radio networks that employ a carrier sensing multiple access (CSMA) protocol with perfect capture. We consider both exponential and nonexponential packet length distributions. Our method preserves the dependence between nodes, characteristic of CSMA, and determines the joint probability that nodes are transmitting. The product form analysis provides the basis for an automated algorithm that determines the maximum throughput in networks of size up to 100 radio nodes. Numerical examples for several networks are presented. This model has led to many theoretical and practical extensions. These include determination of conditions for product form analysis to hold, extension to other access protocols, and consideration of acknowledgments. 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 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. In multi-hop ad hoc networks, the efficiency of a medium access control protocol under heavy traffic load depends mainly on its ability to schedule a large number of simultaneous non-interfering transmissions. However, as each node has only a local view of the network, it is difficult to globally synchronize transmission times over the whole network. How does the lack of global coordination affect spatial reuse in multi-hop wireless networks? We show that in a de-centralized network the spatial reuse does not benefit from global clock synchronization. On the contrary, we demonstrate that non-slotted protocols using collision avoidance mechanisms can achieve a higher spatial reuse than the corresponding slotted protocols. By means of a simple backoff mechanism, one can thus favor the spontaneous emergence of spatially dense transmission schedules. In this paper, we consider the throughput modelling and fairness provisioning in CSMA CA based ad-hoc networks. The main contributions are: firstly, a throughput model based on Markovian analysis is proposed for the CSMA CA network with a general topology. Simulation investigations are presented to verify its performance. Secondly, fairness issues in CSMA CA networks are discussed based on the throughput model. The origin of unfairness is explained and the trade-off between throughput and fairness is illustrated. Thirdly, throughput approximations based on local topology information are proposed and their performances are investigated. Fourthly, three different fairness metrics are presented and their distributed implementations, based on the throughput approximation, are proposed.  