We propose a process algebra for link layer protocols, featuring a unique mechanism for modelling frame collisions. We also formalise suitable liveness properties for link layer protocols specified in this framework. To show applicability we model and analyse two versions of the Carrier-Sense Multiple Access with Collision Avoidance (CSMA CA) protocol. Our analysis confirms the hidden station problem for the version without virtual carrier sensing. However, we show that the version with virtual carrier sensing not only overcomes this problem, but also the exposed station problem with probability 1. Yet the protocol cannot guarantee packet delivery, not even with probability 1.
Beyond model checking, simulation and test-bed experiments, we are only aware of two other formal approaches. In @cite_4 Markov chains are used to derive an accurate, analytical model to compute the throughput of CSMA CA. Calculating throughput is an orthogonal task to our vision of proving (functional) correctness.
@cite_4
2130986870 2158384898 2032566227 2054671542
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. 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. 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. Random-access algorithms such as CSMA provide a popular mechanism for distributed medium access control in large-scale wireless networks. In recent years, tractable stochastic models have been shown to yield accurate throughput estimates for CSMA networks. We consider a saturated random-access network on a general conflict graph, and prove that for every feasible combination of throughputs, there exists a unique vector of back-off rates that achieves this throughput vector. This result entails proving global invertibility of the non-linear function that describes the throughputs of all nodes in the network. We present several numerical procedures for calculating this inverse, based on fixed-point iteration and Newton's method. Finally, we provide closed-form results for several special conflict graphs using the theory of Markov random fields.