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
2152859483 2542265429 2142178125 2125141803 2105177639
Recently, it has been shown that carrier-sense multiple access (CSMA)-type random access algorithms can achieve the maximum possible throughput in ad hoc wireless networks. However, these algorithms assume an idealized continuous-time CSMA protocol where collisions can never occur. In addition, simulation results indicate that the delay performance of these algorithms can be quite bad. On the other hand, although some simple heuristics (such as greedy maximal scheduling) can yield much better delay performance for a large set of arrival rates, in general they may only achieve a fraction of the capacity region. In this paper, we propose a discrete-time version of the CSMA algorithm. Central to our results is a discrete-time distributed randomized algorithm that is based on a generalization of the so-called Glauber dynamics from statistical physics, where multiple links are allowed to update their states in a single timeslot. The algorithm generates collision-free transmission schedules while explicitly taking collisions into account during the control phase of the protocol, thus relaxing the perfect CSMA assumption. More importantly, the algorithm allows us to incorporate heuristics that lead to very good delay performance while retaining the throughput-optimality property. We propose and analyze a distributed backlog-based CSMA policy to achieve fairness and throughput-optimality in wireless multihop networks. The analysis is based on a CSMA fixed point approximation that is accurate for large networks with many small flows and a small sensing period. We use fluid limits to explore the (in)stability properties of wireless networks with queue-based random-access algorithms. Queue-based random-access schemes are simple and inherently distributed in nature, yet provide the capability to match the optimal throughput performance of centralized scheduling mechanisms in a wide range of scenarios. Unfortunately, the type of activation rules for which throughput optimality has been established, may result in excessive queue lengths and delays. The use of more aggressive persistent access schemes can improve the delay performance, but does not offer any universal maximum-stability guarantees. In order to gain qualitative insight and investigate the (in)stability properties of more aggressive persistent activation rules, we examine fluid limits where the dynamics are scaled in space and time. In some situations, the fluid limits have smooth deterministic features and maximum stability is maintained, while in other scenarios they exihibit random oscillatory characteristics, giving rise to major technical challenges. In the latter regime, more aggressive access schemes continue to provide maximum stability in some networks, but may cause instability in others. In order to prove that, we focus on a particular network example and conduct a detailed analysis of the fluid limit process for the associated Markov chain. Specifically, we develop a novel approach based on stopping time sequences to deal with the switching probabilities governing the sample paths of the fluid limit process. Simulation experiments are conducted to illustrate and val- idate the analytical results. Keywords: Carrier-Sense Multiple Access (CSMA), fluid limits, queue-based strategies, stability issues. The popularity of Aloha-like algorithms for resolution of contention between multiple entities accessing common resources is due to their extreme simplicity and distributed nature. Example applications of such algorithms include Ethernet and recently emerging wireless multi-access networks. Despite a long and exciting history of more than four decades, the question of designing an algorithm that is essentially as simple and distributed as Aloha while being efficient has remained unresolved. In this paper, we resolve this question successfully for a network of queues where contention is modeled through independent-set constraints over the network graph. The work by Tassiulas and Ephremides (1992) suggests that an algorithm that schedules queues so that the summation of weight' of scheduled queues is maximized, subject to constraints, is efficient. However, implementing such an algorithm using Aloha-like mechanism has remained a mystery. We design such an algorithm building upon a Metropolis-Hastings sampling mechanism along with selection of weight' as an appropriate function of the queue-size. The key ingredient in establishing the efficiency of the algorithm is a novel adiabatic-like theorem for the underlying queueing network, which may be of general interest in the context of dynamical systems. The stability of a queueing network with interdependent servers is considered. The dependency among the servers is described by the definition of their subsets that can be activated simultaneously. Multihop radio networks provide a motivation for the consideration of this system. The problem of scheduling the server activation under the constraints imposed by the dependency among servers is studied. The performance criterion of a scheduling policy is its throughput that is characterized by its stability region, that is, the set of vectors of arrival and service rates for which the system is stable. A policy is obtained which is optimal in the sense that its stability region is a superset of the stability region of every other scheduling policy, and this stability region is characterized. The behavior of the network is studied for arrival rates that lie outside the stability region. Implications of the results in certain types of concurrent database and parallel processing systems are discussed. >