Adaptive CSMA Under the SINR Model: Efficient Approximation Algorithms for Throughput and Utility Maximization

Abstract

We consider a Carrier Sense Multiple Access (CSMA) based scheduling algorithm for a single-hop wireless network under a realistic Signal-to-interference-plus-noise ratio (SINR) model for the interference. We propose two local optimization based approximation algorithms to efficiently estimate certain attempt rate parameters of CSMA called fugacities. It is known that adaptive CSMA can achieve throughput optimality by sampling feasible schedules from a Gibbs distribution, with appropriate fugacities. Unfortunately, obtaining these optimal fugacities is an NP-hard problem. Further, the existing adaptive CSMA algorithms use a stochastic gradient descent based method, which usually entails an impractically slow (exponential in the size of the network) convergence to the optimal fugacities. To address this issue, we first propose an algorithm to estimate the fugacities, that can support a given set of desired service rates. The convergence rate and the complexity of this algorithm are independent of the network size, and depend only on the neighborhood size of a link. Further, we show that the proposed algorithm corresponds exactly to performing the well-known Bethe approximation to the underlying Gibbs distribution. Then, we propose another local algorithm to estimate the optimal fugacities under a utility maximization framework, and characterize its accuracy. Numerical results indicate that the proposed methods have a good degree of accuracy, and achieve extremely fast convergence to near-optimal fugacities, and often outperform the convergence rate of the stochastic gradient descent by a few orders of magnitude.

Free Energy Approximations for CSMA Networks

“…Second, one could try to relax the conflict graph based interference model considered in this paper to a more realistic SINR (signal-tointerference-plus-noise ratio) model. In fact, such a relaxation of the Bethe approximation presented in [25] was recently developed in [16]. Finally, other free energy approximation techniques such as the treebased reparameterization framework of [21] could be considered as well.…”

Price-Based Joint Offloading and Resource Allocation for Ad Hoc Mobile Cloud

“…In this subsection, we will introduce two communication models in details. To model the wireless contention that the multiple access among users share spectrum, some media access control protocol, such as carrier sense multiple access (CSMA) [28], is implemented for users to capture the channel to transmit data packet. Hence, the expected throughput C w i of User i(i ∈ W ∪ M) for computation offloading over the chosen wireless channel can be modeled as [29]…”

Simulated Annealing for Optimal Resource Allocation in Wireless Networks with Imperfect Communications

“…There are a few works that have extended the CSMA algortihms to the SINR model case [23], [20]. However, these works are restricted to the use of a threshold-type capacity model, i.e., a link obtains a unit capacity if its SINR is above a certain threshold, and zero otherwise.…”