Recently, it has been shown that CSMA algorithms which use queue length-based link weights can achieve throughput optimality in wireless networks. In particular, a key result by Rajagopalan, Shah, and Shin (2009) shows that, if the link weights are chosen to be of the form log log(q) (where q is the queue-length), then throughput optimality is achieved. In this paper, we tighten their result by showing that throughput optimality is preserved even with weight functions of the form log(q)/g(q), where g(q)can be a function that increases arbitrarily slowly. The significance of the result is due to the fact that weight functions of the form log(q)/g(q) seem to achieve the best delay performance in practice. I. INTRODUCTIONEfficient operation of wireless networks has always been a difficult task due to the inherent broadcast nature of the wireless medium. Transmission by a user can cause an interference for its neighbors. If two neighboring users transmit at the same time, the Signal-to-Noise-plus-Interference Ratio (SINR) of the users' links could go below the required SINR for the successful decoding of data packets at their corresponding receivers. In this case, we say that their messages collide with each other. Therefore, multiple users can transmit at the same time provided that they do not cause significant interference for each other. The users need a distributed Medium Access Control (MAC) protocol to determine which users should transmit which makes the optimal operation even harder. 2 CSMA (Carrier sense Multiple access) type protocols are an important class of MAC protocols due to their simplicity of implementation, and have been widely used in practice. e.g., in WLANs or emerging wireless mesh networks. In these protocols, each user listens to the channel and can transmit, with some probability, only when the channel is not busy.Despite the extreme simplicity of the CSMA-type algorithms, their efficiency have been always questionable. In this paper, we consider efficient design of such CSMA-type algorithms that can achieve maximum throughput and good delay performance.The wireless network can be modeled by its conflict graph (or interference model), where two communication links form two neighboring nodes in the conflict graph, if they cannot transmit simultaneously. The well-known result of Tassiulas and Ephremides [1] states that the Maximum Weight Scheduling (MWS) algorithm is throughput optimal, where weights are queue-lengths.However, for a general network, MWS involves finding the maximum weight independent set of the conflict graph in each time slot which is a formidable task, and hence, is not implementable.This has led to a rich amount of literature on design of approximate algorithms to alleviate the computational complexity of the MWS algorithm. A recent result in this direction of research can be found in [9].Recently, it has been shown that it is possible to design CSMA algorithms that are throughputoptimal. Reference [10] develops an algorithm that adaptively chooses the CSMA parameters und...
The process by which new ideas, innovations, and behaviors spread through a large social network can be thought of as a networked interaction game: Each agent obtains information from certain number of agents in his friendship neighborhood, and adapts his idea or behavior to increase his benefit. In this paper, we are interested in how opinions, about a certain topic, form in social networks. We model opinions as continuous scalars ranging from 0 to 1 with 1 (0) representing extremely positive (negative) opinion. Each agent has an initial opinion and incurs some cost depending on the opinions of his neighbors, his initial opinion, and his stubbornness about his initial opinion. Agents iteratively update their opinions based on their own initial opinions and observing the opinions of their neighbors. The iterative update of an agent can be viewed as a myopic cost-minimization response (i.e., the so-called best response) to the others' actions. We study whether an equilibrium can emerge as a result of such local interactions and how such equilibrium possibly depends on the network structure, initial opinions of the agents, and the location of stubborn agents and the extent of their stubbornness. We also study the convergence speed to such equilibrium and characterize the convergence time as a function of aforementioned factors. We also discuss the implications of such results in a few well-known graphs such as Erdos-Renyi random graphs and small-world graphs.
In data-parallel computing frameworks, intermediate parallel data is often produced at various stages which needs to be transferred among servers in the datacenter network (e.g. the shuffle phase in MapReduce). A stage often cannot start or be completed unless all the required data pieces from the preceding stage are received. Coflow is a recently proposed networking abstraction to capture such communication patterns. We consider the problem of efficiently scheduling coflows with release dates in a shared datacenter network so as to minimize the total weighted completion time of coflows. Several heuristics have been proposed recently to address this problem, as well as a few polynomial-time approximation algorithms with provable performance guarantees. Our main result in this paper is a polynomial-time deterministic algorithm that improves the prior known results. Specifically, we propose a deterministic algorithm with approximation ratio of 5, which improves the prior best known ratio of 12. For the special case when all coflows are released at time zero, our deterministic algorithm obtains approximation ratio of 4 which improves the prior best known ratio of 8. The key ingredient of our approach is an improved linear program formulation for sorting the coflows followed by a simple list scheduling policy. Extensive simulation results, using both synthetic and real traffic traces, are presented that verify the performance of our algorithm and show improvement over the prior approaches.
Abstract-For a wireless network with n nodes distributed in an area A, and with n source-destination pairs communicating with each other at some common rate, the hierarchical cooperation scheme proposed in (Ozgur, Leveque, and Tse, 2007) is analyzed and optimized by choosing the number of hierarchical stages and the corresponding cluster sizes that maximize the total throughput. It turns out that increasing the number of stages does not necessarily improve the throughput, and the closed-form solutions for the optimization problem can be explicitly obtained. Based on the expression of the maximum achievable throughput, it is found that the hierarchical scheme achieves a scaling with the exponent depending on n. In addition, to apply the hierarchical cooperation scheme to random networks, a clustering algorithm is developed, which divides the whole network into quadrilateral clusters, each with exactly the number of nodes required.
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