6 research outputs found

    Achievable Performance in Product-Form Networks

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    We characterize the achievable range of performance measures in product-form networks where one or more system parameters can be freely set by a network operator. Given a product-form network and a set of configurable parameters, we identify which performance measures can be controlled and which target values can be attained. We also discuss an online optimization algorithm, which allows a network operator to set the system parameters so as to achieve target performance metrics. In some cases, the algorithm can be implemented in a distributed fashion, of which we give several examples. Finally, we give conditions that guarantee convergence of the algorithm, under the assumption that the target performance metrics are within the achievable range.Comment: 50th Annual Allerton Conference on Communication, Control and Computing - 201

    Fast Mixing of Parallel Glauber Dynamics and Low-Delay CSMA Scheduling

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    Glauber dynamics is a powerful tool to generate randomized, approximate solutions to combinatorially difficult problems. It has been used to analyze and design distributed CSMA (Carrier Sense Multiple Access) scheduling algorithms for multi-hop wireless networks. In this paper we derive bounds on the mixing time of a generalization of Glauber dynamics where multiple links are allowed to update their states in parallel and the fugacity of each link can be different. The results can be used to prove that the average queue length (and hence, the delay) under the parallel Glauber dynamics based CSMA grows polynomially in the number of links for wireless networks with bounded-degree interference graphs when the arrival rate lies in a fraction of the capacity region. We also show that in specific network topologies, the low-delay capacity region can be further improved.Comment: 12 page

    Convergence and Stability of a Distributed CSMA Algorithm for Maximal Network Throughput

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    Designing efficient scheduling algorithms is an important problem in a general class of networks with resourcesharing constraints, such as wireless networks and stochastic processing networks [7]. In [5], we proposed a distributed scheduling algorithm that can achieve the maximal throughput in such networks under certain conditions. This algorithm was inspired by CSMA (Carrier Sense Multiple Access). In this paper, we prove the convergence and stability of the algorithm, with properly-chosen step sizes and update intervals. Convergence of the joint scheduling and congestion control algorithm for utility maximization in [5] can be proved similarly
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