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Scheduling in multichannel wireless networks: Rate function optimality in the smallbuffer regime
, 2009
"... We consider the problem of designing scheduling algorithms for the downlink of cellular wireless networks where bandwidth is partitioned into tens to hundreds of parallel channels, each of which can be allocated to a possibly different user in each time slot. We prove that a class of algorithms call ..."
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Cited by 16 (6 self)
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We consider the problem of designing scheduling algorithms for the downlink of cellular wireless networks where bandwidth is partitioned into tens to hundreds of parallel channels, each of which can be allocated to a possibly different user in each time slot. We prove that a class of algorithms called Iterated Longest Queues First (iLQF) algorithms achieves the smallest buffer overflow probability in an appropriate large deviations sense. The class of iLQF algorithms is quite different from the class of maxweight policies which have been studied extensively in the literature, and it achieves much better performance in the regimes studied in this paper.
Stochastic Network Utility Maximization A tribute to Kelly’s paper published in this journal a decade ago
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Monotonicity properties for multiclass queueing systems. Discrete Event Dynamic Systems DOI
, 2009
"... We study multidimensional stochastic processes that arise in queueing models used in the performance evaluation of wired and wireless networks. The evolution of the stochastic process is determined by the scheduling policy used in the associated queueing network. For general arrival and service pro ..."
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Cited by 4 (2 self)
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We study multidimensional stochastic processes that arise in queueing models used in the performance evaluation of wired and wireless networks. The evolution of the stochastic process is determined by the scheduling policy used in the associated queueing network. For general arrival and service processes, we give sufficient conditions in order to compare samplepath wise the workload and the number of users under different policies. This allows us to evaluate the performance of the system under various policies in terms of stability, the mean overall delay and the mean holding cost. We apply the general framework to linear networks, where users of one class require service from several shared resources simultaneously. For the important family of weighted αfair policies, stability results are derived and monotonicity of the mean holding cost with respect to the fairness parameter α and the relative weights is established. In order to broaden the comparison results, we investigate a heavytraffic regime and perform numerical experiments. In addition, we study a singleserver queue with two user classes, and show that under Discriminatory Processor Sharing (DPS) or Generalized Processor Sharing (GPS) the mean overall sojourn time is monotone with respect to the ratio of the weights. Finally we extend the framework to obtain comparison results that cover the singleserver queue with an arbitrary number of classes as well. 1
Asymptotically optimal parallel resource assignment with interference. Queueing Systems
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Network Stability Under Alpha Fair Bandwidth Allocation With General File Size Distribution
"... Abstract—Rate allocation among a fixed set of endtoend connections in the Internet is carried out by congestion control, which has a well established model: it optimizes a concave network utility, a particular case of which is the alphafair bandwidth allocation. This paper studies the slower dyn ..."
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Cited by 3 (0 self)
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Abstract—Rate allocation among a fixed set of endtoend connections in the Internet is carried out by congestion control, which has a well established model: it optimizes a concave network utility, a particular case of which is the alphafair bandwidth allocation. This paper studies the slower dynamics of connections themselves, that arrive randomly in the network and are served at the allocated rate. It has been shown that under the condition that the mean offered load at each link is less than its capacity, the resulting queueing system is stochastically stable, for the case of exponentially distributed filesizes. The conjecture that the result holds for general filesize distributions has remained open, and is very relevant since heavytailed distributions are often the best models of Internet file sizes. In this paper, building on existing fluid models of the system, we use a partial differential equation to characterize the dynamics. The equation keeps track of residual file size and
How bad is suboptimal rate allocation
 Proc. IEEE INFOCOM
, 2008
"... Abstract—Not too bad. A rate allocation that is suboptimal with respect to a utility maximization formulation still maintains the maximum flowlevel stability when the utility gap is sufficiently small, and provides a minimum size of stability region otherwise. Utilitysuboptimal allocation may als ..."
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Cited by 2 (2 self)
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Abstract—Not too bad. A rate allocation that is suboptimal with respect to a utility maximization formulation still maintains the maximum flowlevel stability when the utility gap is sufficiently small, and provides a minimum size of stability region otherwise. Utilitysuboptimal allocation may also enhance other network performance metrics, e.g., it may increase network throughput and reduce link saturation. Quantifying these intuitions, this paper provides a theoretical support for turning attention from optimal but complex solutions of network optimization to those that are simple even though suboptimal.
Comparison of bandwidthsharing policies in a linear network
 In Proceedings of ValueTools
, 2008
"... In bandwidthsharing networks, users of various classes require service from different subsets of shared resources simultaneously. These networks have been proposed to analyze the performance of wired and wireless networks. For general arrival and service processes, we give sufficient conditions in ..."
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In bandwidthsharing networks, users of various classes require service from different subsets of shared resources simultaneously. These networks have been proposed to analyze the performance of wired and wireless networks. For general arrival and service processes, we give sufficient conditions in order to compare samplepath wise the workload and the number of users under different policies in a linear bandwidthsharing network. This allows us to compare the performance of the system under various policies in terms of stability, the mean overall delay and the weighted mean number of users. For the important family of weighted αfair policies, we derive stability results and establish monotonicity of the weighted mean number of users with respect to the fairness parameter α and the relative weights. In order to broaden the comparison results, we investigate a heavytraffic regime and perform numerical experiments. 1.
Stability and Benefits of Suboptimal Utility
"... Abstract—Network utility maximization has been widely used to model resource allocation and network architectures. But in practice often it cannot be solved optimally due to complexity reasons. Thus motivated, we address the following two questions in this paper: can suboptimal utility maximization ..."
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Abstract—Network utility maximization has been widely used to model resource allocation and network architectures. But in practice often it cannot be solved optimally due to complexity reasons. Thus motivated, we address the following two questions in this paper: can suboptimal utility maximization maintain queue stability? Can underoptimization of utility objective function in fact lead to benefits to other network design objectives? We show that a resource allocation that is suboptimal with respect to a utility maximization formulation still maintains the maximum flowlevel stability when the utility gap is sufficiently small and the information delay is bounded, and can still provide a guaranteed size of stability region otherwise. Utilitysuboptimal rate allocation can also enhance other network performance metrics, e.g., it may increase network throughput and reduce link saturation. Quantifying these intuitions, this paper provides a theoretical support for turning attention from optimal but complex solutions of network optimization to those that are simple even though suboptimal. I.
1Network Stability under Alpha Fair Bandwidth Allocation with General File Size Distribution
"... Abstract—Rate allocation among a fixed set of endtoend connections in the Internet is carried out by congestion control, which has a well established model: it optimizes a concave network utility, a particular case of which is the alphafair bandwidth allocation. This paper studies the slower dyna ..."
Abstract
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Abstract—Rate allocation among a fixed set of endtoend connections in the Internet is carried out by congestion control, which has a well established model: it optimizes a concave network utility, a particular case of which is the alphafair bandwidth allocation. This paper studies the slower dynamics of connections themselves, that arrive randomly in the network and are served at the allocated rate. It has been shown that under the condition that the mean offered load at each link is less than its capacity, the resulting queueing system is stochastically stable, for the case of exponentially distributed filesizes. The conjecture that the result holds for general filesize distributions has remained open, and is very relevant since heavytailed distributions are often the best models of Internet file sizes. In this paper, building on existing fluid models of the sys