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66
Layering as optimization decomposition
 PROCEEDINGS OF THE IEEE
, 2007
"... Network protocols in layered architectures have historically been obtained on an ad hoc basis, and many of the recent crosslayer designs are conducted through piecemeal approaches. They may instead be holistically analyzed and systematically designed as distributed solutions to some global optimiza ..."
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Cited by 63 (23 self)
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Network protocols in layered architectures have historically been obtained on an ad hoc basis, and many of the recent crosslayer designs are conducted through piecemeal approaches. They may instead be holistically analyzed and systematically designed as distributed solutions to some global optimization problems. This paper presents a survey of the recent efforts towards a systematic understanding of “layering ” as “optimization decomposition”, where the overall communication network is modeled by a generalized Network Utility Maximization (NUM) problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the subproblems. There can be many alternative decompositions, each leading to a different layering architecture. This paper summarizes the current status of horizontal decomposition into distributed computation and vertical decomposition into functional modules such as congestion control, routing, scheduling, random access, power control, and channel coding. Key messages and methods arising from many recent work are listed, and open issues discussed. Through case studies, it is illustrated how “Layering as Optimization Decomposition” provides a common language to think
Structural properties of proportional fairness: Stability and insensitivity
 Annals of Applied Probability
"... In this article we provide a novel characterization of the proportionally fair bandwidth allocation of network capacities, in terms of the Fenchel– Legendre transform of the network capacity region. We use this characterization to prove stability (i.e., ergodicity) of network dynamics under proporti ..."
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Cited by 49 (3 self)
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In this article we provide a novel characterization of the proportionally fair bandwidth allocation of network capacities, in terms of the Fenchel– Legendre transform of the network capacity region. We use this characterization to prove stability (i.e., ergodicity) of network dynamics under proportionally fair sharing, by exhibiting a suitable Lyapunov function. Our stability result extends previously known results to a more general model including Markovian users routing. In particular, it implies that the stability condition previously known under exponential service time distributions remains valid under socalled phasetype service time distributions. We then exhibit a modification of proportional fairness, which coincides with it in some asymptotic sense, is reversible (and thus insensitive), and has explicit stationary distribution. Finally we show that the stationary distributions under modified proportional fairness and balanced fairness, a sharing criterion proposed because of its insensitivity properties, admit the same large deviations characteristics. These results show that proportional fairness is an attractive bandwidth allocation criterion, combining the desirable properties of ease of implementation with performance and insensitivity.
Flowlevel stability of data networks with nonconvex and timevarying rate regions
 In Proceedings of ACM Sigmetrics
, 2007
"... In this paper we characterize flowlevel stochastic stability for networks with nonconvex or timevarying rate regions under resource allocation based on utility maximization. Similar to prior works on flowlevel stability, we consider exogenous data arrivals with finite workloads. However, to mode ..."
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Cited by 20 (4 self)
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In this paper we characterize flowlevel stochastic stability for networks with nonconvex or timevarying rate regions under resource allocation based on utility maximization. Similar to prior works on flowlevel stability, we consider exogenous data arrivals with finite workloads. However, to model many realistic situations, the rate region, which constrains the feasibility of resource allocation, may be either nonconvex or timevarying. When the rate region is fixed but nonconvex, we derive sufficient and necessary conditions for stability, which coincide when the set of allocated rate vectors has continuous contours. When the rate region is timevarying according to some stationary, ergodic process, we derive the precise stability region. In both cases, the size of the stability region depends on the resource allocation policy, in particular, on the fairness parameter α in αfair utility maximization. This is in sharp contrast with the substantial existing literature on stability under fixed and convex rate regions, in which the stability region coincides with the rate region for many utilitybased resource allocation schemes, independently of the value of the fairness parameter. We further investigate the tradeoff between fairness and stability when rate region is nonconvex or timevarying. Numerical examples of both wired and wireless networks are provided to illustrate the new stability regions and tradeoffs proved in the paper.
Flowlevel Stability of UtilityBased Allocations for NonConvex Rate Regions
, 2006
"... We investigate the stability of utilitymaximizing allocations in networks with arbitrary rate regions. We consider a dynamic setting where users randomly generate data flows according to some exogenous traffic processes. Network stability is then defined as the ergodicity of the process describing ..."
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Cited by 18 (1 self)
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We investigate the stability of utilitymaximizing allocations in networks with arbitrary rate regions. We consider a dynamic setting where users randomly generate data flows according to some exogenous traffic processes. Network stability is then defined as the ergodicity of the process describing the number of active flows. When the rate region is convex, the stability region is known to coincide with the rate region, independently of the considered utility function. We show that for nonconvex rate regions, the choice of the utility function is crucial to ensure maximum stability. The results are illustrated on the simple case of a wireless network consisting of two interacting base stations.
Stochastic Network Utility Maximization A tribute to Kelly’s paper published in this journal a decade ago
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Stability and fairness of explicit congestion control with small buffers
 SIGCOMM Computer Communication Review
, 2008
"... Rate control protocols that utilise explicit feedback from routers are able to achieve fast convergence to an equilibrium which approximates processorsharing on a single bottleneck link, and hence such protocols allow short flows to complete quickly. For a network, however, processorsharing is not ..."
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Cited by 10 (1 self)
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Rate control protocols that utilise explicit feedback from routers are able to achieve fast convergence to an equilibrium which approximates processorsharing on a single bottleneck link, and hence such protocols allow short flows to complete quickly. For a network, however, processorsharing is not uniquely defined but corresponds with a choice of fairness criteria, and proportional fairness has a reasonable claim to be the network generalization of processorsharing. In this paper, we develop a variant of RCP (rate control protocol) that achieves αfairness when buffers are small, including proportional fairness as the case α = 1. At the level of theoretical abstraction treated, our model incorporates a general network topology, and heterogeneous propagation delays. For our variant of the RCP algorithm, we establish a simple decentralized sufficient condition for local stability. An outstanding question for explicit congestion control is whether the presence of feedback based on queue size is helpful or not, given the presence of feedback based on rate mismatch. We show that, for the variant of RCP considered here, feedback based on queue size may cause the queue to be less accurately controlled. A further outstanding question for explicit congestion control is the scale of the stepchange in rate that is necessary at a resource to accommodate a new flow. We show that, for the variant of RCP considered here, this can be estimated from the aggregate flow through the resource, without knowledge of individual flow rates.
Distributed dynamic load balancing in wireless networks
 in Proc. 20th Int. Teletraffic Conf
, 2007
"... Abstract. Spatial and temporal load variations, e.g. flash overloads and traffic hot spots that persist for minutes to hours, are intrinsic features of wireless networks, and give rise to potentially huge performance repercussions. Dynamic load balancing strategies provide a natural mechanism for d ..."
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Cited by 10 (1 self)
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Abstract. Spatial and temporal load variations, e.g. flash overloads and traffic hot spots that persist for minutes to hours, are intrinsic features of wireless networks, and give rise to potentially huge performance repercussions. Dynamic load balancing strategies provide a natural mechanism for dealing with load fluctuations and alleviating the performance impact. In the present paper we propose a distributed shadowpricebased approach to dynamic load balancing in wireless data networks. We examine two related problem versions: (i) minimizing a convex function of the transmitter loads for given user throughput requirements; and (ii) maximizing a concave function of the user throughputs subject to constraints on the transmitter loads. As conceptual counterparts, these two formulations turn out to be amenable to a common primaldual decomposition framework. Numerical experiments show that dynamic load balancing yields significant performance gains in terms of user throughputs and delays, even in scenarios where the longterm loads are perfectly balanced.
Stochastic stability under network utility maximization: General file size distribution
 In Proceedings of Allerton.[5
, 2006
"... We prove the stochastic stability of resource allocation under Network Utility Maximization (NUM) under general arrival process and file size distribution with bounded support, for αfair utilities with α sufficiently small and possibly different for different sources ’ utility functions. In additio ..."
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Cited by 8 (1 self)
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We prove the stochastic stability of resource allocation under Network Utility Maximization (NUM) under general arrival process and file size distribution with bounded support, for αfair utilities with α sufficiently small and possibly different for different sources ’ utility functions. In addition, our results imply that the system operating under αfair utility is 1/(1 + α)approximate stable for any α ∈ (0, ∞) for any file size distribution with bounded support. Our results are in contrast to the recent stability result of Bramson (2005) for maxmin fair (i.e. α = ∞) under general arrival process and file size distribution, and that of Massoulie (2006) for proportional fair (i.e. α = 1) under Poisson arrival process and phasetype distributions. To obtain our results, we develop an appropriate Lyapunov function for the fluid model established by Gromoll and Williams (2006) 1. I.
Routing Games for Traffic Engineering
 in ICC ’09
"... Abstract—Current data network scenario makes Traffic Engineering (TE) a very challenging task. The ever growing access rates and new applications running on endhosts result in more variable and unpredictable traffic patterns. By providing origindestination pairs with several possible paths, load ..."
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Cited by 8 (6 self)
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Abstract—Current data network scenario makes Traffic Engineering (TE) a very challenging task. The ever growing access rates and new applications running on endhosts result in more variable and unpredictable traffic patterns. By providing origindestination pairs with several possible paths, loadbalancing has proved itself an excellent tool to face this uncertainty. In particular, mechanisms where routers greedily minimize a path cost function (thus requiring minimum coordination) have been studied from a gametheoretic perspective in what is known as a Routing Game (RG). The contribution of this paper is twofold. We first propose a new RG specifically designed for elastic traffic, where we maximize the total utility through loadbalancing only. Secondly, we consider several important RGs from a TE perspective and, using several real topologies and traffic demands, present a thorough comparison of their performance. This paper brings insight into several RGs, which will help one in choosing an adequate dynamic loadbalancing mechanism. The comparison shows that the performance gain of the proposed game can be important.