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Maximizing Queueing Network Utility Subject to Stability: Greedy Primal-dual algorithm (2005)

by Alexander L. Stolyar
Venue:Queueing Systems
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Fairness and optimal stochastic control for heterogeneous networks

by Michael J. Neely, Eytan Modiano, Chih-ping Li - Proc. IEEE INFOCOM, March 2005. TRANSACTIONS ON NETWORKING, VOL , 2008
"... Abstract — We consider optimal control for general networks with both wireless and wireline components and time varying channels. A dynamic strategy is developed to support all traffic whenever possible, and to make optimally fair decisions about which data to serve when inputs exceed network capaci ..."
Abstract - Cited by 266 (63 self) - Add to MetaCart
Abstract — We consider optimal control for general networks with both wireless and wireline components and time varying channels. A dynamic strategy is developed to support all traffic whenever possible, and to make optimally fair decisions about which data to serve when inputs exceed network capacity. The strategy is decoupled into separate algorithms for flow control, routing, and resource allocation, and allows each user to make decisions independent of the actions of others. The combined strategy is shown to yield data rates that are arbitrarily close to the optimal operating point achieved when all network controllers are coordinated and have perfect knowledge of future events. The cost of approaching this fair operating point is an end-to-end delay increase for data that is served by the network.
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...oped in [20]-[28]. This work presents a fundamental approach to stochastic network optimization [1] [2] [3] [4]. We note that alternative optimization approaches have recently been considered in [29] =-=[35]-=- using fluid limit models, and in [36] using stochastic gradient theory (see, for example, [37]). Our Lyapunov optimization technique is related to the theory of static and stochastic gradients (see C...

A tutorial on cross-layer optimization in wireless networks

by Xiaojun Lin, Ness B. Shroff, R. Srikant - IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS , 2006
"... This tutorial paper overviews recent developments in optimization based approaches for resource allocation problems in wireless systems. We begin by overviewing important results in the area of opportunistic (channel-aware) scheduling for cellular (single-hop) networks, where easily implementable my ..."
Abstract - Cited by 248 (29 self) - Add to MetaCart
This tutorial paper overviews recent developments in optimization based approaches for resource allocation problems in wireless systems. We begin by overviewing important results in the area of opportunistic (channel-aware) scheduling for cellular (single-hop) networks, where easily implementable myopic policies are shown to optimize system performance. We then describe key lessons learned and the main obstacles in extending the work to general resource allocation problems for multi-hop wireless networks. Towards this end, we show that a clean-slate optimization based approach to the multi-hop resource allocation problem naturally results in a “loosely coupled” crosslayer solution. That is, the algorithms obtained map to different layers (transport, network, and MAC/PHY) of the protocol stack are coupled through a limited amount of information being passed back and forth. It turns out that the optimal scheduling component at the MAC layer is very complex and thus needs simpler (potentially imperfect) distributed solutions. We demonstrate how to use imperfect scheduling in the crosslayer framework and describe recently developed distributed algorithms along these lines. We conclude by describing a set of open research problems.
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... This idea has been further developed into a general class of queue-length-based (or, equivalently, delaybased) opportunistic scheduling schemes that focus on stability and throughput optimality [16]–=-=[20]-=-. For example, in [16], [17], simple index scheduling policies of the following form are shown to be throughput optimal: where is a constant, is the head-of-the-line packet delay at queue , and as bef...

Fair Resource Allocation in Wireless Networks using Queue-length-based Scheduling and Congestion Control

by Atilla Eryilmaz, R. Srikant
"... We consider the problem of allocating resources (time slots, frequency, power, etc.) at a base station to many competing flows, where each flow is intended for a different re-ceiver. The channel conditions may be time-varying and different for different receivers. It is well-known that appropriate ..."
Abstract - Cited by 202 (45 self) - Add to MetaCart
We consider the problem of allocating resources (time slots, frequency, power, etc.) at a base station to many competing flows, where each flow is intended for a different re-ceiver. The channel conditions may be time-varying and different for different receivers. It is well-known that appropriately chosen queue-length based policies are throughput-optimal while other policies based on the estimation of channel statistics can be used to allocate resources fairly (such as proportional fairness) among competing users. In this paper, we show that a combination of queue-length-based scheduling at the base station and congestion control implemented either at the base station or at the end users can lead to fair resource allocation and queue-length stability.

Energy optimal control for time varying wireless networks

by Michael J. Neely - IEEE Trans. Inform. Theory , 2006
"... Abstract — We develop a dynamic control strategy for minimizing energy expenditure in a time varying wireless network with adaptive transmission rates. The algorithm operates without knowledge of traffic rates or channel statistics, and yields average power that is arbitrarily close to the minimum p ..."
Abstract - Cited by 184 (50 self) - Add to MetaCart
Abstract — We develop a dynamic control strategy for minimizing energy expenditure in a time varying wireless network with adaptive transmission rates. The algorithm operates without knowledge of traffic rates or channel statistics, and yields average power that is arbitrarily close to the minimum possible value achieved by an algorithm optimized with complete knowledge of future events. Proximity to this optimal solution is shown to be inversely proportional to network delay. We then present a similar algorithm that solves the related problem of maximizing network throughput subject to peak and average power constraints. The techniques used in this paper are novel and establish a foundation for stochastic network optimization.

Cross-layer congestion control, routing and scheduling design in ad hoc wireless networks

by Lijun Chen, Steven H. Low, Mung Chiang, John C. Doyle - PROC. IEEE INFOCOM , 2006
"... This paper considers jointly optimal design of crosslayer congestion control, routing and scheduling for ad hoc wireless networks. We first formulate the rate constraint and scheduling constraint using multicommodity flow variables, and formulate resource allocation in networks with fixed wireless ..."
Abstract - Cited by 151 (10 self) - Add to MetaCart
This paper considers jointly optimal design of crosslayer congestion control, routing and scheduling for ad hoc wireless networks. We first formulate the rate constraint and scheduling constraint using multicommodity flow variables, and formulate resource allocation in networks with fixed wireless channels (or single-rate wireless devices that can mask channel variations) as a utility maximization problem with these constraints. By dual decomposition, the resource allocation problem naturally decomposes into three subproblems: congestion control, routing and scheduling that interact through congestion price. The global convergence property of this algorithm is proved. We next extend the dual algorithm to handle networks with timevarying channels and adaptive multi-rate devices. The stability of the resulting system is established, and its performance is characterized with respect to an ideal reference system which has the best feasible rate region at link layer. We then generalize the aforementioned results to a general model of queueing network served by a set of interdependent parallel servers with time-varying service capabilities, which models many design problems in communication networks. We show that for a general convex optimization problem where a subset of variables lie in a polytope and the rest in a convex set, the dual-based algorithm remains stable and optimal when the constraint set is modulated by an irreducible finite-state Markov chain. This paper thus presents a step toward a systematic way to carry out cross-layer design in the framework of “layering as optimization decomposition ” for time-varying channel models.
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...ng channels. Our result is applicable to a variety of time-varying systems that can be solved or modelled by dual algorithms. Similar result is obtained in other contexts through different techniques =-=[28]-=-, [6]. Our goal is to present a systematic approach to cross-layer design, not only to improve the performance, but more importantly, to make the interactions between different layers more transparent...

On the Complexity of Scheduling in Wireless Networks

by Gaurav Sharma, Ness B. Shroff, et al. - MOBICOM '06 , 2006
"... We consider the problem of throughput-optimal scheduling in wireless networks subject to interference constraints. We model the interference using a family of K-hop interference models. We define a K-hop interference model as one for which no two links within K hops can successfully transmit at the ..."
Abstract - Cited by 129 (3 self) - Add to MetaCart
We consider the problem of throughput-optimal scheduling in wireless networks subject to interference constraints. We model the interference using a family of K-hop interference models. We define a K-hop interference model as one for which no two links within K hops can successfully transmit at the same time (Note that IEEE 802.11 DCF corresponds to a 2-hop interference model.). For a given K, a throughput-optimal scheduler needs to solve a maximum weighted matching problem subject to the K-hop interference constraints. For K = 1, the resulting problem is the classical Maximum Weighted Matching problem, that can be solved in polynomial time. However, we show that for K> 1, the resulting problems are NP-Hard and cannot be approximated within a factor that grows polynomially with the number of nodes. Interestingly, we show that for specific kinds of graphs, that can be used to model the underlying connectivity graph of a wide range of wireless networks, the resulting problems admit polynomial time approximation schemes. We also show that a simple greedy matching algorithm provides a constant factor approximation to the scheduling problem for all K in this case. We then show that under a setting with single-hop traffic and no rate control, the maximal scheduling policy considered in recent related works can achieve a constant fraction of the capacity region for networks whose connectivity graph can be represented using one of the above classes of graphs. These results are encouraging as they suggest that one can develop distributed algorithms to achieve near optimal throughput in case of a wide range of wireless networks.

Joint congestion control, routing and MAC for stability and fairness in wireless networks

by A. Eryilmaz, R. Srikant - IEEE Journal on Selected Areas in Communications , 2006
"... In this work, we describe and analyze a joint scheduling, routing and congestion control mecha-nism for wireless networks, that asymptotically guarantees stability of the buffers and fair allocation of the network resources. The queue lengths serve as common information to different layers of the ne ..."
Abstract - Cited by 126 (23 self) - Add to MetaCart
In this work, we describe and analyze a joint scheduling, routing and congestion control mecha-nism for wireless networks, that asymptotically guarantees stability of the buffers and fair allocation of the network resources. The queue lengths serve as common information to different layers of the network protocol stack. Our main contribution is to prove the asymptotic optimality of a primal-dual congestion controller, which is known to model different versions of TCP well.

Distributed link scheduling with constant overhead

by Sujay Sanghavi, Loc Bui, R. Srikant - In Proceedings of ACM Sigmetrics , 2007
"... This paper proposes a new class of simple, distributed algorithms for scheduling in wireless networks. The algorithms generate new schedules in a distributed manner via simple local changes to existing schedules. The class is parameterized by integers k ≥ 1. We show that algorithm k of our class ach ..."
Abstract - Cited by 102 (3 self) - Add to MetaCart
This paper proposes a new class of simple, distributed algorithms for scheduling in wireless networks. The algorithms generate new schedules in a distributed manner via simple local changes to existing schedules. The class is parameterized by integers k ≥ 1. We show that algorithm k of our class achieves k/(k +2) of the capacity region, for every k ≥ 1. The algorithms have small and constant worst-case overheads: in particular, algorithm k generates a new schedule using (a) time less than 4k + 2 round-trip times between neighboring nodes in the network, and (b) at most three control transmissions by any given node, for any k. The control signals are explicitly specified, and face the same interference effects as normal data transmissions. Our class of distributed wireless scheduling algorithms are the first ones guaranteed to achieve any fixed fraction of the capacity region while using small and constant overheads that do not scale with network size. The parameter k explicitly captures the tradeoff between control overhead and scheduler throughput performance and provides a tuning knob protocol designers can use to harness this trade-off in practice. 1.

H.: Self-organizing dynamic fractional frequency reuse in ofdma systems

by Alexander L. Stolyar, Harish Viswanathan - In: Proceeding of INFOCOM’2008 (2008
"... Abstract—Self-optimization of the network, for the purposes of improving overall capacity and/or cell edge data rates, is an important objective for next generation cellular systems. We propose algorithms that automatically create efficient, soft fractional frequency reuse (FFR) patterns for enhanci ..."
Abstract - Cited by 83 (3 self) - Add to MetaCart
Abstract—Self-optimization of the network, for the purposes of improving overall capacity and/or cell edge data rates, is an important objective for next generation cellular systems. We propose algorithms that automatically create efficient, soft fractional frequency reuse (FFR) patterns for enhancing performance of orthogonal frequency division multiple access (OFDMA) based cellular systems for forward link best effort traffic. The Multisector Gradient (MGR) algorithm adjusts the transmit powers of the different sub-bands by systematically pursuing maximization of the overall network utility. We show that the maximization can be done by sectors operating in a semi-autonomous way, with only some gradient information exchanged periodically by neighboring sectors. The Sector Autonomous (SA) algorithm adjusts its transmit powers in each sub-band independently in each sector using a non-trivial heuristic to achieve outof-cell interference mitigation. This algorithm is completely autonomous and requires no exchange of information between sectors. Through extensive simulations, we demonstrate that both algorithms provide substantial performance improvements. In particular, they can improve the cell edge data throughputs significantly, by up to 66 % in some cases for the MGR, while maintaining the overall sector throughput at the same level as that achieved by the traditional approach. The simulations also show that both algorithms lead the system to ”self-organize ” into efficient, soft FFR patterns with no a priori frequency planning. I.
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... this problem as described below. To solve the linear program (5)-(8), we apply a simple “shadow scheduling” algorithm, defined next, which is a special case of the Greedy Primal-Dual (GPD) algorithm =-=[12]-=-. SHADOW ALGORITHM: For the cell under consideration, BS maintains variable (virtual queue) Qj for each sub-band j - these are to “keep track” of the constraints (6). It also maintains variable (virtu...

Low-complexity distributed scheduling algorithms for wireless networks

by Abhinav Gupta, Xiaojun Lin, R. Srikant - IEEE/ACM Trans. on Netw
"... Abstract — We consider the problem of distributed scheduling in wireless networks. We present two different algorithms whose performance is arbitrarily close to that of maximal schedules, but which require low complexity due to the fact that they do not necessarily attempt to find maximal schedules. ..."
Abstract - Cited by 81 (6 self) - Add to MetaCart
Abstract — We consider the problem of distributed scheduling in wireless networks. We present two different algorithms whose performance is arbitrarily close to that of maximal schedules, but which require low complexity due to the fact that they do not necessarily attempt to find maximal schedules. The first algorithm requires each link to collect local queue-length information in its neighborhood, and its complexity is independent of the size and topology of the network. The second algorithm is presented for the node-exclusive interference model, does not require nodes to collect queue-length information even in their local neighborhoods, and its complexity depends only on the maximum node degree in the network. I.
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.... Using the max-weight or backpressure algorithms for scheduling, a number of recent papers have studied the problem of joint congestion control, routing, and scheduling in multihop wireless networks =-=[3]-=-–[10]; see [11] for a survey. The focus of this paper is on designing distributed scheduling algorithms with low complexity and low implementation overhead. We consider two simple collision models in ...

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