## Fairness and optimal stochastic control for heterogeneous networks (2005)

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Venue: | Proceedings of IEEE INFOCOM |

Citations: | 160 - 34 self |

### BibTeX

@INPROCEEDINGS{Neely05fairnessand,

author = {Michael J. Neely and Eytan Modiano and Chih-ping Li},

title = {Fairness and optimal stochastic control for heterogeneous networks},

booktitle = {Proceedings of IEEE INFOCOM},

year = {2005},

pages = {1723--1734}

}

### Years of Citing Articles

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### Abstract

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. Analysis is performed at the packet level and considers the full effects of queueing.

### Citations

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Citation Context ...n of a periodic transmission schedule. A similar scheduling problem is shown to be NP-complete in [28]. The capacity of a multi-user wireless downlink with randomly varying channels is established in =-=[29]-=-, and utility optimization in a similar system is treated in [13]. These formulations do not consider stochastic arrivals and queueing, and solutions require perfect knowledge of channel statistics (a... |

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Citation Context ...mance optimization to be achieved simultaneously, and presents a fundamental approach to stochastic network optimization [1] [2]. We note that an alternate Lyapunov approach was recently developed in =-=[26]-=- for scheduling in a wireless downlink with infinite backlog. There, the authors use Lyapunov theory to prove stability, and demonstrate fairness by relating the system dynamics to that of a correspon... |

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Citation Context ... VOL. 16, NO. 2, APRIL 2008, PP. 396-409 3 simultaneously, extending the stability results developed 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 L... |

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Citation Context ...re several basic network models for which it is possible to come within a constant factor of optimality using simplified scheduling techniques, and this is an area of recent active interest [15] [42] =-=[43]-=-. For example, consider a wireless network where every node transmits over an orthogonal frequency band. Assume nodes can transmit or receive from at most one link at a time, and nodes cannot simultan... |

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Citation Context ...t hold [recall discussion after (27)]. The result of Theorem 2 follows by optimizing the performance bounds over 0 < ɛ < µsym in a manner similar to the proof of Theorem 1. λ91 λ93 λ48 λ42 REFERENCES =-=[1]-=- M. J. Neely. Dynamic Power Allocation and Routing for Satellite and Wireless Networks with Time Varying Channels. PhD thesis, Massachusetts Institute of Technology, LIDS, 2003. [2] J. W. Lee, R. R. M... |

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Citation Context ...ere are several basic network models for which it is possible to come within a constant factor of optimality using simplified scheduling techniques, and this is an area of recent active interest [15] =-=[42]-=- [43]. For example, consider a wireless network where every node transmits over an orthogonal frequency band. Assume nodes can transmit or receive from at most one link at a time, and nodes cannot sim... |

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Citation Context ...hown to decrease like 1/V , where V is a control parameter affecting a tradeoff in average delay for data that is served by the network. Previous work on network fairness and optimization is found in =-=[5]-=--[17]. Utility optimization problems similar to (2)- (3) are considered for static wireless downlinks with infinite backlog in [5], and for static multi-hop wireless networks in [8]. Further static re... |

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Citation Context ...ire perfect knowledge of channel statistics (approximate policies can be implemented based on long-term measurements). Stochastic control policies for wireless queueing networks are developed in [15]-=-=[21]-=- based on a theory of Lyapunov drift. This theory has been extremely powerful in the development of stabilizing control laws for data networks [15]-[23], but cannot be used to address performance opti... |

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Citation Context ...lity with respect to a θ scaled version of the capacity region. The above corollary is related to similar “sub-optimal” Lyapunov scheduling results presented for stability analysis (see, for example, =-=[40]-=- [41], E. Maximum Throughput and the Threshold Rule Suppose utilities are linear, so that g (c) n (r) = α (c) n r for some non-negative weights α (c) n . The resulting objective is to maximize the wei... |

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Citation Context ...[25] [26], but do not yield optimal performance for all input rates, as discussed in the next section. A wireless downlink with deterministic ON/OFF channels and arbitrary input rates is developed in =-=[27]-=-, and a modified version of the Serve-the-Longest-ON-Queue policy is shown to yield maximum throughput. However, the analysis in [27] is closely tied to the channel modeling assumptions, and does not ... |

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Citation Context ...s learn “good” directions to route and “good” amounts of data to admit, and the “noise” of fluctuating queues will have less influence when queue sizes are large. We note that in our more recent work =-=[38]-=-, we characterize the fundamental tradeoff between utility and delay. D. Algorithm Performance To analyze the performance of the above CLC1 algorithm, we define the maximum transmission rates out of a... |

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Citation Context ...ireless queueing networks are developed in [15]-[21] based on a theory of Lyapunov drift. This theory has been extremely powerful in the development of stabilizing control laws for data networks [15]-=-=[23]-=-, but cannot be used to address performance optimization and fairness. Dynamic algorithms for fair scheduling in wireless downlinks are addressed in [24] [25] [26], but do not yield optimal performanc... |

19 |
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Citation Context ... achieved throughput of CLC2 approaches the optimal operating point (0.23, 0.57) as V is increased. A. Packet Switches Here we consider a simple 3 × 3 packet switch with a crossbar switch fabric [23] =-=[26]-=-. Packets arrive from three different input ports, and each packet is destined for one of three output ports. We let λij represent the rate of packets arriving to input i and destined for output j. Al... |

13 |
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Citation Context ...) is no more than the incoming traffic rate of this session. Let (r ∗ nc) represent the solution of the above optimization. Such a solution exists because the set Λ is compact and contains the origin =-=[31]-=-. Because the functions gnc(r) are nondecreasing, it is clear that (r ∗ nc) = (λnc) whenever (λnc) ∈ Λ. If (λnc) /∈ Λ there must be at least one value r ∗ nc that is strictly less than λnc. The above ... |

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Citation Context ...with respect to a θ scaled version of the capacity region. The above corollary is related to similar “sub-optimal” Lyapunov scheduling results presented for stability analysis (see, for example, [40] =-=[41]-=-, E. Maximum Throughput and the Threshold Rule Suppose utilities are linear, so that g (c) n (r) = α (c) n r for some non-negative weights α (c) n . The resulting objective is to maximize the weighted... |

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Citation Context ...assachusetts Institute of Technology, LIDS, 2003. [2] J. W. Lee, R. R. Mazumdar, and N. B. Shroff. Downlink power allocation for multi-class cdma wireless networks. IEEE Proceedings of INFOCOM, 2002. =-=[3]-=- R. Berry, P. Liu, and M. Honig. Design and analysis of downlink utility-based schedulers. Proceedings of the 40th Allerton Conference on Communication, Control, and Computing, Oct. 2002. [4] P. Marba... |

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Citation Context ... metrics. In [12] [13], distributed pricing mechanisms are used to provide proportional fairness in static flow networks. Control laws based on continuous time differential equations are used in [13] =-=[16]-=- to ensure flows converge to a utility optimal operating point, and dual sub-gradient methods are considered in [14]. The relationship between duality theory, utility optimization, and classical inter... |

5 |
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Citation Context ...izing control laws for data networks [15]-[23], but cannot be used to address performance optimization and fairness. Dynamic algorithms for fair scheduling in wireless downlinks are addressed in [24] =-=[25]-=- [26], but do not yield optimal performance for all input rates, as discussed in the next section. A wireless downlink with deterministic ON/OFF channels and arbitrary input rates is developed in [27]... |