## A lagrangian approach for the optimal placement of wireless relay nodes in wireless local area networks (2006)

Venue: | in Proc. of the International IFIP-TC6 Networking Conference |

Citations: | 5 - 4 self |

### BibTeX

@INPROCEEDINGS{So06alagrangian,

author = {Aaron So and Ben Liang},

title = {A lagrangian approach for the optimal placement of wireless relay nodes in wireless local area networks},

booktitle = {in Proc. of the International IFIP-TC6 Networking Conference},

year = {2006},

pages = {160--172}

}

### OpenURL

### Abstract

Abstract. The throughput capacity of WLANs can be improved by a carefully designed relay infrastructure. In this work, we propose an optimization formulation based on Lagrangian relaxation and a subgradient algorithm to compute the best placement of a fixed number of relay nodes (RNs) in a WLAN. We apply this optimization framework to a multi-rate WLAN based on the IEEE 802.11g standard under Rayleigh fading. We then study the expected throughput capacity of a WLAN with relay infrastructure and investigate how the optimal placement of RNs is affected by the number of RNs, path-loss characteristics, and the traffic pattern. Our numerical results show that, in some network scenarios, more than 120 % performance gain can be achieved when RNs are strategically installed in the network. Furthermore, we also show that for a wide range of system parameters, optimally placed RNs can significantly increase the network throughput capacity over random placement. Key words: WLAN, immobile relays, throughput capacity, optimal placement 1

### Citations

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Citation Context ...nsmitter, and α is a positive constant representing the path loss roll off factor. The reference power P1 can be obtained via field measurement or calculated using the free space path loss formula in =-=[12]-=-. In addition to large scale propagation, multipath fading may have a prominent effect on reliable communication. Under Rayleigh fading, the instantaneous power, γ, is exponentially distributed with t... |

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Citation Context ...the RNs. Finally, concluding remarks are given in Section 7. 2 Related Work There has been much research in relaying and routing through mobile nodes. Inspired by recent advances in ad hoc networking =-=[1]-=-, the concept of using peer mobile hosts to relay data has been explored in the context of cellular networks [2]. In a more recent work, the problem of joint routing, link scheduling and power control... |

134 |
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Citation Context ...ying and routing through mobile nodes. Inspired by recent advances in ad hoc networking [1], the concept of using peer mobile hosts to relay data has been explored in the context of cellular networks =-=[2]-=-. In a more recent work, the problem of joint routing, link scheduling and power control in such multihop networks has been investigated [3]. Moreover, issues about frequency assignment and frequency ... |

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Citation Context ... data has been explored in the context of cellular networks [2]. In a more recent work, the problem of joint routing, link scheduling and power control in such multihop networks has been investigated =-=[3]-=-. Moreover, issues about frequency assignment and frequency recycling in such multihop networks have been addressed in [4]. In the context of multi-rate WLAN, [5] and [6] have shown that by using othe... |

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Citation Context ... This analytical framework is then used to cast the RN placement problem as an optimization problem. We show that the resulting optimization can be converted to a form similar to the p-median problem =-=[10]-=- with an additional constraint. Finally, we present an efficient solution based on Lagrangian relaxation and a subgradient optimization algorithm.s4 AP RN d l 4.1 RN Relaying MH – xd = downlink packet... |

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Citation Context ...proved under DCF and PCF respectively. However, the concept of using immobile relay nodes to relay traffic, which is what we consider in this paper, has received less attention. The iCar architecture =-=[7]-=- is one such example for the cellular environment. Immobile relay nodes have several advantages when compared with mobile relay nodes. First, because of their sedentariness, it is reasonable to assume... |

29 | rDCF: a relay-enabled medium access control protocol for wireless ad hoc networks
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Citation Context ...ltihop networks has been investigated [3]. Moreover, issues about frequency assignment and frequency recycling in such multihop networks have been addressed in [4]. In the context of multi-rate WLAN, =-=[5]-=- and [6] have shown that by using other mobile hosts to perform relaying, the performance of the network can be improved under DCF and PCF respectively. However, the concept of using immobile relay no... |

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Citation Context ...etworks has been investigated [3]. Moreover, issues about frequency assignment and frequency recycling in such multihop networks have been addressed in [4]. In the context of multi-rate WLAN, [5] and =-=[6]-=- have shown that by using other mobile hosts to perform relaying, the performance of the network can be improved under DCF and PCF respectively. However, the concept of using immobile relay nodes to r... |

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(Show Context)
Citation Context ... scheduling and power control in such multihop networks has been investigated [3]. Moreover, issues about frequency assignment and frequency recycling in such multihop networks have been addressed in =-=[4]-=-. In the context of multi-rate WLAN, [5] and [6] have shown that by using other mobile hosts to perform relaying, the performance of the network can be improved under DCF and PCF respectively. However... |

6 |
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(Show Context)
Citation Context ...s not a constraint. Second, the fixed relay nodes can be optimally configured to maximize their beneficial effects. The problem of fixed relay placement to maximize WLAN capacity was first studied in =-=[8]-=-. In [9], we proposed an efficient extension point placement algorithm aiming at improving the network layer throughput of a rectilineal network, using a divide-and-conquer searching algorithm. In thi... |

5 |
An efficient algorithm for the optimal placement of wireless extension points in rectilineal wireless local area networks
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(Show Context)
Citation Context ...constraint. Second, the fixed relay nodes can be optimally configured to maximize their beneficial effects. The problem of fixed relay placement to maximize WLAN capacity was first studied in [8]. In =-=[9]-=-, we proposed an efficient extension point placement algorithm aiming at improving the network layer throughput of a rectilineal network, using a divide-and-conquer searching algorithm. In this work, ... |

3 |
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Citation Context ...acement can be calculated by using (7). This value is an upper bound of (8). The lower bound for the current iteration is simply the objective function (14) with the values of X and Y found in Step 2 =-=[11]-=-. Step 4: Modifying the Lagrange multipliers. The Lagrange multipliers are revised using a standard subgradient optimization procedure [11]. At the n th iteration of the Lagrangian procedure, we first... |

2 |
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Citation Context ...e system parameters such as bit rate power thresholds, antenna gains, and transmitter powers are taken from the CISCO Aironet 1100 Series Access Point and mobile network interface card specifications =-=[13]-=-. The other system parameters are selected based on a typical urban environment. 6.1 Convergence of Lagrangian Iteration In Fig. 4, we show the convergence of the algorithm in two typical network scen... |