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## Degenerate Delay-Capacity Tradeoffs in Ad-Hoc Networks with Brownian Mobility (2006)

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Venue: | IEEE/ACM Trans. Netw |

Citations: | 63 - 2 self |

### Citations

3187 | The capacity of wireless networks
- Gupta, Kumar
- 2000
(Show Context)
Citation Context ...he per-node capacity must be O(1/ √ n). This result is in sharp contrast to other results that have recently been reported in the literature. I. INTRODUCTION Since the seminal work of Gupta and Kumar =-=[1]-=-, there has been a lot of interest in characterizing the capacity region of ad hoc networks. A major contribution in this direction was made in [2], where the authors show that mobility can significan... |

1316 | Probability: Theory and Examples
- Durrett
- 1991
(Show Context)
Citation Context ... the time a Brownian motion process spends in a region is in proportion to the area of the region. This also points to the well-known result that the path of Brownian motion is nowhere differentiable =-=[11, p380]-=-. Hence, it is inappropriate to define the “velocity” of a node that is moving in accordance with the Brownian motion model. 3sIV. THE DEGENERATE CAPACITY-DELAY TRADE-OFF In this section, we show that... |

1199 | Mobility increases the capacity of ad hoc wireless networks
- Grossglauser, Tse
- 2002
(Show Context)
Citation Context ... mobility models. Thus, we would like to understand more deeply their delay performance under the Brownian motion model. These schemes are similar to the 2-hop relaying scheme of Grossglauser and Tse =-=[2]-=-. Hence, we refer to them as generalized 2-hop relaying schemes. Compared with the more general class of schemes that we considered in Section IV, these schemes have one additional restriction: For ea... |

1173 | A survey of mobility models for ad hoc network research
- Camp, Boleng, et al.
- 2002
(Show Context)
Citation Context ... n ) delay, but nothing in between! Finally, although Proposition 1 is shown under the Brownian motion model, it is not difficult to see that the result also applies to the random walk mobility model =-=[9]-=-, or the Markovian mobility model in [4]. This is because as n → ∞, the difference between these mobility models vanishes. The result of Proposition 1 is in sharp contrast to the results reported in t... |

867 |
A second course in stochastic processes
- Karlin, Taylor
- 1981
(Show Context)
Citation Context ...t time that Yt hits a or b. Let Ua∧b(x) be the second moment of the travel time for Yt from x to either a or b, i.e., Ua∧b(x) � E[τa∧b 2 |Y0 = x] ��� τa∧b = E 1dτ 0 � 2 |Y0 = x Using the technique of =-=[14, p202]-=-, Ua∧b(x) must satisfy the following differential equation: where 1 2 σ2 (x) d2Ua∧b(x) dx2 + µ(x) dUa∧b(x) + 2Va∧b(x) = 0, dx � �� � τa∧b Va∧b(x) = E 1dτa∧b|Y0 = x 0 = E[τa∧b|Y0 = x], i.e., Va∧b(x) is... |

536 | Reversible Markov chains and random walks on graphs, http://www.stat.berkeley.edu/users/aldous/RWG/book.html - Aldous, Fill |

238 | Throughput-delay trade-off in wireless networks
- Gamal, Mammen, et al.
- 2004
(Show Context)
Citation Context ...that the 2-hop relaying scheme could potentially incur an unbounded delay. There has been substantial recent work on the joint characterization of the delay and capacity in the mobile ad hoc networks =-=[3]-=-, [4], [5], [6], [7], [8]. The type of node mobility studied in the literature includes the so-called i.i.d mobility [4], [7], [8], random way-point mobility [5], [6], Brownian motion [3], [6], and Ma... |

186 | Capacity and delay tradeoffs for ad hoc mobile networks
- Neely, Modiano
- 1937
(Show Context)
Citation Context ...at is, relay nodes holding a packet are not allowed to replicate it further. Remark 4: Note that almost all scheduling schemes that have been proposed in the literature satisfy Assumption A [2], [3], =-=[4]-=-, [5], [6], [7], [8]. If the relay nodes were allowed to replicate, then additional cooperation among the relay nodes would most likely be required (see, for example, the scheme in [12], where the rel... |

140 | Delay and capacity tradeoffs in mobile ad hoc networks: A global perspective - Sharma, Mazumdar, et al. - 2006 |

139 |
Stochastic processes with applications
- Bhattacharya, Waymire
- 1990
(Show Context)
Citation Context ...vel time for Yt from x to a. It is then not difficult to see that, as b → 1, Ua∧b(x) → Ua(x), and Va∧b(x) → Va(x). Using Lemma 1, we have Va(x) = 2 σ2 1 + x log n 1 + a . We now use the techniques of =-=[15, p422]-=- for treating the inaccessible point at b = 1. Note that and S(b) → ∞, as b → 1, � 1 x Va(η)m(η)dη < ∞. Letting b → 1 in (23), we obtain � �� 1 � Ua(x) = 4 (S(x) − S(a)) Va(ξ)m(ξ)dξ � x �� η a � � − V... |

127 | Capacity, delay and mobility in wireless ad-hoc networks
- Bansal, Liu
- 2003
(Show Context)
Citation Context ...ion A [2], [3], [4], [5], [6], [7], [8]. If the relay nodes were allowed to replicate, then additional cooperation among the relay nodes would most likely be required (see, for example, the scheme in =-=[12]-=-, where the relay nodes know the location of the static destination, and also have some knowledge of the future direction of other nodes’ movement, based on which they can cooperate to make selective ... |

116 | Large wireless networks under fading, mobility, and delay constraints - Toumpis, Goldsmith - 2004 |

100 | Capacity bounds for ad hoc and hybrid wireless networks - Agarwal, Kumar - 2004 |

56 | The fundamental capacity-delay tradeoff in large mobile ad hoc networks
- Lin, Shroff
- 2004
(Show Context)
Citation Context ...cheme could potentially incur an unbounded delay. There has been substantial recent work on the joint characterization of the delay and capacity in the mobile ad hoc networks [3], [4], [5], [6], [7], =-=[8]-=-. The type of node mobility studied in the literature includes the so-called i.i.d mobility [4], [7], [8], random way-point mobility [5], [6], Brownian motion [3], [6], and Markovian mobility [4]. The... |

46 | On the throughput capacity of random wireless networks - Franceschetti, Dousse, et al. |

36 | Delay and capacity trade-off in wireless ad hoc networks with random way-point mobility,” 2005, http://ece.purdue.edu/ gsharma
- Sharma
(Show Context)
Citation Context ...-hop relaying scheme could potentially incur an unbounded delay. There has been substantial recent work on the joint characterization of the delay and capacity in the mobile ad hoc networks [3], [4], =-=[5]-=-, [6], [7], [8]. The type of node mobility studied in the literature includes the so-called i.i.d mobility [4], [7], [8], random way-point mobility [5], [6], Brownian motion [3], [6], and Markovian mo... |

27 | A particle migrating randomly on a sphere
- Brillinger
- 1997
(Show Context)
Citation Context ...ng the shape of the area from the surface of a sphere to a square or a circle will not change the main results of this paper. 2sstochastic differential equations for the process (θt, φt) are given by =-=[10]-=-: and dθt = σndBt + σ2 n dt, (2) 2 tan θt dφt = σn dB sin θt ′ t, (3) where Bt and B ′ t are independent standard one-dimensional Brownian motions (i.e., with variance 1). We call σ 2 n the variance o... |

15 | Large Wireless Networks under Fading - Toumpis, Goldsmith - 2004 |

15 | Capacity, Delay and Mobility - Bansal, Liu - 2003 |

1 |
Achievable Delay/Capacity Trade-offs in Mobile Ad Hoc Networks
- “On
- 2004
(Show Context)
Citation Context ...ay nodes holding a packet are not allowed to replicate it further. Remark 4: Note that almost all scheduling schemes that have been proposed in the literature satisfy Assumption A [2], [3], [4], [5], =-=[6]-=-, [7], [8]. If the relay nodes were allowed to replicate, then additional cooperation among the relay nodes would most likely be required (see, for example, the scheme in [12], where the relay nodes k... |