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MotionCast for Mobile Wireless NetworksMotionCast: Delay and Capacity Tradeoff Analysis

MotionCast for Mobile Wireless Networks: MotionCast: Delay and Capacity Tradeoff Analysis [In this chapter, multicast capacity-delay tradeoff of the wireless network combining mobile wireless nodes with base stations is studied. m=nb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m = n^b$$\end{document} base stations are located in a square region and divide it into m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m$$\end{document} super cells according to their coverage. Their transmission power is large enough to directly transmit to any nodes in the same super cell. We further assume that mobile nodes move in an independently and identically distributed (i.i.d.) pattern and each wants to send packets to k=nd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k = n^d$$\end{document} distinctive destinations. Packets are delivered to destinations or base stations via node’s mobility. Under this model, we study capacity, delay and their tradeoff in three transmission protocols: one uses two-hop relay algorithm without redundancy, another adopts the scheme of redundant packets transmissions to improve delay, and the third one cancels the constriction of 2-hop. The upper bound of per-node throughput of 2-hop relay algorithm without redundancy is O(n−min{1,1−b+d})\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n^{-\min \{1, 1 - b + d\}})$$\end{document} and its delay is Θ(nmin{1,1−b+d})\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varTheta (n^{\min \{1, 1 - b + d\}})$$\end{document}. The lower bound is Θ(n1−b)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varTheta (n^{1-b})$$\end{document}, with a smaller capacity O(nb−2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n^{b-2})$$\end{document}. It obtains a better tradeoff than using ad-hoc only in [4] when k=Θ(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k = \varTheta (n)$$\end{document} or b>min{1+d2,2−d2}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b > \min \{\frac{1+d}{2}, \frac{2 - d}{2}\}$$\end{document}. For two-hop relay algorithm with redundancy, the biggest capacity and its corresponding delay are O(n−min{1,1−b+d})\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n^{-\min \{1, 1 - b + d\}})$$\end{document} and Θ(nmin{1,1−b+d}2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varTheta (n^{\frac{\min \{1, 1 - b + d\}}{2}})$$\end{document}. The smallest delay and the related capacity are Θ(n1−b2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varTheta (n^{\frac{1 - b}{2}})$$\end{document} and O(nb−32)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n^{\frac{b - 3}{2}})$$\end{document}. When d>12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d > \frac{1}{2}$$\end{document} or b>min{1+d3,1−d}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b > \min \{\frac{1+d}{3}, 1 - d\}$$\end{document}, adding base stations will enhance the tradeoff mentioned in [4]. As to multi-hop relay algorithm with redundancy, if m=Θ(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m = \varTheta (n)$$\end{document}, we prefer passing through base stations to ad-hoc only.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

MotionCast for Mobile Wireless NetworksMotionCast: Delay and Capacity Tradeoff Analysis

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Publisher
Springer New York
Copyright
© The Author(s) 2013
ISBN
978-1-4614-5634-6
Pages
1 –34
DOI
10.1007/978-1-4614-5635-3_1
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Abstract

[In this chapter, multicast capacity-delay tradeoff of the wireless network combining mobile wireless nodes with base stations is studied. m=nb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m = n^b$$\end{document} base stations are located in a square region and divide it into m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m$$\end{document} super cells according to their coverage. Their transmission power is large enough to directly transmit to any nodes in the same super cell. We further assume that mobile nodes move in an independently and identically distributed (i.i.d.) pattern and each wants to send packets to k=nd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k = n^d$$\end{document} distinctive destinations. Packets are delivered to destinations or base stations via node’s mobility. Under this model, we study capacity, delay and their tradeoff in three transmission protocols: one uses two-hop relay algorithm without redundancy, another adopts the scheme of redundant packets transmissions to improve delay, and the third one cancels the constriction of 2-hop. The upper bound of per-node throughput of 2-hop relay algorithm without redundancy is O(n−min{1,1−b+d})\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n^{-\min \{1, 1 - b + d\}})$$\end{document} and its delay is Θ(nmin{1,1−b+d})\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varTheta (n^{\min \{1, 1 - b + d\}})$$\end{document}. The lower bound is Θ(n1−b)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varTheta (n^{1-b})$$\end{document}, with a smaller capacity O(nb−2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n^{b-2})$$\end{document}. It obtains a better tradeoff than using ad-hoc only in [4] when k=Θ(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k = \varTheta (n)$$\end{document} or b>min{1+d2,2−d2}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b > \min \{\frac{1+d}{2}, \frac{2 - d}{2}\}$$\end{document}. For two-hop relay algorithm with redundancy, the biggest capacity and its corresponding delay are O(n−min{1,1−b+d})\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n^{-\min \{1, 1 - b + d\}})$$\end{document} and Θ(nmin{1,1−b+d}2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varTheta (n^{\frac{\min \{1, 1 - b + d\}}{2}})$$\end{document}. The smallest delay and the related capacity are Θ(n1−b2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varTheta (n^{\frac{1 - b}{2}})$$\end{document} and O(nb−32)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n^{\frac{b - 3}{2}})$$\end{document}. When d>12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d > \frac{1}{2}$$\end{document} or b>min{1+d3,1−d}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b > \min \{\frac{1+d}{3}, 1 - d\}$$\end{document}, adding base stations will enhance the tradeoff mentioned in [4]. As to multi-hop relay algorithm with redundancy, if m=Θ(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m = \varTheta (n)$$\end{document}, we prefer passing through base stations to ad-hoc only.]

Published: Jan 23, 2013

Keywords: Mobile Nodes; Relay Algorithm; Adding Base Stations; Random Walk Mobility; Source Node Need

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