The Capacity of Wireless Networks

Size: px
Start display at page:

Download "The Capacity of Wireless Networks"

Transcription

1 The Capacity of Wireless Networks Piyush Gupta & P.R. Kumar Rahul Tandra --- EE228 Presentation

2 Introduction We consider wireless networks without any centralized control. Try to analyze the capacity of such networks. We consider two types of networks: a) Arbitrary networks b) Random networks

3 Arbitrary Networks n nodes are arbitrarily located in a disc of unit area. Traffic pattern is completely arbitrary. Range or power level is also arbitrary. Two models for successful reception of a transmission over one hop: a) Protocol Model b) Physical Model

4 The protocol Model Suppose X i transmits over the m-th sub-channel to a node X j. This transmission is successfully received by node X j if X k X (1 + ) j for every node X k simultaneously transmitting over the same sub-channel. The quantity > 0 models situations where a guard zone is specified by the protocol. X i X j

5 The Physical Model { } Let X k ;k Τ be the subset of nodes simultaneously transmitting at some time instant over a certain sub-channel. Let P k be the power level chosen by node X k. Then the transmission from a node X i is successfully received by a node X j if N + X i k Τ k i P X i X k j P α k X j α β

6 Transport Capacity of Arbitrary Networks We say that the network transports one bit-meter when one bit has been transported a distance of one meter towards it s destination. This sum of products of bits and the distances over which they are carried is called the transport capacity of the network.

7 Main Results for Arbitrary Networks Main Result 1: The transport Capacity of an Arbitrary Network under the protocol Model is Θ( W n) bit-meters/sec if the nodes are optimally placed, the traffic pattern and the range are optimally chosen. If the transport capacity is equitably divided between all W the n nodes, then each node would obtain Θ ( ) bitmeters/sec. n Further if, each node has its destination about the same distance of 1 meter away, then each node would W obtain a throughput capacity of Θ( ) bits/sec. n

8 Results cont. Main Result 2: For the Physical Model, cw n α 1 bit-meters/sec is feasible, while ' α c Wn bit-meters/sec is not, for appropriate constants c and c.

9 Arbitrary Networks: An upper bound on transport capacity We consider the setting on a planar disk of unit area with the following assumptions: (A1) There are n nodes arbitrarily located in disk of unit area on the plane. (A2) The network transports λnt bits over T seconds. (A3) The average distance between the source and the destination is L.

10 Assumptions cont. (A4) Each node can transmit over any subset of M sub-channels with capacities W m bits/sec,, where W. 1 m M W (A5) Transmissions are slotted into synchronized τ slots of length. M m=1 m =

11 Upper bound for the Transport Capacity Theorem 1: In the Protocol model the transport capacity is bounded as follows: λnl 8 π 1 W n bit-meters/sec

12 Lower bound on the Transport Capacity Theorem 2: There is a placement of nodes and an assignment of traffic patterns such that the network can W n achieve bit-meters/sec under the n + Protocol Model. 8π

13 Random Networks n nodes are randomly, i.e., independently and uniformly located on the surface of a sphere of surface area 1 sq. meter. Each node randomly chooses a destination to transmit. The destination node is independently chosen to be the node nearest to this randomly located point. Also, we assume that all nodes are homogeneous ( same power or range).

14 The Protocol Model All nodes employ a common range r for transmission. When node X i transmits to node X j, the transmission is successfully received by X j if: (i) X i X j r (ii) For every other node X k transmitting over the same sub-channel X k X j ( 1+ ) r

15 The Physical Model All nodes choose a common power level P for transmission. Let { X k ;k Τ} be the subset of nodes simultaneously transmitting at some time instant over a certain sub-channel. Then the transmission from a node X i is successfully received by a node X j if N + X i k k Τ i P X X k j α P X j α β

16 The Throughput Capacity of Random Networks Main Result 3: The order of the throughput capacity for the Protocol model is λ( n) = Θ bits/sec nlog n Main Result 4: For the Physical Model a cw λ( n) = Throughput Capacity of nlog n bits/sec is c' W feasible, while λ( n) = bits/sec is not for n appropriate constants c and c W

17 Outline of the Proof We use Voronoi tessellation on the surface S 2 of the sphere. Let {a 1,a 2,,a p } be a set of p points on S 2. The Voronoi cell V(a i ) is the set of point which are closer to a i than to any of the other a j s. Note that the distances are measured on the surface of S 2 by segments of great circles connection two points.

18 ε Lemma 1: For ever > 0, there is a Voronoi tessellation of S 2 with the property that every Voronoi cell contains a disk of radius ε and is contained in a disk of radius 2 ε. In the rest of the proof we will use a Voronoi tessellation V n for which: (a) Every Voronoi cell contains a disk of area (100logn)/n. Let ρ(n) be the radius of this disk. (b) Every Voronoi cell is contained in a disk of radius 2 ρ(n)

19 Adjacency and interference We say that two cells are adjacent, if they share a common point. Let us choose the range r(n) of each transmission so that r( n) = 8ρ( n) Lemma 2: Every node in a cell is within a distance of r(n) from every node in its own cell or adjacent cell. We say that two cells are interfering neighbors if there is a point in one cell which is within a distance 2 + ) r( of some point in the other cell. ( n)

20 Bound on the number of interfering neighbors of a cell Lemma 3: Every cell in V n has no more than c 1 interfering neighbors. c 1 depends only on 2 and grows no faster than linearly in ( 1+ ) Lemma 4: In the Protocol model there is a schedule for transmitting packets such that in every (1+c 1 ) slots, each cell in the tessellation V n gets one slot in which to transmit, and such that all transmissions are successfully received within a distance of r(n) from their transmitters.

21 The source-destination Pairs Each node wishes to communicate with the node nearest to a randomly chosen location. Let Y i be a randomly chosen location such that X i and Y i are independently and uniformly distributed on S 2, and the sequence {(X i,y i )} is i.i.d.

22 Some intermediate results They prove that each cell contains atleast one node with high probability (whp). Routing is done through cells. The traffic carried per each route is λ(n) The number of routes intersecting each cell is of the order if c nlog n whp. Hence we have cλ( n) nlog n W 1+ c 1

23 Some possible implications The throughput of a wireless network goes to zero as the number of nodes increases. Perhaps designers should target their efforts on networks with small number of users. A feasible scenario is where nodes communicate only with nearby neighbors.

24 Implications cont. In Random networks it is observed that one can group the nodes into small clusters or cells, where in each cell one can designate a specific node to relay the multi-hop traffic, if so desired. This would reduce the total transmission power consumed by the nodes. Also note that dividing the channel into subchannels does not change any of the results.

Queuing Delay and Achievable Throughput in Random Access Wireless Ad Hoc Networks

Queuing Delay and Achievable Throughput in Random Access Wireless Ad Hoc Networks Queuing Delay and Achievable Throughput in Random Access Wireless Ad Hoc Networks Nabhendra Bisnik and Alhussein Abouzeid Rensselaer Polytechnic Institute Troy, NY bisnin@rpi.edu, abouzeid@ecse.rpi.edu

More information

Hierarchical Cooperation Achieves Optimal Capacity Scaling in Ad Hoc Networks

Hierarchical Cooperation Achieves Optimal Capacity Scaling in Ad Hoc Networks Hierarchical Cooperation Achieves Optimal Capacity Scaling in Ad Hoc Networks Presentation: Alexandros Manolakos EE 360 Stanford University February 13, 2012 Table of Contents What are we trying to solve?

More information

Wireless Network Capacity. Nitin Vaidya

Wireless Network Capacity. Nitin Vaidya Wireless Network Capacity Nitin Vaidya 2009 1 Wireless Networks Why use multi-hop routes to delivery data? Is this optimal? What s the best performance achievable? Capacity analysis can help answer such

More information

Delay-Throughput Tradeoff for Supportive Two-Tier Networks

Delay-Throughput Tradeoff for Supportive Two-Tier Networks Delay-Throughput Tradeoff for Supportive Two-Tier Networks arxiv:082.4826v [cs.it] 28 Dec 2008 Long Gao, Rui Zhang, Changchuan Yin, Shuguang Cui Department of Electrical and Computer Engineering Texas

More information

Geometric Routing: Of Theory and Practice

Geometric Routing: Of Theory and Practice Geometric Routing: Of Theory and Practice PODC 03 F. Kuhn, R. Wattenhofer, Y. Zhang, A. Zollinger [KWZ 02] [KWZ 03] [KK 00] Asymptotically Optimal Geometric Mobile Ad-Hoc Routing Worst-Case Optimal and

More information

Lifetime Analysis of Random Event-Driven Clustered Wireless Sensor Networks. Presented by Yao Zheng

Lifetime Analysis of Random Event-Driven Clustered Wireless Sensor Networks. Presented by Yao Zheng Lifetime Analysis of Random Event-Driven Clustered Wireless Sensor Networks Presented by Yao Zheng Contributions Analyzing the lifetime of WSN without knowing the lifetime of sensors Find a accurate approximation

More information

Multihop Hierarchical MIMO A Multicast Structure in wireless ad hoc networks

Multihop Hierarchical MIMO A Multicast Structure in wireless ad hoc networks Multihop Hierarchical MIMO A Multicast Structure in wireless ad hoc networks January 11, 2008 Abstract In this paper, we study multicast in large-scale wireless ad hoc networks. Consider N nodes that are

More information

Throughput Capacity of Random Ad Hoc Networks with Infrastructure Support

Throughput Capacity of Random Ad Hoc Networks with Infrastructure Support Throughput Capacity of Random Ad Hoc Networks with Infrastructure Support Ulaş C. Kozat kozat@isr.umd.edu Leandros Tassiulas leandros@isr.umd.edu Department of Electrical and Computer Engineering Institute

More information

Geographic Routing with Limited Information in Sensor Networks

Geographic Routing with Limited Information in Sensor Networks Geographic Routing with Limited Information in Sensor Networks Sundar Subramanian and Sanjay Shakkottai Abstract Geographic routing with greedy relaying strategies have been widely studied as a routing

More information

Connection-Level Scheduling in Wireless Networks Using Only MAC-Layer Information

Connection-Level Scheduling in Wireless Networks Using Only MAC-Layer Information Connection-Level Scheduling in Wireless Networks Using Only MAC-Layer Information Javad Ghaderi, Tianxiong Ji and R. Srikant Coordinated Science Laboratory and Department of Electrical and Computer Engineering

More information

Topology Control in 3-Dimensional Networks & Algorithms for Multi-Channel Aggregated Co

Topology Control in 3-Dimensional Networks & Algorithms for Multi-Channel Aggregated Co Topology Control in 3-Dimensional Networks & Algorithms for Multi-Channel Aggregated Convergecast Amitabha Ghosh Yi Wang Ozlem D. Incel V.S. Anil Kumar Bhaskar Krishnamachari Dept. of Electrical Engineering,

More information

Ad Hoc Wireless Networks : Analysis, Protocols, Architecture and Convergence

Ad Hoc Wireless Networks : Analysis, Protocols, Architecture and Convergence Ad Hoc Wireless Networks : Analysis, Protocols, Architecture and Convergence P. R. Kumar (with P. Gupta, V. Kawadia, S. Narayanaswamy, R. Rozovsky, R. S. Sreenivas) Dept. of Electrical and Computer Engineering,

More information

Delay and Capacity Trade-offs in Mobile Ad Hoc Networks: A Global Perspective

Delay and Capacity Trade-offs in Mobile Ad Hoc Networks: A Global Perspective Delay and Capacity Trade-offs in Mobile Ad Hoc Networks: A Global Perspective Gaurav Sharma, Ravi Mazumdar, Ness Shroff School of Electrical and Computer Engineering Purdue University West Lafayette, IN

More information

Clustering: Centroid-Based Partitioning

Clustering: Centroid-Based Partitioning Clustering: Centroid-Based Partitioning Yufei Tao Department of Computer Science and Engineering Chinese University of Hong Kong 1 / 29 Y Tao Clustering: Centroid-Based Partitioning In this lecture, we

More information

Do Directional Antennas Facilitate In Reducing Interferences?

Do Directional Antennas Facilitate In Reducing Interferences? Do Directional Antennas Facilitate In Reducing Interferences? Presented by Ury Matarazzo Ben-Gurion University, Beer-Sheva, Israel November 25, 2012 1 Introduction The question 2 The converge cast 3 Asymmetric

More information

Physical Layer Security from Inter-Session Interference in Large Wireless Networks

Physical Layer Security from Inter-Session Interference in Large Wireless Networks Physical Layer Security from Inter-Session Interference in Large Wireless Networks Azadeh Sheikholeslami, Dennis Goeckel, Hossein Pishro-Nik, Don Towsley University of Massachussets, Amherst Outline 1.

More information

Bounds on the Benefit of Network Coding for Multicast and Unicast Sessions in Wireless Networks

Bounds on the Benefit of Network Coding for Multicast and Unicast Sessions in Wireless Networks Bounds on the Benefit of Network Coding for Multicast and Unicast Sessions in Wireless Networks Alireza Keshavarz-Haddad Rudolf Riedi Department of Electrical and Computer Engineering and Department of

More information

Near Optimal Broadcast with Network Coding in Large Sensor Networks

Near Optimal Broadcast with Network Coding in Large Sensor Networks in Large Sensor Networks Cédric Adjih, Song Yean Cho, Philippe Jacquet INRIA/École Polytechnique - Hipercom Team 1 st Intl. Workshop on Information Theory for Sensor Networks (WITS 07) - Santa Fe - USA

More information

IMPROVING THE DATA COLLECTION RATE IN WIRELESS SENSOR NETWORKS BY USING THE MOBILE RELAYS

IMPROVING THE DATA COLLECTION RATE IN WIRELESS SENSOR NETWORKS BY USING THE MOBILE RELAYS IMPROVING THE DATA COLLECTION RATE IN WIRELESS SENSOR NETWORKS BY USING THE MOBILE RELAYS 1 K MADHURI, 2 J.KRISHNA, 3 C.SIVABALAJI II M.Tech CSE, AITS, Asst Professor CSE, AITS, Asst Professor CSE, NIST

More information

Voronoi Diagrams and Delaunay Triangulations. O Rourke, Chapter 5

Voronoi Diagrams and Delaunay Triangulations. O Rourke, Chapter 5 Voronoi Diagrams and Delaunay Triangulations O Rourke, Chapter 5 Outline Preliminaries Properties and Applications Computing the Delaunay Triangulation Preliminaries Given a function f: R 2 R, the tangent

More information

Mitigation of Capacity Region of Network and Energy Function for a Delay Tolerant Mobile Ad Hoc Network

Mitigation of Capacity Region of Network and Energy Function for a Delay Tolerant Mobile Ad Hoc Network International Journal of Scientific & Engineering Research, Volume 3, Issue 10, October-01 1 ISSN 9-5518 Mitigation of Capacity Region of Network and Energy Function for a Delay Tolerant Mobile Ad Hoc

More information

Coloring. Radhika Gupta. Problem 1. What is the chromatic number of the arc graph of a polygonal disc of N sides?

Coloring. Radhika Gupta. Problem 1. What is the chromatic number of the arc graph of a polygonal disc of N sides? Coloring Radhika Gupta 1 Coloring of A N Let A N be the arc graph of a polygonal disc with N sides, N > 4 Problem 1 What is the chromatic number of the arc graph of a polygonal disc of N sides? Or we would

More information

IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 52, NO. 2, FEBRUARY An Aloha Protocol for Multihop Mobile Wireless Networks

IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 52, NO. 2, FEBRUARY An Aloha Protocol for Multihop Mobile Wireless Networks IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 52, NO. 2, FEBRUARY 2006 421 An Aloha Protocol for Multihop Mobile Wireless Networks François Baccelli, Bartłomiej Błaszczyszyn, and Paul Mühlethaler Abstract

More information

How does the Information Capacity of Ad Hoc Networks Scale?

How does the Information Capacity of Ad Hoc Networks Scale? How does the Information Capacity of Ad Hoc Networks Scale? Ayfer Özgür, Olivier Lévêque, David Tse Abstract n source and destination pairs randomly located in an area want to communicate with each other.

More information

On the Impact of Mobility on Multicast Capacity of Wireless Networks

On the Impact of Mobility on Multicast Capacity of Wireless Networks On the Impact of Mobility on Multicast Capacity of Wireless Networs Jubin Jose, Ahmed Abdel-Hadi, Piyush Gupta and Sriram Vishwanath University of Texas at Austin, Austin, TX Bell Labs, Alcatel-Lucent,

More information

SAMPLING AND THE MOMENT TECHNIQUE. By Sveta Oksen

SAMPLING AND THE MOMENT TECHNIQUE. By Sveta Oksen SAMPLING AND THE MOMENT TECHNIQUE By Sveta Oksen Overview - Vertical decomposition - Construction - Running time analysis - The bounded moments theorem - General settings - The sampling model - The exponential

More information

Lecture-12: Closed Sets

Lecture-12: Closed Sets and Its Examples Properties of Lecture-12: Dr. Department of Mathematics Lovely Professional University Punjab, India October 18, 2014 Outline Introduction and Its Examples Properties of 1 Introduction

More information

A Review on 3-Dimention in Wireless Networks

A Review on 3-Dimention in Wireless Networks A Review on 3-Dimention in Wireless Networks Eiman Alotaibi Department of Computer Science University of California, Davis Introduction 7/31/2009 2 Introduction 7/31/2009 3 Introduction 7/31/2009 4 Introduction

More information

An Ant-Based Routing Algorithm to Achieve the Lifetime Bound for Target Tracking Sensor Networks

An Ant-Based Routing Algorithm to Achieve the Lifetime Bound for Target Tracking Sensor Networks An Ant-Based Routing Algorithm to Achieve the Lifetime Bound for Target Tracking Sensor Networks Peng Zeng Cuanzhi Zang Haibin Yu Shenyang Institute of Automation Chinese Academy of Sciences Target Tracking

More information

Quantification of Capacity and Transmission Delay for Mobile Ad Hoc Networks (MANET)

Quantification of Capacity and Transmission Delay for Mobile Ad Hoc Networks (MANET) Quantification of Capacity and Transmission Delay for Mobile Ad Hoc Networks (MANET) 1 Syed S. Rizvi, 2 Aasia Riasat, and 3 Khaled M. Elleithy 1, 3 Computer Science and Engineering Department, University

More information

Optimal Delay Throughput Tradeoffs in Mobile Ad Hoc Networks Lei Ying, Member, IEEE, Sichao Yang, and R. Srikant, Fellow, IEEE

Optimal Delay Throughput Tradeoffs in Mobile Ad Hoc Networks Lei Ying, Member, IEEE, Sichao Yang, and R. Srikant, Fellow, IEEE IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 54, NO. 9, SEPTEMBER 2008 4119 Optimal Delay Throughput Tradeoffs in Mobile Ad Hoc Networks Lei Ying, Member, IEEE, Sichao Yang, and R. Srikant, Fellow, IEEE

More information

Infrastructure Support Increases the Capacity of Ad Hoc Wireless Networks

Infrastructure Support Increases the Capacity of Ad Hoc Wireless Networks Infrastructure Support Increases the Capacity of Ad Hoc Wireless Networks Jeong-woo Cho, Seong-Lyun Kim and Song Chong Dept. of Electrical Engineering and Computer Science, Korea Advanced Institute of

More information

CLASSIFICATION OF SURFACES

CLASSIFICATION OF SURFACES CLASSIFICATION OF SURFACES JUSTIN HUANG Abstract. We will classify compact, connected surfaces into three classes: the sphere, the connected sum of tori, and the connected sum of projective planes. Contents

More information

On the Scalability of Hierarchical Ad Hoc Wireless Networks

On the Scalability of Hierarchical Ad Hoc Wireless Networks On the Scalability of Hierarchical Ad Hoc Wireless Networks Suli Zhao and Dipankar Raychaudhuri Fall 2006 IAB 11/15/2006 Outline Motivation Ad hoc wireless network architecture Three-tier hierarchical

More information

Optimal Routing and Scheduling in Multihop Wireless Renewable Energy Networks

Optimal Routing and Scheduling in Multihop Wireless Renewable Energy Networks Optimal Routing and Scheduling in Multihop Wireless Renewable Energy Networks ITA 11, San Diego CA, February 2011 MHR. Khouzani, Saswati Sarkar, Koushik Kar UPenn, UPenn, RPI March 23, 2011 Khouzani, Sarkar,

More information

Midpoint Routing algorithms for Delaunay Triangulations

Midpoint Routing algorithms for Delaunay Triangulations Midpoint Routing algorithms for Delaunay Triangulations Weisheng Si and Albert Y. Zomaya Centre for Distributed and High Performance Computing School of Information Technologies Prologue The practical

More information

NETWORK scalability has emerged as a pivotal problem in

NETWORK scalability has emerged as a pivotal problem in 4302 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 57, NO. 7, JULY 2011 On Scalability of Routing Tables in Dense Flat-Label Wireless Networks Li-Yen Chen and Petar Momčilović Abstract Consider a large

More information

Computational Geometry

Computational Geometry Lecture 12: Lecture 12: Motivation: Terrains by interpolation To build a model of the terrain surface, we can start with a number of sample points where we know the height. Lecture 12: Motivation: Terrains

More information

Chapter 7 TOPOLOGY CONTROL

Chapter 7 TOPOLOGY CONTROL Chapter 7 TOPOLOGY CONTROL Distributed Computing Group Mobile Computing Winter 2005 / 2006 Overview Topology Control Gabriel Graph et al. XTC Interference SINR & Scheduling Complexity Distributed Computing

More information

The Role of Network Coding in Wireless Unicast

The Role of Network Coding in Wireless Unicast The Role of Network Coding in Wireless Unicast Ramakrishna Gummadi (Ramki), UIUC Laurent Massoulie, Thomson Paris Research Lab Ramavarapu Sreenivas, UIUC June 10, 2010 Introduction Wireline: Some well

More information

Capacity of Ad Hoc Wireless Networks With Infrastructure Support

Capacity of Ad Hoc Wireless Networks With Infrastructure Support IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 23, NO. 3, MARCH 2005 657 Capacity of Ad Hoc Wireless Networks With Infrastructure Support Alexander Zemlianov, Student Member, IEEE, and Gustavo

More information

Capacity and Delay Tradeoffs for Ad-Hoc Mobile Networks

Capacity and Delay Tradeoffs for Ad-Hoc Mobile Networks Capacity and Delay Tradeoffs for Ad-Hoc Mobile etworks Michael J. eely University of Southern California http://www-rcf.usc.edu/ mjneely Eytan Modiano Massachusetts Inst. of Technology http://web.mit.edu/modiano/www/

More information

Heterogeneity Increases Multicast Capacity in Clustered Network

Heterogeneity Increases Multicast Capacity in Clustered Network Heterogeneity Increases Multicast Capacity in Clustered Network Qiuyu Peng Xinbing Wang Huan Tang Department of Electronic Engineering Shanghai Jiao Tong University April 15, 2010 Infocom 2011 1 / 32 Outline

More information

Approximating Node-Weighted Multicast Trees in Wireless Ad-Hoc Networks

Approximating Node-Weighted Multicast Trees in Wireless Ad-Hoc Networks Approximating Node-Weighted Multicast Trees in Wireless Ad-Hoc Networks Thomas Erlebach Department of Computer Science University of Leicester, UK te17@mcs.le.ac.uk Ambreen Shahnaz Department of Computer

More information

Compact Sets. James K. Peterson. September 15, Department of Biological Sciences and Department of Mathematical Sciences Clemson University

Compact Sets. James K. Peterson. September 15, Department of Biological Sciences and Department of Mathematical Sciences Clemson University Compact Sets James K. Peterson Department of Biological Sciences and Department of Mathematical Sciences Clemson University September 15, 2017 Outline 1 Closed Sets 2 Compactness 3 Homework Closed Sets

More information

5088 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 57, NO. 8, AUGUST We use the following notation: i) f (x) =O(g(x)) means that there exist

5088 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 57, NO. 8, AUGUST We use the following notation: i) f (x) =O(g(x)) means that there exist 5088 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 57, NO. 8, AUGUST 2011 Improved Capacity Scaling in Wireless Networks With Infrastructure Won-Yong Shin, Member, IEEE, Sang-Woon Jeon, Student Member,

More information

I. INTRODUCTION. and > 0 is any positive real number. We also show that for k = O( ), the per-flow multicast capacity under Gaussian

I. INTRODUCTION. and > 0 is any positive real number. We also show that for k = O( ), the per-flow multicast capacity under Gaussian IEEE/ACM TRANSACTIONS ON NETWORKING, VOL 18, NO 4, AUGUST 2010 1145 Multicast Capacity of Wireless Ad Hoc Networks Under Gaussian Channel Model Xiang-Yang Li, Senior Member, IEEE, Yunhao Liu, Senior Member,

More information

Optimizing the Data Collection in Wireless Sensor Network

Optimizing the Data Collection in Wireless Sensor Network Optimizing the Data Collection in Wireless Sensor Network R.Latha 1,Valarmathi.M 2 1 Assistant Professor, 2 PG Scholar 1,2 Computer Application 1,2 Vel Tech High Tech DR.Rangarajan DR.Sakunthala Engineering

More information

Topology Control in Wireless Networks 4/24/06

Topology Control in Wireless Networks 4/24/06 Topology Control in Wireless Networks 4/4/06 1 Topology control Choose the transmission power of the nodes so as to satisfy some properties Connectivity Minimize power consumption, etc. Last class Percolation:

More information

Many-to-Many Communication: A New Approach for Collaboration in MANETs

Many-to-Many Communication: A New Approach for Collaboration in MANETs Many-to-Many Communication: A New Approach for Collaboration in MANETs Renato M. de Moraes Dept. of Computing Systems University of Pernambuco Recife, PE 5070-00, Brazil Email: renato@dsc.upe.br Hamid

More information

Simulations of the quadrilateral-based localization

Simulations of the quadrilateral-based localization Simulations of the quadrilateral-based localization Cluster success rate v.s. node degree. Each plot represents a simulation run. 9/15/05 Jie Gao CSE590-fall05 1 Random deployment Poisson distribution

More information

Mobility Increases the Capacity of Ad-hoc Wireless Networks

Mobility Increases the Capacity of Ad-hoc Wireless Networks Mobility Increases the Capacity of Ad-hoc Wireless Networks Matthias Grossglauser David Tse AT&T Labs- Research Department of EECS 8 Park Avenue University of California Florham Park NJ 7932 Berkeley CA

More information

Efficient Aggregation Scheduling in Multihop Wireless Sensor Networks with SINR Constraints

Efficient Aggregation Scheduling in Multihop Wireless Sensor Networks with SINR Constraints 1 Efficient Aggregation Scheduling in Multihop Wireless Sensor Networks with SINR Constraints Xiaohua Xu, Xiang-Yang Li, Senior Member, IEEE, and Min Song, Senior Member, IEEE Abstract We study delay efficient

More information

Convex hulls of spheres and convex hulls of convex polytopes lying on parallel hyperplanes

Convex hulls of spheres and convex hulls of convex polytopes lying on parallel hyperplanes Convex hulls of spheres and convex hulls of convex polytopes lying on parallel hyperplanes Menelaos I. Karavelas joint work with Eleni Tzanaki University of Crete & FO.R.T.H. OrbiCG/ Workshop on Computational

More information

Geographical routing 1

Geographical routing 1 Geographical routing 1 Routing in ad hoc networks Obtain route information between pairs of nodes wishing to communicate. Proactive protocols: maintain routing tables at each node that is updated as changes

More information

CALCULATION OF INFERENCE IN AD-HOC NETWORK

CALCULATION OF INFERENCE IN AD-HOC NETWORK CALCULATION OF INFERENCE IN AD-HOC NETWORK POOJA GROVER, 2 NEHA GUPTA, 3 RANJIT KUMAR Asst. Prof., Department of Computer Science & Engineering, MDU, Rohtak, India-3300 2 Lecturer, Department of Information

More information

Ad hoc and Sensor Networks Chapter 10: Topology control

Ad hoc and Sensor Networks Chapter 10: Topology control Ad hoc and Sensor Networks Chapter 10: Topology control Holger Karl Computer Networks Group Universität Paderborn Goals of this chapter Networks can be too dense too many nodes in close (radio) vicinity

More information

A Novel Geometric Diagram and Its Applications in Wireless Networks

A Novel Geometric Diagram and Its Applications in Wireless Networks A Novel Geometric Diagram and Its Applications in Wireless Networks Guangbin Fan * and Jingyuan Zhang * Department of Computer and Information Science, University of Mississippi University, MS 38677, Email:

More information

Minimum Delay Packet-sizing for Linear Multi-hop Networks with Cooperative Transmissions

Minimum Delay Packet-sizing for Linear Multi-hop Networks with Cooperative Transmissions Minimum Delay acket-sizing for inear Multi-hop Networks with Cooperative Transmissions Ning Wen and Randall A. Berry Department of Electrical Engineering and Computer Science Northwestern University, Evanston,

More information

Routing over Multi-hop Wireless Networks with Non-ergodic Mobility

Routing over Multi-hop Wireless Networks with Non-ergodic Mobility Routing over Multi-hop Wireless Networks with Non-ergodic Mobility Chris Milling, Sundar Subramanian and Sanjay Shakkottai Department of ECE The University of Texas at Austin Email: {milling,ssubrama,shakkott}@ece.utexas.edu

More information

The Prices of Packets: End-to-end delay Guarantees in Unreliable Networks

The Prices of Packets: End-to-end delay Guarantees in Unreliable Networks This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 Unported License. See http://creativecommons.org/licenses/by-nc-nd/3.0/ The Prices of Packets: End-to-end

More information

A Cluster-Based Energy Balancing Scheme in Heterogeneous Wireless Sensor Networks

A Cluster-Based Energy Balancing Scheme in Heterogeneous Wireless Sensor Networks A Cluster-Based Energy Balancing Scheme in Heterogeneous Wireless Sensor Networks Jing Ai, Damla Turgut, and Ladislau Bölöni Networking and Mobile Computing Research Laboratory (NetMoC) Department of Electrical

More information

An efficient implementation of the greedy forwarding strategy

An efficient implementation of the greedy forwarding strategy An efficient implementation of the greedy forwarding strategy Hannes Stratil Embedded Computing Systems Group E182/2 Technische Universität Wien Treitlstraße 3 A-1040 Vienna Email: hannes@ecs.tuwien.ac.at

More information

June 20th, École Polytechnique, Paris, France. A mean-field model for WLANs. Florent Cadoux. IEEE single-cell WLANs

June 20th, École Polytechnique, Paris, France. A mean-field model for WLANs. Florent Cadoux. IEEE single-cell WLANs Initial Markov under Bianchi s École Polytechnique, Paris, France June 20th, 2005 Outline Initial Markov under Bianchi s 1 2 Initial Markov under Bianchi s 3 Outline Initial Markov under Bianchi s 1 2

More information

THE past decade has seen an emergence of wireless communication

THE past decade has seen an emergence of wireless communication IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 50, NO. 6, JUNE 2004 1041 A Deterministic Approach to Throughput Scaling in Wireless Networks Sanjeev R. Kulkarni, Fellow, IEEE, and Pramod Viswanath, Member,

More information

Integral Geometry and the Polynomial Hirsch Conjecture

Integral Geometry and the Polynomial Hirsch Conjecture Integral Geometry and the Polynomial Hirsch Conjecture Jonathan Kelner, MIT Partially based on joint work with Daniel Spielman Introduction n A lot of recent work on Polynomial Hirsch Conjecture has focused

More information

CS 177 Homework 1. Julian Panetta. October 22, We want to show for any polygonal disk consisting of vertex set V, edge set E, and face set F:

CS 177 Homework 1. Julian Panetta. October 22, We want to show for any polygonal disk consisting of vertex set V, edge set E, and face set F: CS 177 Homework 1 Julian Panetta October, 009 1 Euler Characteristic 1.1 Polyhedral Formula We want to show for any polygonal disk consisting of vertex set V, edge set E, and face set F: V E + F = 1 First,

More information

Non-Parametric Modeling

Non-Parametric Modeling Non-Parametric Modeling CE-725: Statistical Pattern Recognition Sharif University of Technology Spring 2013 Soleymani Outline Introduction Non-Parametric Density Estimation Parzen Windows Kn-Nearest Neighbor

More information

CAPACITY of wireless ad hoc networks is constrained. Multicast Performance With Hierarchical Cooperation

CAPACITY of wireless ad hoc networks is constrained. Multicast Performance With Hierarchical Cooperation This article has been accepted for inclusion in a future issue of this journal Content is final as presented, with the exception of pagination IEEE/ACM TRANSACTIONS ON NETWORKING 1 Multicast Performance

More information

3. Voronoi Diagrams. 3.1 Definitions & Basic Properties. Examples :

3. Voronoi Diagrams. 3.1 Definitions & Basic Properties. Examples : 3. Voronoi Diagrams Examples : 1. Fire Observation Towers Imagine a vast forest containing a number of fire observation towers. Each ranger is responsible for extinguishing any fire closer to her tower

More information

Load Balanced Short Path Routing in Wireless Networks Jie Gao, Stanford University Li Zhang, Hewlett-Packard Labs

Load Balanced Short Path Routing in Wireless Networks Jie Gao, Stanford University Li Zhang, Hewlett-Packard Labs Load Balanced Short Path Routing in Wireless Networks Jie Gao, Stanford University Li Zhang, Hewlett-Packard Labs Aravind Ranganathan University of Cincinnati February 22, 2007 Motivation Routing in wireless

More information

A Joint Performance-Vulnerability Metric Framework for Designing Ad Hoc Routing Protocols

A Joint Performance-Vulnerability Metric Framework for Designing Ad Hoc Routing Protocols The 2010 Military Communications Conference - Unclassified rogram - Cyber Security and Network Management A Joint erformance-vulnerability Metric Framework for Designing Ad Hoc Routing rotocols Andrew

More information

CS133 Computational Geometry

CS133 Computational Geometry CS133 Computational Geometry Voronoi Diagram Delaunay Triangulation 5/17/2018 1 Nearest Neighbor Problem Given a set of points P and a query point q, find the closest point p P to q p, r P, dist p, q dist(r,

More information

Chapter 8. Voronoi Diagrams. 8.1 Post Oce Problem

Chapter 8. Voronoi Diagrams. 8.1 Post Oce Problem Chapter 8 Voronoi Diagrams 8.1 Post Oce Problem Suppose there are n post oces p 1,... p n in a city. Someone who is located at a position q within the city would like to know which post oce is closest

More information

Capacity and Delay Tradeoffs for Ad-Hoc Mobile Networks

Capacity and Delay Tradeoffs for Ad-Hoc Mobile Networks IEEE TRASACTIOS O IFORMATIO THEORY TO APPEAR JUE 2005 Capacity and Delay Tradeoffs for Ad-Hoc Mobile etworks Michael J. eely, Eytan Modiano Abstract We consider the throughput/delay tradeoffs for scheduling

More information

Dual Power Management for Network Connectivity in Wireless Sensor Networks

Dual Power Management for Network Connectivity in Wireless Sensor Networks Dual Power Management for Network Connectivity in Wireless Sensor Networks Yanxia Rong, Hongsik Choi and Hyeong-Ah Choi Department of Computer Science George Washington University Washington DC Department

More information

Advanced Computer Networks Exercise Session 4. Qin Yin Spring Semester 2013

Advanced Computer Networks Exercise Session 4. Qin Yin Spring Semester 2013 Advanced Computer Networks 263-3501-00 Exercise Session 4 Qin Yin Spring Semester 2013 1 Administration If you haven't received any email about your submission We got your solutions for A1 & A2 About solutions

More information

Computing Aggregate Functions in Sensor Networks

Computing Aggregate Functions in Sensor Networks Computing Aggregate Functions in Sensor Networks Antonio Fernández Anta 1 Miguel A. Mosteiro 1,2 Christopher Thraves 3 1 LADyR, GSyC,Universidad Rey Juan Carlos 2 Dept. of Computer Science, Rutgers University

More information

CHAPTER 5 PROPAGATION DELAY

CHAPTER 5 PROPAGATION DELAY 98 CHAPTER 5 PROPAGATION DELAY Underwater wireless sensor networks deployed of sensor nodes with sensing, forwarding and processing abilities that operate in underwater. In this environment brought challenges,

More information

Efficient Universal Recovery in Broadcast Networks

Efficient Universal Recovery in Broadcast Networks Efficient Universal Recovery in Broadcast Networks Thomas Courtade and Rick Wesel UCLA September 30, 2010 Courtade and Wesel (UCLA) Efficient Universal Recovery Allerton 2010 1 / 19 System Model and Problem

More information

Chapter 6 Medium Access Control Protocols and Local Area Networks

Chapter 6 Medium Access Control Protocols and Local Area Networks Chapter 6 Medium Access Control Protocols and Local Area Networks Part I: Medium Access Control Part II: Local Area Networks CSE 3213, Winter 2010 Instructor: Foroohar Foroozan Chapter Overview Broadcast

More information

Capacity Deficit in Mobile Wireless Ad Hoc Networks Due to Geographic Routing Overheads

Capacity Deficit in Mobile Wireless Ad Hoc Networks Due to Geographic Routing Overheads Capacity Deficit in Mobile Wireless Ad Hoc Networks Due to Geographic Routing Overheads Nabhendra Bisnik, Alhussein Abouzeid Abstract Mobility of nodes may cause routing protocols to incur large overheads

More information

Figure 1: An example of a hypercube 1: Given that the source and destination addresses are n-bit vectors, consider the following simple choice of rout

Figure 1: An example of a hypercube 1: Given that the source and destination addresses are n-bit vectors, consider the following simple choice of rout Tail Inequalities Wafi AlBalawi and Ashraf Osman Department of Computer Science and Electrical Engineering, West Virginia University, Morgantown, WV fwafi,osman@csee.wvu.edug 1 Routing in a Parallel Computer

More information

CMPS 3130/6130 Computational Geometry Spring Voronoi Diagrams. Carola Wenk. Based on: Computational Geometry: Algorithms and Applications

CMPS 3130/6130 Computational Geometry Spring Voronoi Diagrams. Carola Wenk. Based on: Computational Geometry: Algorithms and Applications CMPS 3130/6130 Computational Geometry Spring 2015 Voronoi Diagrams Carola Wenk Based on: Computational Geometry: Algorithms and Applications 2/19/15 CMPS 3130/6130 Computational Geometry 1 Voronoi Diagram

More information

2 Related Work. 1 Introduction. 3 Background

2 Related Work. 1 Introduction. 3 Background Modeling the Performance of A Wireless Node in Multihop Ad-Hoc Networks Ping Ding, JoAnne Holliday, Aslihan Celik {pding, jholliday, acelik}@scu.edu Santa Clara University Abstract: In this paper, we model

More information

NODE LOCALIZATION IN WSN: USING EUCLIDEAN DISTANCE POWER GRAPHS

NODE LOCALIZATION IN WSN: USING EUCLIDEAN DISTANCE POWER GRAPHS CHAPTER 6 NODE LOCALIZATION IN WSN: USING EUCLIDEAN DISTANCE POWER GRAPHS Abstract Localization of sensor nodes in a wireless sensor network is needed for many practical purposes. If the nodes are considered

More information

Achieve Significant Throughput Gains in Wireless Networks with Large Delay-Bandwidth Product

Achieve Significant Throughput Gains in Wireless Networks with Large Delay-Bandwidth Product Available online at www.sciencedirect.com ScienceDirect IERI Procedia 10 (2014 ) 153 159 2014 International Conference on Future Information Engineering Achieve Significant Throughput Gains in Wireless

More information

Topology 550A Homework 3, Week 3 (Corrections: February 22, 2012)

Topology 550A Homework 3, Week 3 (Corrections: February 22, 2012) Topology 550A Homework 3, Week 3 (Corrections: February 22, 2012) Michael Tagare De Guzman January 31, 2012 4A. The Sorgenfrey Line The following material concerns the Sorgenfrey line, E, introduced in

More information

TSIN01 Information Networks Lecture 3

TSIN01 Information Networks Lecture 3 TSIN01 Information Networks Lecture 3 Danyo Danev Division of Communication Systems Department of Electrical Engineering Linköping University, Sweden September 10 th, 2018 Danyo Danev TSIN01 Information

More information

7. The Gauss-Bonnet theorem

7. The Gauss-Bonnet theorem 7. The Gauss-Bonnet theorem 7.1 Hyperbolic polygons In Euclidean geometry, an n-sided polygon is a subset of the Euclidean plane bounded by n straight lines. Thus the edges of a Euclidean polygon are formed

More information

CAPACITY COMPATIBLE TWO-LEVEL LINK STATE ROUTING FOR MOBILE AD HOC NETWORKS

CAPACITY COMPATIBLE TWO-LEVEL LINK STATE ROUTING FOR MOBILE AD HOC NETWORKS CAPACITY COMPATIBLE TWO-LEVEL LINK STATE ROUTING FOR MOBILE AD HOC NETWORKS John Sucec and Ivan Marsic Rutgers University ABSTRACT The throughput of mobile ad hoc networks (MANETs has been analyzed previously.

More information

Subject: Adhoc Networks

Subject: Adhoc Networks ISSUES IN AD HOC WIRELESS NETWORKS The major issues that affect the design, deployment, & performance of an ad hoc wireless network system are: Medium Access Scheme. Transport Layer Protocol. Routing.

More information

The Complexity of Connectivity in Wireless Networks. Roger WISARD

The Complexity of Connectivity in Wireless Networks. Roger WISARD The Complexity of Connectivity in Wireless Networks Roger Wattenhofer @ WISARD 2008 1 The paper Joint work with Thomas Moscibroda Former PhD student of mine Now researcher at Microsoft Research, Redmond

More information

An Optimal Bound for the MST Algorithm to Compute Energy Efficient Broadcast Trees in Wireless Networks. Qassem Abu Ahmad February 10, 2008

An Optimal Bound for the MST Algorithm to Compute Energy Efficient Broadcast Trees in Wireless Networks. Qassem Abu Ahmad February 10, 2008 An Optimal Bound for the MST Algorithm to Compute Energy Efficient Broadcast Trees in Wireless Networks Qassem Abu Ahmad February 10, 2008 i Contents 1 Introduction 1 2 Main Results 2 3 An Optimal bound

More information

Distributed Computing over Communication Networks: Leader Election

Distributed Computing over Communication Networks: Leader Election Distributed Computing over Communication Networks: Leader Election Motivation Reasons for electing a leader? Reasons for not electing a leader? Motivation Reasons for electing a leader? Once elected, coordination

More information

Surface Reconstruction with MLS

Surface Reconstruction with MLS Surface Reconstruction with MLS Tobias Martin CS7960, Spring 2006, Feb 23 Literature An Adaptive MLS Surface for Reconstruction with Guarantees, T. K. Dey and J. Sun A Sampling Theorem for MLS Surfaces,

More information

CAD & Computational Geometry Course plan

CAD & Computational Geometry Course plan Course plan Introduction Segment-Segment intersections Polygon Triangulation Intro to Voronoï Diagrams & Geometric Search Sweeping algorithm for Voronoï Diagrams 1 Voronoi Diagrams Voronoi Diagrams or

More information

Fractional Cascading in Wireless. Jie Gao Computer Science Department Stony Brook University

Fractional Cascading in Wireless. Jie Gao Computer Science Department Stony Brook University Fractional Cascading in Wireless Sensor Networks Jie Gao Computer Science Department Stony Brook University 1 Sensor Networks Large number of small devices for environment monitoring 2 My recent work Lightweight,

More information

274 Curves on Surfaces, Lecture 5

274 Curves on Surfaces, Lecture 5 274 Curves on Surfaces, Lecture 5 Dylan Thurston Notes by Qiaochu Yuan Fall 2012 5 Ideal polygons Previously we discussed three models of the hyperbolic plane: the Poincaré disk, the upper half-plane,

More information

Geometric approximation of curves and singularities of secant maps Ghosh, Sunayana

Geometric approximation of curves and singularities of secant maps Ghosh, Sunayana University of Groningen Geometric approximation of curves and singularities of secant maps Ghosh, Sunayana IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish

More information