Presented by Jehn-Ruey Jiang Department of Computer Science and Information Engineering
description
Transcript of Presented by Jehn-Ruey Jiang Department of Computer Science and Information Engineering
Expected Quorum Overlap Sizes of Optimal Quorum Systems with the Rotation Closure Property for Asynchronous Power-Saving Algorithms in Mobile Ad Hoc Networks
Presented by
Jehn-Ruey JiangDepartment of Computer Science and Information Engineering
National Central University
2/38
Outline
Mobile Ad hoc Networks Quorum-Based Asynchronous Power
Saving Algorithm Expected Quorum Overlap Size The f-Torus Quorum System Analysis and Simulation Results of
EQOS Conclusion
Mobile Ad hoc Network
MANET
3/38
4/38
MANET Applications
BattlefieldsDisaster RescueSpontaneous MeetingsOutdoor Activities
5/38
Power Saving Problem
Battery is a limited resource for portable devices
Battery technology does not progress fast enough
Power saving becomes a critical issue in MANETs, in which devices are all supported by batteries
6/38
IEEE 802.11 PS Mode
An IEEE 802.11 Card is allowed to turn off its radio to be in the PS mode to save energyPower Consumption:(ORiNOCO IEEE 802.11b PC Gold Card)
Vcc:5V, Speed:11Mbps
7/38
MAC Layer Power-Saving Algorithm
Two types of MAC layer PS algorithm for IEEE 802.11-based MANETs Synchronous (IEEE 802.11 PS Algorithm)
Synchronous Beacon IntervalsFor sending beacons and ATIM (Ad hoc Traffic
Indication Map) Asynchronous [Jiang et al. 2005]
Asynchronous Beacon IntervalsFor sending beacons and MTIM (Multi-Hop
Traffic Indication Map)
8/38
Beacon:
1.For a device to notifyothers of its existence
2.For devices to synchronize their clocks
9/38
How to sense others?
10/38
IEEE 802.11 Syn. PS Algorithm
Beacon Interval Beacon Interval
Host A
Host B
ATIM Window
ATIM Window
Beacon Frame
Target Beacon Transmission Time(TBTT)
No ATIM means no data to send
or to receive with each other
ATIM Window
Clock Synchronized by TSF (Time Synchronization Function)
ATIM Window
ATIM
ACK
Data Frame
ACK
Active mode
Active modePower saving Mode
Power saving Mode
11/38
Clock Drift Example
Max. clock drift for IEEE 802.11 TSF (200 DSSS nodes, 11Mbps, aBP=0.1s)
200 s MaximumTolerance
12/38
Network-Partitioning Example
Host A
Host B
A
B
C D
E
F
Host C
Host D
Host E
Host F
╳
╳
ATIM window
╳
╳
Network Partition
The blue ones do not know the existence of the red ones, not to
mention the time when they are awake.
The red ones do not know the existence of the blue ones, not to
mention the time when they are awake.
13/38
Asynchronous PS Algorithms (1/2)
Try to solve the network partitioning problem to achieve Neighbor discovery Wakeup prediction
Without synchronizing hosts’ clocks
14/38
Asynchronous PS Algorithms (2/2)
Three existent asynchronous PS algorithms
Dominating-Awake-Interval
Periodical-Fully-Awake-Interval
Quorum-Based (QAPS)
15/38
Quorum System
What is a quorum system?A collection of mutually intersecting subsets of an universal set U, where each subset is called a quorum.E.G. {{1, 2},{2, 3},{1,3}} is a quorum system under U={1,2,3}, where {1, 2}, {2, 3} and {1,3} are quorums.
Not all quorum systems are applicable to QAPS algorithms
Only those quorum systems with the rotation closure property are applicable. [Jiang et al. 2005]
16/38
Optimal Quorum System (1/2)
Quorum Size Lower Bound for quorum systems satisfying the rotation closure property:k, where k(k-1)+1=n, the cardinality of the universal set, and k-1 is a prime power(k n ) [Jiang et al. 2005]
17/38
Optimal Quorum System (2/2)
Optimal quorum system FPP quorum system
Near optimal quorum systems Grid quorum system Torus quorum system Cyclic (difference set) quorum system E-Torus quorum system
18/38
Numbering Beacon Intervals
0 1 2 3
4 5 6 7
8 9 10 11
12 13 14 15
And they are organized
as a n n array
n consecutive beacon intervals are numbered as 0 to n-1
101514131211109876543210 …
Beacon interval
19/38
Quorum Intervals (1/4)
Intervals from one row and one column are called
Quorum Intervals
0 1 2 3
4 5 6 7
8 9 10 11
12 13 14 15
Example:Quorum intervals arenumbered by2, 6, 8, 9, 10, 11, 14
20/38
Quorum Intervals (2/4)
Intervals from one row and one column are called
Quorum Intervals
0 1 2 3
4 5 6 7
8 9 10 11
12 13 14 15
Example:Quorum intervals arenumbered by0, 1, 2, 3, 5, 9, 13
21/38
Quorum Intervals (3/4)
Any two sets of quorum intervals have two common members
For example:The set of quorum intervals {0, 1, 2, 3, 5, 9, 13} and the set of quorum intervals{2, 6, 8, 9, 10, 11, 14} have two common members:
2 and 915141312
111098
7654
3210
22/38
Quorum Intervals (4/4)
1514131211109876543210
2 151413121110987654310
2 overlapping quorum intervals
Host DHost C
2 151413121110987654310Host D
1514131211109876543210Host C
Even when the beacon interval numbers are not aligned (they are rotated), there are always at least two overlapping quorum intervals
23/38
Structure of Quorum Intervals
24/38
FPP quorum system
Constructed with a hypergraph An edge can connect more than 2 vertices
FPP:Finite Projective Plane A hypergraph with each pair of edges
having exactly one common vertex Also a Singer difference set quorum
system
25/38
FPP quorum system Example
0 1 2
3 4
5
6
A FPP quorum system:{ {0,1,2}, {1,5,6}, {2,3,6}, {0,4,6}, {1,3,4}, {2,4,5}, {0,3,5} }
0
3
5
26/38
Torus quorum system
For a tw torus, a quorum contains all elements from some column c, plus w/2 elements, each of which comes from column c+i, i=1.. w/2
171615141312
11109876
543210
One full column
One half column cover in a wrap around manner
{ {1,7,13,8,3,10}, {5,11,17,12,1,14},…}
27/38
Cyclic (difference set) quorum system
Def: A subset D={d1,…,dk} of Zn is called a difference set if for every e0 (mod n), thereexist elements di and djD such that di-dj=e.
{0,1,2,4} is a difference set under Z8
{ {0, 1, 2, 4}, {1, 2, 3, 5}, {2, 3, 4, 6}, {3, 4, 5, 7},{4, 5, 6, 0}, {5, 6, 7, 1}, {6, 7, 0, 2}, {7, 0, 1, 3} }is a cyclic (difference set) quorum system C(8)
28/38
E-Torus quorum system
Trunk
Branch
Branch
Branch
Branch
cyclic
cyclic
E(t x w, k)
29/38
Outline
Mobile Ad hoc Networks Quorum-Based Asynchronous Power
Saving Algorithm Expected Quorum Overlap Size The f-Torus Quorum System Analysis and Simulation Results of
EQOS Conclusion
30/38
Performance Metrics
SQOS: smallest quorum overlap sizefor worst-case neighbor sensibility
MQOS: maximum quorum overlap separationfor longest delay of discovering a neighbor
EQOS: expected quorum overlap sizefor average-case neighbor sensibility
New Contribution
f-torus quorum system
31/38
New Contributio
n
32/38
33/38
New Contributio
n
34/38
35/38
36/38
Conclusion (1/2)
We have proposed to evaluate the average-case neighbor sensibility of a QAPS algorithm by EQOS
We have proposed a new quorum system, called the fraction torus (f-torus) quorum system, for the construction of flexible mobility-adaptive PS algorithms.
We have analyzed and simulate EQOS for the FPP, grid, cyclic, torus, e-torus and f-torus quorum systems
37/38
Conclusion (2/2)
f-torus quorum systems may be applied to other applications: location management, information dissemination/retrieval data aggregation
in mobile ad hoc networks (MANETs)and/or wireless sensor networks (WSNs)
38/38
Thanks
39/38
Rotation Closure Property (1/3)
Definition. Given a non-negative integer i and a quorum H in a quorum system Q under U = {0,…, n1}, we define rotate(H, i) = {j+ijH} (mod n).
E.G. Let H={0,3} be a subset of U={0,…,3}. We have rotate(H, 0)={0, 3}, rotate(H, 1)={1,0}, rotate(H, 2)={2, 1}, rotate(H, 3)={3, 2}
40/38
Rotation Closure Property (2/3)
Definition. A quorum system Q under U = {0,…, n1} is said to have the rotation closure property ifG,H Q, i {0,…, n1}: G rotate(H, i) .
41/38
Rotation Closure Property (3/3)
For example, Q1={{0,1},{0,2},{1,2}} under
U={0,1,2}} Q2={{0,1},{0,2},{0,3},{1,2,3}}
under U={0,1,2,3}
Because {0,1} rotate({0,3},3) =
{0,1} {3, 2} = Closure