Transcript Homework Review

Homework Review
20-751 ECOMMERCE TECHNOLOGY
SUMMER 2002
COPYRIGHT © 2002 MICHAEL I. SHAMOS
Valuable Objects
• How many objects on Earth are worth more than one
dollar?
• What is an “object”?
• Is a manufactured article one object, or do all its parts
count separately?
• Is an animal an object? Does it matter?
• Are all objects owned by someone?
• Approach: for what purpose are we defining objects?
• To track their movements and allow them to
communicate. Easy for fixed objects.
20-751 ECOMMERCE TECHNOLOGY
SUMMER 2002
COPYRIGHT © 2002 MICHAEL I. SHAMOS
Students Methods
• I own 173 objects. The world population is 6 billion.
Therefore there are 1.038 trillion objects.
• Problems:
– Can’t extrapolate from one case. May not be
representative
– Doesn’t deal with definition of “object”
– Doesn’t deal with objects that are not owned
• Similarly: I have 205 objects in 1024 square feet of
space. Therefore there are 205 * square footage of
Earth land area / 1024 objects
20-751 ECOMMERCE TECHNOLOGY
SUMMER 2002
COPYRIGHT © 2002 MICHAEL I. SHAMOS
Student Methods
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The U.S. GDP is $10T; world GDP is $40T
Consumption is 67% of GDP
Each object is worth $1
Therefore, there are $40T x .67 = 27T objects
Problems:
– Assumes all objects are the same low value
– Assumes all objects are manufactured
– Assumes objects only live for one year
• Correction: allow for lifetimes of objects
20-751 ECOMMERCE TECHNOLOGY
SUMMER 2002
COPYRIGHT © 2002 MICHAEL I. SHAMOS
Better Approaches
• Define “object”
– Something whose location needs to be tracked or that needs
to communicate
– Therefore, a manufactured good is a single object
– Fixed objects (buildings, trees, mountains, etc.) do not need
to be tracked. Therefore we count man-made moveable
objects
• Where are the objects?
– Home, office, fixed infrastructure (trains, planes … )
– Big things are very expensive, so there aren’t many of them
– Focus attention on small objects (cheap, numerous)
20-751 ECOMMERCE TECHNOLOGY
SUMMER 2002
COPYRIGHT © 2002 MICHAEL I. SHAMOS
Counting Small Objects
• Personal effects
– Books, food containers, clothing, furniture, entertainment
media (records, CD) …
– Most furniture doesn’t matter (too few pieces)
• Approach:
– Estimate categories separately
– Take world variations into account (big countries)
– 2/3 of world live in the top 15 countries
– Divide into socioeconomic categories
– Add up classes of objects for each category
– Deal with corporate ownership (most people have two
venues: home and office)
20-751 ECOMMERCE TECHNOLOGY
SUMMER 2002
COPYRIGHT © 2002 MICHAEL I. SHAMOS
World’s Largest Countries
What about UK, France, etc.?
20-751 ECOMMERCE TECHNOLOGY
SUMMER 2002
COPYRIGHT © 2002 MICHAEL I. SHAMOS
Data Reporting
• Reporting object position of N objects
– Must decide on resolution. Earth’s circumference
is ~40,000 km. All objects are below 8 km in
altitude.
– For 1 meter resolution, need 26 bits for latitude
and longitude, 13 bits for altitude.
– Also need log N bits for object ID
< 10,000 objects
• N < 104 x 6 x 109 = 6 x 1013 objects
per person
• log2(6 x 1013) ~ 46
• Number of bits < 26 + 26 + 13 + 46 = 111 bits
• Every 5 minutes = 111 bits/300 sec ~ 0.37 bps/object
• Data rate = 2.2 x 1013 bps ~ 22 terabits/sec
20-751 ECOMMERCE TECHNOLOGY
SUMMER 2002
COPYRIGHT © 2002 MICHAEL I. SHAMOS
Backbone
• World backbone capacity 1-2 Tb/sec. (See FCC
Report)
• Capacity doubles every 10 months
• Another method: there are ~100,000 networks that
make up the Internet. If each one has T3 capacity of
44 Mbps, that’s 4.4 x 1011 bps = .4 Tb
20-751 ECOMMERCE TECHNOLOGY
SUMMER 2002
COPYRIGHT © 2002 MICHAEL I. SHAMOS
Power Density
• Objects are transmitting at 0.37 bps
• An 802.11 card can transmit at 11 Mbps, enough for
30 million objects, if transmission is synchronized.
IT’S NOW OBVIOUS WE CAN NEVER HAVE
A POWER PROBLEM. NO ONE CAN GET
NEAR 30 MILLION OBJECTS
• Power radiated by an 11 Mb card is < 100 mW
• If my mean-squared distance from a collection of
802.11 cards is 10 meters, how many cards can
transmit before the radiation is harmful to me?
20-751 ECOMMERCE TECHNOLOGY
SUMMER 2002
COPYRIGHT © 2002 MICHAEL I. SHAMOS
Power Density
• The area of a 10-meter sphere is 400p ~ 1250 m2 =
1.25 x 103 x 104 = 1.25 x 107 cm2
• If a point source radiates at 100 mW, then at 10
meters the power density is 10-1 / (1.25 x 107 ) =
8 x 10-9 watts/cm2
• To get to 5 x 10-3 watts/cm2, I would need
5 x 10-3 / (8 x 10-9 ) ~ 6 x 105 = 600,000 cards to be
within 10 meters of me
• This is enough for 6 x 105 x 3 x 107 ~ 2 x 1013
objects, basically all the objects in the world!
• LESSON: A HUGE AMOUNT OF INFORMATION
CAN BE TRANSITTED WITH VERY LITTLE POWER
20-751 ECOMMERCE TECHNOLOGY
SUMMER 2002
COPYRIGHT © 2002 MICHAEL I. SHAMOS
Food Company Data
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50K employees, 100 bytes every 5 minutes
800 bits/5 minutes = 2.67 bps per employee
2.7 bps x 50K employees ~ 135 Kbps
Number of seconds in a year = 365 x 24 x 3600 =
31,536,000
• Bits per year = 1.35 x 105 x 3.2 x 107 ~ 4.32 x 1012
bits = 5.4 x 1011 bytes = 540 GB
• 10 years = 5.4 TB
20-751 ECOMMERCE TECHNOLOGY
SUMMER 2002
COPYRIGHT © 2002 MICHAEL I. SHAMOS