Optimizing Cellular Paging

1
Optimizing Cellular Paging

• Diana Dugas
• Southwestern University
• dugasd_at_southwestern.edu

2
Notes and Background

• Cellular partitions (cells) resembles puzzle
  pieces
• Each cell contains a tower
• When someone makes a phone call, the call goes
  first to the cell tower and then the cell phone

3
The Two Extremes
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Paging Everyone at Once

• Fast
• Requires a lot of resources for one call
• What happens if two calls come in at the same
  time?

5
Paging Each Cell Individually

• Uses resources in a more friendly manner
• Takes a long time
• The caller will hang up before the tower can
  locate the cell phone

6
The Problem

• Figure out a way to locate the user before the
  caller hangs up because s/he is tired of waiting
  for a connection.

7
How Do We Solve This Problem?
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Solution Find a Happy Medium

• We try to organize the cells in such a manner
  that a program can group the cells and activate
  them in a particular order which minimizes time
  and resources while maximizing results

9
The Algorithm
10
The Cells

• First we have to organize the cells into
  decreasing probability.
• The values of probability are assigned to the
  cells through past use.
• Cells with a high probability are ones from which
  or to which past calls have been frequent.

11
The Divisors

• The divisors are the places where the cells will
  be broken up
• They are like signs to let the user know where to
  best break up the cells
• Their value is equal to the number of areas
  before them

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The Idea!

• Take each cell and order them
• Place the divisors evenly throughout the cells
• Move one divisor and check the output and repeat
  unless the value goes up
• Move the next divisor in the same manner

13
The Results

• The algorithm will find a minimum for the
  information given to it.
• The program will find minimums that are not that
  statistically different from the absolute minimum

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What does the program do?
1 2 3 4

• Some examples
• 6 Areas and 2 Divisors
• 6 Areas and 3 Divisors

1 2 3 4 5 6
1 2 3
1 2 3 4 5 6 7 8 9
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6 Areas and 2 Divisors

• 6 5 4 3 2 1 68
• (65) 2 (43) 4 (21) 6
• 11 2 7 4 3 6
• 22 28 18 68

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6 Areas and 2 Divisors

• 6 5 4 3 2 1 68
• 6 5 4 3 2 1 72

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6 Areas and 2 Divisors

• 6 5 4 3 2 1 68
• 6 5 4 3 2 1 72
• 6 5 4 3 2 1 70
• The minimum value is therefore the 1st bullet

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6 Areas and 3 Divisors

• 6 5 4 3 2 1 64

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6 Areas and 3 Divisors

• 6 5 4 3 2 1 64
• 6 5 4 3 2 1 67

20
6 Areas and 3 Divisors

• 6 5 4 3 2 1 64
• 6 5 4 3 2 1 67
• 6 5 4 3 2 1 62

21
6 Areas and 3 Divisors

• 6 5 4 3 2 1 64
• 6 5 4 3 2 1 67
• 6 5 4 3 2 1 62
• 6 5 4 3 2 1 64
• So the minimum value here would be 62, that of
  the 3rd bullet

22
Some Specific Problems

• The previous equations give the minimum, but that
  is not the value the program would find.
• The program would find the value of 64
• 6 5 4 3 2 1 64
• This is close to the correct minimum, but not
  exactly it.

Oops!
23
Where does this take us?
?
?
?
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The Program

• The program is a Java applet which, will find a
  minimum as described by the algorithm.
• Since Java is not a mathematical language, the
  program poses unique difficulties in
  communication.

25
Accuracy of the Program

• There are few ways to test the accuracy of such a
  program.
• There is a program that runs an exhaustive
  search.
• Are our variables defined the same way?
• How do we know that they truly performed an
  exhaustive search?

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Problems with the Program

• One problem, as seen in an earlier example is
  that the way the divisors are initially placed
  will affect the outcome.
• Since the program does not run an exhaustive
  search, it will not always find the absolute
  minimum.

27
Kinds of Implementation

• Instead of using decreasing numbers the program
  can store the different users probabilities and
  when the number corresponding to that person is
  called, bring those up and run the diagnostic
• This can decrease the amount of time the server
  is now taking to find the user

28
Areas for Expansion

• Instead of only running a diagnostic for
  minimizing time, the program can be expanded to
  also include cost (i.e. The cost required to
  activate the towers.)
• A program which only minimizes cost may also
  prove useful in the future.