Paging Area Optimization Based on Interval Estimation in Wireless Personal Communication Networks

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Paging Area Optimization Based on Interval
Estimation in Wireless Personal Communication
Networks

• By Z. Lei, C. U. Saraydar and N. B. Mandayam

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Roadmap

• Introduction / the problem
• Background
• Modeling
• Optimization
• Experimental results
• Conclusion

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Introduction Definitions

• Paging Area (PA) Region of the line/plane. Send
  paging signals from all base stations within the
  paging area
• Want to minimize PA because cost is proportional
  to PA
• At the same time, want to have a high probability
  of finding the mobile in the PA because a missed
  page is even more expensive
• In other words, want to OPTIMIZE the PA.

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Introduction Motivation

• Minimize transmissions, energy use
• Similar techniques may be applicable with other
  cost structures
• Keep track of user locations for other
  algorithms, such as location aided routing

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Introduction Problems

• Optimization given user location probabilities -
  Given probabilities of user locations, whats the
  least amount of effort required to find user
  (I.e. whats the optimal PA)?
• Optimization given user movement over time -Given
  a time-varying probability distribution, what are
  the optimal paging procedures?
• Determining user motion patterns - How can these
  time-varying distributions be estimated based on
  measurements and models of user motion?
• All three problems need to be solved.

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Problem Definition Cost Structure

• What are we trying to optimize?
• Fix a probability of finding the user within the
  PA.
• Subject to this probability, minimize the cost
  function
• Equivalent to minimizing , the area of
  the PA

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Background Location Distributions

• The density function is related to the
  probability of being at a location.
• Shaded area is probability of being in the
  interval

• Higher density implies greater likelihood of
  presence at that point
• This density is Unimodal and Symmetric, both are
  useful properties

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Background Confidence Intervals

• Specify the probability of an interval
• There are infinitely many intervals with the
  specified probability here, they are and
• Select the smallest one for symmetric, unimodal
  densities this is easy the region

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Background 2-D Densities

• 2-D density is a function defined on the plane
• Regions in the plane correspond to intervals on
  the line. Shown using contours here
• Probability of being in a region equals volume
  under the density function over that region

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Modeling The Set-up
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Modeling Illustration
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Modeling Formal Mobility Model

• Uses Brownian Motion with Drift as the mobility
  model
• Start at time tn, at location xn. Let x(t) be
  location at time t, t gt tn. Then
• Ex(t) xn V(t tn)
• Varx(t) D(t tn)
• V is the velocity of motion
• D is the diffusion parameter it represents
  location uncertainty/erraticity of motion
• The primary result of the paper is an estimate
  for V

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Optimization Parameter Estimation

• If D is known, it is easier to estimate V with
  fixed confidence G.
• Can calculate the mean location from V (location
  is simply xn V(t tn)) based on Gaussian
  confidence intervals.

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Optimization Parameter Estimation Contd.

• The size of the interval in which V lies turns
  out to be
• Increasing in the confidence parameter G
• Proportional to sqrt(D)
• Inversely proportional to square root of the
  interval over which observations were taken (I.e.
  tn t0)
• Roughly proportional to (t tn)
• The estimate itself is not dependent on the
  number of sample points, but the variance of the
  estimate decreases as the number of sample points
  increases.

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Optimization Parameter Estimation Contd.

• If D is unknown, we must first estimate D. This
  can be done if the observation time increments
  are all equal. D is estimated as sample variance,
  denoted
• The estimate for V is now based on a Students t
  distribution instead of a Gaussian distribution

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Optimization Parameter Estimation Contd.

• The characteristics of the estimate obtained
  here are the same as those for the known-D case,
  except that its size is proportional to the
  square root of , the estimate for D, rather
  than the square root of D itself

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Simulation Results Known D
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Simulation Results PA Sizes
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Simulation Results Actual PA Sizes
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Simulation Results Effect of Sample Size
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Conclusions

• The results are analytically optimal under the
  assumptions made in the paper (cant do better)
• Growth of paging area is linear as time
  progresses, which is good
• The parameter G, which determines probability of
  a correct page, is crucial when G is very close
  to 1, PA increases drastically
• V doesnt affect paging area this is expected
• Can select an optimal sample size for a given
  problem as well

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Observations/Reservations

• The results in the paper have been well known for
  over 50 years
• No results on whether the model chosen is
  representative of real user mobility
• What happens if D and V are dependent on time,
  I.e. of the form D(t) and V(t)?
• depends on several factors signaling
  cost, pressure on MAC layers, etc. How easy is it
  to determine?
• G depends the cost of a missed page. How easily
  can it be determined?

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Problem Definition Role of