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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. Roadmap. Introduction / the problem Background Modeling Optimization Experimental results Conclusion. Introduction: Definitions.
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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
Roadmap • Introduction / the problem • Background • Modeling • Optimization • Experimental results • Conclusion
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.
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
Introduction: Problems • Optimization given user location probabilities - Given probabilities of user locations, what’s the least amount of effort required to find user (I.e. what’s 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.
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
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
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
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
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 > tn. Then: • E[x(t)] = xn + V(t – tn) • Var[x(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
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.
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.
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 Student’s t distribution instead of a Gaussian distribution
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
Conclusions • The results are analytically optimal under the assumptions made in the paper (can’t 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 doesn’t affect paging area – this is expected • Can select an optimal sample size for a given problem as well
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?
