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Cosmo Zheng. Can we reliably forecast individual 3G usage data?. An analysis using mathematical simulation of time series algorithms. Background. Fluctuations in daily demand for bandwidth make ordinary usage pricing inefficient - PowerPoint PPT Presentation
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Can we reliably forecast individual 3G usage data?
An analysis using mathematical simulation of time series algorithms
Cosmo Zheng
Background
• Fluctuations in daily demand for bandwidth make ordinary usage pricing inefficient
• Solution: Time-dependent pricing to persuade users to defer usage
http://scenic.princeton.edu/tube/overview.html
Our Problem
• Users must be informed of expected future prices, to assess the costs of deferring usage
• We need a reliable way to predict future usage based on past data
http://scenic.princeton.edu/tube/technology.html
The Algorithms
• Nonlinear regression – generate a fitted function of the form D + A*sin(2πt/24) + B*sin(2πt/12) + C*sin(2πt/6)
• Use fitted function to extrapolate
Algorithms (cont.)
• Time series decomposition – isolate trend, seasonal, and residual components
• Extend trend and seasonal components into the future
Algorithms (cont.)
• Exponential smoothing – generate {St} based on a weighted average of previous data
• Simplest form is S1 = X0, St = αXt-1 + (1-α)St-1 for t>1, where α is a smoothing factor
The Data
• Use simulated datasets, representing usage each hour over 5 days
• {Xt} for 1 <= t <= 120• First 4 days are
historical data (training set), 5th day is the test set
Algorithm 1: Regression
Regression (cont.)
R2 = 0.424
Algorithm 2: Decomposition
Decomposition (cont.)
R2 = 0.693
Algorithm 3: Smoothing
Smoothing (cont.)
R2 = 0.516
Additional Trials
Trial # Regression Decomposition Smoothing
1 64.1 46.2 56.4
2 76 47.4 61.1
3 65.5 53.9 53.4
4 61.7 48.9 46.8
5 58.8 43.1 53.3
6 68.9 43.5 51.3
7 59.1 45.4 40.8
8 59.6 56.6 58.6
9 75.6 56.4 59.2
10 52.8 46.9 54.1
Average 64.21 48.83 53.5
Trial # Regression Decomposition Smoothing
1 0.424 0.693 0.516
2 0.374 0.721 0.455
3 0.388 0.577 0.543
4 0.53 0.601 0.593
5 0.383 0.687 0.527
6 0.382 0.64 0.682
7 0.515 0.722 0.783
8 0.457 0.459 0.389
9 0.506 0.612 0.719
10 0.468 0.507 0.348
Average 0.4427 0.6219 0.5555
Sum of absolute error R2
Conclusions
• Time series decomposition provided most accurate prediction of future usage, followed by exponential smoothing, then regression
• Possible explanation: usage pattern is strongly cyclic; repeats itself on a daily basis
• Suggestion: investigate further into better means of isolating seasonal data; some more sophisticated algorithms exist (ARIMA, stochastic volatility models).