1. Conceptual Differences Between Cube Analyst and Cube Analyst Drive Austen C. Duffy, Ph.D. Computational Mathematician, Citilabs

2. The Cube Analyst Suite
The Cube Analyst Suite consists of two OD matrix estimation programs, each possessing some unique features and capabilities.
Cube Analyst - The original matrix estimation program capable of a wide variety of static type estimation problems.
Cube Analyst Drive – The new matrix estimation program designed for dynamic estimation, but possessing some nice static estimation features as well.

3. Matrix Estimation w/ the Analyst Suite

4. Cube Analyst vs. Cube Analyst Drive: The Basics
Methodology: Statistics Based Estimation using Maximum Likelihood Method
Problem Types: Small Static Matrices, Public Transit
Supporting Programs: Highway, PT, TRIPS- MVESTE, MVESTL, etc.
Methodology: Estimation Based on Data Assimilation Techniques
Problem Types: Dynamic Matrices and Large Static Matrices
Supporting Programs: Highway, Avenue, any dynamic assignment program

5. Maximum Likelihood Method (Analyst)
The maximum likelihood method applies a statistical model utilizing maximum likelihood estimators (MLE’s) to a given data set (e.g. observed counts) to provide estimates for model parameters (e.g. OD matrix) that maximize a likelihood function.
“How likely is it that our OD matrix matches the observed count data”

6. Data Assimilation (Analyst Drive)
In Data Assimilation, we seek to minimize the squared error between a forecasted analysis (e.g. simulated volume) and a set of data observations (e.g. traffic counts) weighted by the reliability of the observations (e.g. confidence values), while simultaneously seeking to preserve a defined structure within our background solution (e.g. Input OD matrix).

7. Cube Analyst vs. Cube Analyst Drive: Mathematical Models
Analyst Applies the maximum likelihood method.
Solution estimates obtained via likelihood functions represented by PDF’s
Essentially minimizes a sum of logarithmic function terms representing screenline counts, trip origins, trip destinations and prior matrix along with a term for the derived cost matrix
Derivation and details available in the Cube Analyst Reference Guide
Analyst Drive’s primary objective aims to minimize the distance between the simulated volume AX and the count data b… i.e we wish to find a solution where
AX-b=0
Secondary objective: Preserve the background matrix structure

8. Cube Analyst Drive: Static Estimation Single Class Estimation Problem (Multiple Class in Parallel)

9. Cube Analyst vs. Cube Analyst Drive: Multiple Static User Classes
Multiclass static and dynamic estimation capabilities
Static capabilities allow users to estimate multiple classes from fewer count sets
New file format allows for multiple user class data to be stored in a single ICP file, requiring only a single Highway run.
Analyst does not allow the user to estimate Multiple User Classes
Must perform a separate Analyst run for each user class
May require multiple Highway runs to produce individual files (e.g. ICP) for each class

10. Estimating Multiple User Classes with Fewer Count Sets in Analyst Drive
Screenline Preprocessing
Aggregate Estimation
Given multiple matrices to estimate with fewer count sets, Analyst Drive will preprocess the input screenline files to produce an individual count set for each, and run the single class estimation problem in parallel
Numerically Superior (more data points)
Requires The assumption that the proportionality of class counts does not change with the evolving matrices
Volume contributions from multiple class sets are summed and matched against a single count set
Numerically Inferior (fewer data points)
More theoretically sound as it does not require any assumptions on end behavior

11. Cube Analyst Drive: Static Estimation Aggregate Multiple Class Estimation Problem

12. Cube Analyst Drive: Dynamic Estimation Single Class Estimation Problem (Multiple Class in Parallel)

13. Differences In The Use Of Confidence Values
Analyst
Analyst Drive
Uses confidence values to statistically provide value ranges for an estimated entry.
→ Less Reliable Data Provides for a larger variance and hence a wider range of possible values.
Uses Confidences values to determine the weight a particular value contributes to the problem.
→ Less Reliable data contributes less to the cost function, and hence is not as important in the estimation.

14. Cube Analyst vs. Cube Analyst Drive: Numerical Methods
Objective Function is minimized using the quasi-Newton BFGS method which requires an approximation to the Hessian matrix (expensive to compute, large storage penalty)
Sequential Computation
Objective Function is minimized via a conjugate gradient method which does not require a Hessian matrix
Parallel Computation at various levels

15. Cube Analyst vs. Cube Analyst Drive: Capabilities
Static Matrix Estimation with Highway X
Static Matrix Estimation with PT
Static Matrix Estimation for Large Networks (> 5000 Zones)
Dynamic Matrix Estimation with Avenue
Dynamic Matrix Estimation for any dynamic traffic assignment program
Estimation with static screenline counts
Estimation with static turning counts
Estimation with dynamic screenline counts

16. Cube Analyst vs. Cube Analyst Drive: Capabilities Cont.
Estimation with dynamic turning counts X
Estimation with part trip matrices
Simultaneous Estimation of Multiple User Classes
Aggregate Multi-Class Static Estimation
Static screenline count processing for estimating multiple user classes simultaneously from fewer sets of count data
Available 64 bit program with no inherent memory constraints
Multi-threaded for increased performance
Advanced parallel computing capabilities for high performance clusters using the message passing interface (MPI)

17. Analyst vs. Analyst Drive: Files
Analyst Drive does not accept all files that the original Analyst does
New Format ICP files developed for Analyst Drive allow for multiple user classes and provide up to 80% space savings
Matrix files contain multiple tabs for multiple user classes (static) and multiple time periods (dynamic)

18. Cube Analyst vs. Cube Analyst Drive: Block Diagrams

19. Cube File Compatibility
Cube/Voyager Files
Analyst
Analyst Drive
Cube Matrix X
Highway Old Format ICP
Highway New Format ICP
Highway RCP
Highway Screenline
PT ICP
PT Lines
PT Screenline
Voyager Path
Network Network File
Avenue Packet Log
Static Turning counts
Static Trip Ends

20. Cube File Compatibility Cont.: Analyst Specific Files
Analyst Drive
Model Params X
Grad Search
Dstr Defn Binr
Local Mat Cntr
Coordinates

21. Cube File Compatibility Cont.: Analyst Drive Specific Files
Dynamic Screenline X
Dynamic Turning counts
GEN DYN FILES

22. So How Do The Solutions Compare?
Both Analyst and Analyst Drive should produce similar solutions, but will not be identical.
Because Analyst is statistics based, it is able to provide a solution within a range of values (similar to a confidence interval) w/ sensitivities.
Analyst Drive is better able to preserve the structure of the background matrix.

23. Analyst vs. Analyst Drive Use Summary
Good for small static problems with a wide range of input options
Public Transit Networks.
Maximum Likelihood Method: Better at using poor input to generate reasonable matrices ‘from scratch’.
Dynamic Matrices
Large Static Matrices
Multiple Class Estimation
FAST!
Data Assimilation Method: Better at producing reliable matrices which preserve the defining structure of the background matrix.

24. Cube Analyst Drive Reference Guide - Version 1.01.12
References
Cube Analyst Drive Reference Guide - Version
Cube Analyst Reference Guide – Version 6.1.0

25. Where to Find Reference Guides

26. Questions?