1. Mohamed Mahmoud, Ph.D. Senior Planner, Forecasting TransLink
Implementation of a flexible destination balance to multiple productions tool in EMME
Mohamed Mahmoud, Ph.D.
Senior Planner, Forecasting
TransLink
INRO City Model Seminar, Portland, Oregon
September 21st, 2016

2. Context
The Regional Transportation Model (RTM) is a trip-based model of Vancouver, BC.
The model is initiated by splitting the demand segments by household size, number of workers, income level, and auto-availability level - resulting in 117 segments.
After trip generation, the segments collapse down to nine segments.
This segmentation is carried through trip distribution and mode choice, and then income-specific demand matrices are maintained for multi-class trip assignments.
To maintain this segmentation in trip distribution, the EMME balance to multiple productions tool is used.
Nine segments: 3 income levels crossed by 3 auto ownership levels.
--Mainly because we don’t have the data to support such thin segmentation and we only really need income and auto ownership levels at mode choice--
At the trip distribution level: productions are sliced by socio-economic information, but the attractions are not. So … we need to balance multiple productions (9) to 1 attraction
And that ‘s when the EMME balance to multiple productions tool comes handy.

3. EMME’s Balance to Multiple Productions Tool
The tool performs a two-dimensional (i.e. doubly-constrained) balancing using multiple classes of productions and a single destination vector.
There are two common ways of performing matrix balancing:
Singly-constrained
Doubly-constrained
Which is exactly what we want … trip productions 9 segments and trip attractions 1 segment.
When we distribute trips We either control for the total productions only, this is called singly-constrained. Or control for both productions and attractions, and that is called doubly-constrained.
The singly-constrained gravity model formulation ensures that in the resulting trip table would have:
the same number of trips leaving each TAZ (row sum) is equal to the number of productions given to the model. But, the same is not true for attractions (column sum). That’s what the doubly-constrained model does in an iterative fashion.
The difference between the two ways speaks to the difference between sensitivity to travel impedance and the number of attractions.
forcing convergence implies that the trip attraction estimate is more important or reliable than the travel time effects on the gravity model.
Singly  weights travel impedance more than the number of attractions ---- which reflects short-term decisions
Doubly  weights the number of attractions more than travel impedance ---- which reflects long-term decisions

4. Balancing
For commuting purposes, there is a clear physical constraint on the number of attractions (i.e. jobs) to each destination and as such trip rates are more certain.
Therefore, forcing convergence to match a fixed number of attractions is a reasonable assumption for work and school trips.
However, this assumption does not always hold true for discretionary trip purposes. There is no physical constraint on the number of attraction in each zone.
Proposed approach
Doubly-constrained: HBW, HBS, and HBU purposes
Singly-(or relaxed) constrained : all other purposes
Hybrid (flexible) approach.
For work/school trips, it is a reasonable assumption that there will be a little less than two HBW trips attracted for each employee … and that work locations are largely immaterial to the LOS changes.
For instance if we have two identical malls, one with a convenient location, and the other much less accessible. It is likely that the less accessible mall will have fewer shopping trip attractions. But, if the doubly-constrained model is applied, then both malls will get the same number of trips despite the difference in accessibility.
flexible approach: (a model with relaxed constrains using relaxation scaling factors: 0 doubly ~ 1 singly) in other words – run until fully converge or run a few iteration (instead of a closed form)

5. Implementation
We developed a flexible destination balance to multiple productions tool using Python to access the EMME matrix calculator via the modeller API.
The tool provides options to perform either type of matrix balancing.
Additional testing
This work in-progress and we yet to test the application of either the singly-constrained or the flexible approach.
The trip distribution model is expected to exhibit logical elasticities with respect to polices affecting level-of-service attributes such as pricing.

6. Thank you!
Notes:
In our understanding … one iteration of the doubly constrained tool will adjust the attraction totals then the production totals .. So we can think about singly-constrained as an half iteration.
The singly constrained is a closed form .. So no iterations but the flexible approach is to use a couple iterations which will adjust both attractions and productions but only productions will be matched and attractions will not hardly matched.