Transport Demand - Trip Distribution Flashcards
What is trip distribution?
Where do the trips start and end?
What is the trip matrix?
The output of the trip distribution Two dimensional nxn array - n = number of zones in the study area - rows = trip productions/origins - columns = trip attractions / destinations
Tij = trips from zones i to zone j
Seperate matrices by purpose (p) and mode (k)
T^pk subscript ij
Diagonal (Tij) = intra-zonal trips
What is the generalised cost of travel?
- Linear summation of the cost of travel
(in vehicle time, vehicle operating cost, walking time, waiting time, fares, tolls or parking, interchange penalty and modal penalty)
Weights are used to convert each attribute to appropriate measure of time or money
Varies by mode and time of day
Represents the dis-utility of travel perceived by the trip maker
What is uniform growth factoring? and what are the assumptions for it?
Tij = F x tij
Where tij = existing cell value
F = growth factor
Tij = forecast cell value
Assumes uniform growth generally unrealistic (except for short time spans)
Would usually also expect differential growth rates for different parts of the study area
What is singly constrained growth factoring?
Information available on the expected change in trips origins or destination
Apply specific growth factors to origin and destination separately
What is doubly constrained growth factoring?
Different origin and destination growth rates - application of an average growth rate a poor approximation
Tij = tij x a x b
where a and b are balancing factors
What are some of the limiting factors of growth factoring?
- Need a starting matrix and expected trip growth
- Dependent upon the accuracy of the starting matrix
- Suitable only for short term forecasting ( 1-2 years)
- Zero cells in starting matrix remain zero in forecasting matrix
- Ignores changes in transport costs
- Not suitable for the analysis of new models, links, pricing and new zones
What is the gravity model?
A model that is used to forecast changes in transport
Tij = aj x bj x f(cij)
where a and b are balancing factors that incorporate trip end estimates
Cij = generalised cost of travel between zones i and j
f(cij) = deterrence function
When is a gravity model appropriate? and what does it rely on?
Appropriate when changes in transport supply need to be considered
Does not rely on an existing trip matrix
True or False
In the gravity model, separate trip matrices are required for each mode and purpose.
True
What is a skim matrix?
A matrix that is analogous to trip tables
- two dimensional n x n array
- n = number of zones in the study area
- cij = generalised cost of travel from zone i to zone j
- diagonal = intra zonal travel costs
- separate matrices by mode k cij^k
Produced by skimming the network to determine the cost of travel on the cheapest route from zone i to zone j
May vary by time of day and mode
- Blended skims: Weighted average travel costs ( over day, over a network) , an approximation of perceived travel costs)
When is a deterrence function used?
In gravity model to reflect propensity for cost saving in travel decisions. Once calibrated assumed to hold constant.
- vary by trip purpose and study area
- ——-> steeper for compact study areas and discretionary travel
Shape of curve determined through gravity model calibration process
What are the three types of deterrence functions?
Power - f(c) = c ^alpha
Exponential - f(c) = e^(ßc)
Gamma - f(c) = (c^ alpha) x (e^ßc)
What is the gravity model calibration process?
Inputs - zonal trips production and attractions
- skim matrix
- observed trip length frequency distribution
Process:
- set initial values of a and b i deterrence function
- generate estimated matrix by solving Tij = ai x bj f(cij)
- compare observed and estimated average trip lengths
- go to step 1 until differences are small
What is matrix furnessing?
- Set all bj = 1 and calculated values for ai that satisfy trip production
- With the latest set of ai, calculate new values for bj that satisfy trip attraction/destination constraints
- With the latest set of bj, calculate new values for ai, repeating steps 2 and 3 until the changes are small
Converges to 3-5% of target value within a few iterations
