transport modelling - visual transport modeller: distribution

visual transport modeller: distribution model

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What is a Distribution Model?

A distribution model produces a new origin-destination trip matrix to reflect new trips in the future made by population, employment and other demographic changes so as to reflect changes in people's choice of destination. They are used to forecast the origin-destination pattern of travel into the future and produce a trip matrix, which can be assigned in an assignment model or put into a mode choice model. The trip matrix can change as a result of improvements in the transport system or as a result of new developments, shops, offices etc and the distribution model seeks to model these effects so as to produce a new trip matrix for the future travel situation.

Visual transport modeller has a number of distribution model options:

Furness

The Furness procedure is used to make a trip matrix represent a future year. It does this by growthing-up the matrix to a set of forecast year trip ends. This forecast year trip matrix can be assigned to a network in the normal way so as to forecast the traffic on the network. To produce the forecast year trip matrix the software requires as input the file name of the base year trip matrix, the file name of the forecast year trip ends and the file name which is to hold the forecast year trip matrix.

The trip ends of a matrix comprise the row totals (which represent the number of trips which originate from a zone), and the column totals (which represent the number of trips destined for a zone). The number of trips originating from each zone and destined for each zone can be calculated for a future year (e.g. from the National trip end model) and applied to the base year trip matrix to produce a forecast year trip matrix.

The algorithm the software uses to produce the forecast year trip matrix starts by applying the growth to each origin of the base year trip matrix so as to match the forecast row totals. However this then gives a new matrix, which has new column totals that do not in general match the forecast column totals. The software then applies the growth to each column of the matrix in turn so as to match the forecast column totals. This then produces new row totals, which in general do not match the forecast ones. The process is iterated so that each successive iteration updates the base year trip matrix by factoring up each row and column in turn until both the rows and columns match the forecast row and column totals. Convergence is achieved when the row and columns change by only a few trips between each iteration which in practice is usually within about five or six iterations. If certain conditions are met (e.g. that there are no negative cells) then the theory shows that the procedure converges on a unique solution.

There are two major issues with the Furness procedure. The first is that if the base year matrix has zero trips coming from a zone or destined for a zone then no traffic can be forecast for that zone. This typically occurs where a zone has no development in it in the base year but which is developed in the future year. The second is where the base year matrix contains certain cells which are zero but which would have some trips in them. This can occur if the matrix is constructed from roadside (or on board public transport) interviews in which case certain cells of the matrix could have a zero estimated number of trips when in fact they could contain trips - it is just that the survey did not detect any. The common way round this is to seed the matrix with small value so as to give the Furness something to growth-up on.

Another problem with this is that the destination of the new trips is unrelated to the distance between the origin and destination zone when there is strong empirical evidence to show that the number of trips between origin and destination drops off as the distance between them increases. In addition when the transport links between a zone pair are improved then the evidence shows that some trips are diverted from one destination to the now more attractive destination using the improved transport link. Changes in the transport network should therefore be reflected in the distribution model.

An alternative distribution model, which incorporates this factor, is Gravity Modelling.

Gravity modelling

Click Distribution on the Models menu and select the Gravity Model option to display the Gravity Model form. Two runs are required to produce the output – a calibration run to produce the beta values followed by the actual forecast run. The table below indicates which files are required for which runs.

Distribution Models

Run Types, Required Files and Their Structure.

Text Box Label File Description File Format Header Data Format Required for Calibration Run Required for Forecast Run

Input Matrix Input Trip Matrix .csv No of Zones, No of Market Segments O, D, Trips1, Trips2, Trips3, etc. Yes No

Input Target Trip Ends Forecast Trip End File .txt No of Zones, No of Market Segments Zone Number, Origin TE1, Dest TE1, Origin TE2, Dest TE2, etc. No Yes

Base Year Cost Skim or Logsum Cost Skim Base Year .csv No of Zones, No of Market Segments O, D, Cost Mseg1, Cost Mseg2, etc. Yes Yes

Forecast Year Cost Skim or Logsum Cost Skim Future Year .csv No of Zones, No of Market Segments O, D, Cost Mseg1, Cost Mseg2, etc. No Optional

Switch Matrix File to specify which Distribution model type to use .csv No of Zones, No of Market Segments O, D, Model to use for MSeg1, Model to use for MSeg2, etc. Yes Yes

Indicator Matrix Beta Values to use for Synthesised output
1 = Use 1st Beta
2 = Use 2nd Beta etc. .csv No of Zones, No of Market Segments O, D, Beta to use MS1, Beta to use MS2, etc. Yes Yes

Cells To Calibrate Over Cells to calibrate beta over
1 = use 1st Beta
2 = use 2nd Beta etc. .csv No of zones, No of Market Segments O,D,Beta to use Yes Yes

Sector Pattern File Secpat file .par None Secpat.par No Optional

Output Trip Matrix Synthesised Output Matrix .csv No of Zones, No of Market Segments O, D, Trips1, Trips2, Trips3, etc. Yes Yes

Print File Log of model actions .txt Misc Misc Optional Optional

Input Coefficients File containing the calibrated beta values .pdo Standard PDC Header followed by No of Zones, No of Coefficients, No of Market Segments Beta No, Alpha Value, Beta Value Yes Yes

Output Coefficients File containing the calibrated beta values .pdo Standard PDC Header followed by No of Zones, No of Coefficients, No of Market Segments Beta No, Alpha Value, Beta Value Yes No

Input Row and Column balancing factors Output balancing factors from a previous run Optional Optional

Output Row and Column balancing factors Final set of balancing factors produced from this run Optional Optional

Of the eight files for the calibration run, six are inputs and two, the output trip matrix and output coefficients, are outputs. Ensure that the Calibrate Gravity Model option is selected. Put the required eight file names in the text boxes and click Go to do the Calibration run.

Having done the calibration run, the Output Coefficients file is put in to the forecast run as the Input Coefficients. Choose the Gravity Model Forecast option and the Input Target Trip Ends and Forecast Year Cost Skim or Logsum text boxes are revealed. Ensure that the required eight input files have been selected and an output matrix name entered and then click Go to do the Forecast run.

The Advanced button reveals optional files that may also be used. For calibration, these are a Print File and Input and Output Row and Column Balancing Factors. For Forecasting, the same three files are made available, and also a Secpat file.

The Print File contains details of what happened during the run. If no name is entered, it is still produced but with the default name of pdModelLogDistrib.dat and it will be in the Project's \System\Working directory.

Calibration Run

Forecast Run

The formulae for the distribution model are displayed below.

Equation 5.1: The Doubly constrained gravity distribution model Equation

T_ij = a_i * P_i * b_j * A_j * exp^{( - β Cij)}

a_i = (Summation of T_ij over all destination zones j)/P_i

b_j = (Summation of T_ij over all origin zones i)/A_j

Where

T_ij = the number of trips between origin zone i and destination zone j

C_ij = the composite utility of travel between zones i and j

P_i,A_j, = productions from zone i and attractions to zone j

a_i, b_j = balancing factors

beta = calibration coefficient

The C_ij is a measure of the separation between zones that represented all modes and the attributes of mode choice. This is similar to conventional generalised cost but was the composite utility expressed as the natural logarithm of the denominator of the mode choice model. This was output by the mode choice model as a composite utility matrix in a form suitable for the distribution model. The multinomial logit model was the model form used because it has been found to represent the decision making process reasonably well and is computationally reasonably efficient. It is given by equation 5.2.

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