next up previous
Next: Generating Normally Distributed Random Numbers Up: EMME/2 NEWS 14 April 1993 Previous: INRO Announcements

Incremental Logit Demand Functions

Even though the variable demand auto assignment has been available since the introduction of Release 4 in May 1989, it is still not as widely applied in practice as one might expect. One reason for this might be that we normally associate the variable demand assignment with full fledged multi-modal demand models in which complex demand or modal choice functions are estimated from survey results and socio-economic zonal data. Such models are, of course, not available for all applications. However, variable demand assignments can also be very useful in applications for which no such full demand or mode choice model has been calibrated. In this article, we show how to use the variable demand assignment to implement an incremental (or pivot point) mode choice model without any need for socio-economic data, by simply using the observed base year demand and impedances.

Consider the following standard bimodal logit mode choice demand function


in which the auto demand tex2html_wrap_inline313 is expressed as a function of the total demand tex2html_wrap_inline315 , the auto and transit impedances tex2html_wrap_inline317 and tex2html_wrap_inline319 , and the combined effect of the socio-economic variables tex2html_wrap_inline321 . Besides estimating the coefficients tex2html_wrap_inline323 and tex2html_wrap_inline325 , the main effort in estimating a full demand model is spent selecting the significant socio-economic variables tex2html_wrap_inline327 and estimating their coefficients tex2html_wrap_inline329 .

Assume now that we know for the base year the (observed) demand tex2html_wrap_inline331 and tex2html_wrap_inline333 , as well as the corresponding network impedances tex2html_wrap_inline335 and tex2html_wrap_inline337 . This information can be used to estimate the unknown bias tex2html_wrap_inline339 , by inserting the base year values into the above equation and solving for tex2html_wrap_inline341 , which yields


These estimators can now be used to replace the combined effect of the socio-economic variables in the logit model. Doing so results in the following incremental mode choice function


If we assume that the total demand is constant, the formula can further be simplified to obtain


Since the above demand function uses for each O-D pair the base year data as pivot point, this model will, if applied to the base year network, reproduce exactly the base year data (a property which does not hold for full demand models). If any change in the network is applied, the model computes the change in the auto demand due to the induced mode shift.

The incremental model only needs the specification of the two sensitivity parameters tex2html_wrap_inline323 and tex2html_wrap_inline325 - a much easier task compared to the calibration of a full mode choice function. (Note that tex2html_wrap_inline325 is actually only needed if the considered scenario includes changes in the transit impedances.) Even if these coefficients are not known for a given application, it is possible to use values from model calibrated for similar areas or to test several values in the spirit of ``what if?'' games.

If any socio-economic variable tex2html_wrap_inline327 is also subject to change for the scenario to be studied (such as changes in the parking costs), this can easily be incorporated into the incremental model, by simply adding the term tex2html_wrap_inline357 to the argument of the exponential term.

For implementing this type of incremental logit function in a variable demand assignment, we need to define the corresponding EMME/2 auto demand function. In the simplest case, i.e. when considering changes in the auto network only and assuming fixed transit impedances, the following function can be used:

fa1 = (mat1+mat2)/(mat1+mat2*exp( tex2html_wrap_inline323 *(upqau-mat3)))*mat1

where mat1= tex2html_wrap_inline331 , mat2= tex2html_wrap_inline333 and mat3= tex2html_wrap_inline335 . Note that the multiplication with mat1 was coded at the end of the expression in order to avoid problems due to division by zero that otherwise occur for O-D pairs with zero total demand. The value sensitivity parameter tex2html_wrap_inline323 can either be coded directly into the demand function, or it can be stored in a scalar (where it can be modified without recoding the function) and accessed in the function via the ms() intrinsic.

If the scenario to be analyzed affects auto and transit impedances, the following function can be used:

fa2 = (mat1+mat2)/(mat1+mat2*exp( tex2html_wrap_inline323 *upqau+mat3))*mat1

where mat1= tex2html_wrap_inline331 , mat2= tex2html_wrap_inline333 and mat3= tex2html_wrap_inline375 (which is computed prior to the assignment with module 3.21). Of course it would also be possible to use mat3, mat4 and mat5 to represent explicitly tex2html_wrap_inline335 , tex2html_wrap_inline319 and tex2html_wrap_inline337 , but computationally this would be much less efficient. As can be seen from the above, incremental mode choice models can be implemented very easily if the base year data is available for an application, and -if carefully applied- provide important insight into expected mode shifts that are likely to result from the studied network interventions.

next up previous
Next: Generating Normally Distributed Random Numbers Up: EMME/2 NEWS 14 April 1993 Previous: INRO Announcements

Heinz Spiess, EMME/2 Support Center, Thu Jun 6 14:50:50 MET DST 1996