In Spiess (1993) the problem of modeling the intermediate destination choice for mixed mode trips (such as park&ride or kiss&ride) has been discussed as one example of a distribution model based on an activity chain. It was shown how such models, if based on a logit distribution, can be implemented efficiently by the use of simple algebraic matrix multiplications.
The purpose of this note is to focus on the intermediate destination choice for park&ride trips in particular, i.e. on modeling a logit type choice of a convenient parking lot. After a brief recapitulation of the model without parking capacities in section 2, the remainder of this note concentrates on the problem in the presence of explicit capacities at the parking lots and shows how this problem can be formulated and solved efficiently.
While we will refer to the model discussed here specifically as a ``park&ride'' model, it should be noted that the same model is of course also applicable to other kinds of mixed mode travel which impose some capacity constraints at the intermediate destinations. In particular, it can be applied to ferry choice models, such as the one used by the Washington State Ferries (see Dehghani and Gihring, 1995).
Parking choice model without capacities
In the absence of any parking capacity constraints a simple logit type parking lot choice model for park&ride trips is given by the following formula:
where 
is the number of trips between p and q choosing parking site k, according to the (properly weighted) mode specific travel impedances 
