Modal Split Model

Modal split models aim to determine the number of trips on different modes given the travel demand between different pairs of nodes (zones). These models try to mathematically describe the mode choice phase of the sequential demand analysis procedure. Generally choice models are used for modal split analysis. That is, it is assumed that the probability of choosing a particular mode is the probability that the perceived utility from that mode is greater than the perceived utility from each of the other available modes. Since, choice models were discussed while presenting destination choice models in the section on trip distribution they are not repeated here. This section only discusses the factors which are generally assumed to affect the perceived utility of modes. An example problem is also solved.

The factors which affect the choice of a mode (and hence the perceived utility from a mode) are:

• Socio-economic factors like income, automobile ownership, age, etc.
• Service-related factors like in-vehicle travel time, access to public transport (or transit systems), frequency of transit system operation, out-of-pocket cost, etc.

Example

For a particular zone pair, three modes of travel between the zones exist -- private transport like automobiles (PT), bus (B), and urban rapid transit system like local trains (RT). It is given that all trip makers have access to private transport and that the perceived utility of a mode, $m$, $v(m)$ is given by

$$v(m) = - 0.004t_m - 0.005c_m - 0.003w_m + 0.15d_m$$

where, $t_m$ is the in-vehicle travel time in minutes for mode $m$, $c_m$ is the out-of-pocket cost in rupees for mode $m$, $w_m$ is the waiting time in minutes for mode $m$, and $d_m$ is a dummy variable which is 1 when the mode is private transport, 0 otherwise. Assuming that the variable values are as shown in Table  and that 1000 trips are made from the origin zone to the destination zone determine the number of trips made by the different modes. Use Logit model.

表: Variable values used in the example under modal split models.

Mode	Variable values
	$t_m$ (mins.)	$c_m$ (Rs.)	$w_m$ (mins)	$d_m$
PT	65	60	0	1
B	75	5	5	0
RT	25	8	20	0

Solution

First, calculate the perceived utility for each mode:

$$v(PT) = -0.004 \times 65 - 0.005 \times 60 - 0.003 \times 0 + 0.15 = -0.41$$

$$v(B) = -0.004 \times 75 - 0.005 \times 5 - 0.003 \times 5 = -0.34$$

$$v(RT) = -0.004 \times 25 - 0.005 \times 8 - 0.003 \times 20 = -0.20$$

Next, use Logit model to determine the probability, $\pi_m$ that a particular mode, $m$, will be chosen.

$$\pi_{PT} = \frac{e^{-0.41}}{e^{-0.41}+ e^{-0.34} + e^{-0.20}} = 0.302$$

$$\pi_{B} = \frac{e^{-0.34}}{e^{-0.41}+ e^{-0.34} + e^{-0.20}} = 0.324$$

$$\pi_{RT} = \frac{e^{-0.20}}{e^{-0.41}+ e^{-0.34} + e^{-0.20}} = 0.374$$

Hence, 302 trips will be made using private transport, 324 will use buses, and 374 will use the rapid transit system.