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The endogenous inclusion of modal choice allows energy system models to determine the optimal pathway towards a policy target as a combination of technological and fuel switching, efficiency improvement and modal shifting, without relying on external assumptions on modal shares. Transport simulation models such as LTM (Rich et al., 2010) have traditionally addressed modal choice using a 4-step model structure, including trip generation, trip distribution, mode choice and route assignment. In the third step, modal shares are normally computed via MNL or NMNL models using a large number of attributes describing the level of service of the alternative modes and the socio-economic composition of the population. Such an approach has some limitations: firstly, there is a need to conduct travel surveys to calibrate the model parameters (normally by means of log likelihood estimation). Secondly, the methodology is limited to simulation models – the logit model

structure based on exponential functions cannot be implemented in the linear optimization models commonly used for energy system analysis.

Modal choice proves to be a relevant behavioural feature to be included in ‘E+T’ models, being present in 12 out of the 14 models analysed. One of the main variables driving modal choice is travel time. Thus, an ongoing tendency to emphasize time importance in mode selection is that of

including a constraint on the total travel time of the system: four of the models reviewed set a limit to the overall travel time within the linear optimization program. The main approaches identified for the representation of modal choice are: (i) Travel Time Budget (TTB), (ii) discrete choice models and (iii) constant elasticities of substitution.

5.4.3.1 Travel Time Budget (TTB)

The rationale behind the adoption of the concept of travel time budget (TTB) has been provided by Schäfer and Victor (2000), who claim that across different societies, geographical areas and income classes, people spend roughly the same amount of time per day travelling. Ahmed and Stopher (2014) provide an updated review of TTB studies, reporting a universal range for the TTB, equal to 60-90 minutes per person per day.

Models including the concept of TTB require changing the model structure to incorporate the parameter of speed, specified for every mode, eventually for every trip distance, and, within the optimization program, an upper bound on time consumption is set equal to the TTB.

Daly et al. (2014) apply the TTB concept to the TIMES models of Ireland and of California. This study aggregates all the mode-specific travel demands into a few “trans-modal” demand segments to allow a shift between modes, and subsequently uses a TTB to enable competition between fast but expensive technologies and cheap but slow technologies. With such a modelling approach, the optimal solution is not just the one that minimizes total system cost, but it also guarantees that the total system travel time does not exceed the TTB. The approach based on the TTB can be

complemented by the concept of travel time investment (TTI), a proxy variable simulating the relationship between modal speed and infrastructure investment. Once TTI is incorporated in the model, it is possible to assess the influence of investing in the infrastructure of a certain mode on the market share of that mode. For instance, in Daly et al. (2014), TTI is used so that the model can invest endogenously in the infrastructure of modes, hence increasing their speed and reducing the travel time. Even if the model results shown by Daly et al. (2014) are sensitive to TTI, the use of this variable requires being refined. With the cost of TTI being critical to the determination of the modal

shares, additional efforts should be directed at determining a rigorous methodology to calibrate this variable. Determining a mode-specific stepwise cost curve, which includes speed reduction

potentials from several infrastructure investments at different costs, could be a promising but also time-intensive approach.

Pye and Daly (2015) overcome some of the limitations and challenges of the TTI in the bottom-up optimization model ESME. They incorporate the approach by Daly et al. (2014), with some

differences and they restrict the study to urban passenger transport and to trips shorter than 55 km. Two new constraints are introduced to better represent modal choice: the maximum level of modal shift potential and the rate of modal shift for each mode, which are determined by considering the historic trip distance profiles. Moreover, an adjustment factor on the TTB (equal to 0.95

hours/person/day) is used so that average urban speeds do not have to increase despite increasing demand. An important distinction from Daly et al. (2014) is that infrastructure is still considered, but only restricted to its cost, to give a more comprehensive picture of the cost of the modes.

Infrastructure investments do not lead to improvements in travel time associated with different modes. However, the model must ensure that the sum of existing and new infrastructure is enough to accommodate the demand of mobility.

In the CGE model IMACLIM-R (Waisman et al., 2013) households derive utility from the consumption of goods and from the use of mobility services provided by four main transport modes (air, road, public and non-motorized). The value of the utility function is maximized, while subjected to two constraints:

i. A standard budget constraint, which trades-off between transport-related expenditures and consumption of other goods.

ii. A time budget constraint (TTB), which restricts the demand for transportation services purchased by households, considering that the speed of each mode is associated with the utilization rate of that mode (i.e. congestion effect). The induction effect of infrastructure deployment on mobility demand (TTI) is therefore addressed: an expansion of the

infrastructure network makes modes faster, allowing households to travel more with equal time budget.

The main advantage of the TTB method lies in not requiring additional data but simply in introducing a general constraint to the problem. The concept of TTB has been criticized since it conflicts with

utility maximization, or with the principle that travel is a derived demand. Additionally, it has been argued that TTB is constant at an aggregate level while large differences may emerge as soon as one starts disaggregating populations in demographics, travel types and different spatial areas

(Mokhtarian and Chen, 2004).

5.4.3.2 Discrete Choice Models

Within the 12 models reviewed which features modal choice representation, four adopt a discrete choice model to predict the choice probabilities of the different transport modes on the basis of travel time and travel cost, with GCAM (Kyle and Kim, 2011) accounting only for travel cost. In the hybrid model CIMS (Horne et al., 2005), an MNL model has been built from surveys in which

respondents were asked to select among five modes (driving alone, carpooling, taking public transit, using a park and ride service, and walking or cycling), defined by the attribute travel time, cost, pick- up/drop-off time, walking/waiting time, number of transfers and bike route access. Survey data has been translated into parameters of the utility functions, used in CIMS through Equation 5.4.

In the bottom-up simulation model TRAVEL, an NMNL model calculates the mode shares based on a mode cost 𝐶𝑜𝑠𝑡𝑟,𝑚,𝑡 (for every region 𝑟, mode 𝑚 and time 𝑡), where both travel cost and travel time are included:

𝐶𝑜𝑠𝑡_{𝑟,𝑚,𝑡} = 𝑘_{𝑟,𝑚,𝑡}× 𝐶𝑜𝑠𝑡𝑃𝑒𝑟𝐾𝑚_{𝑟,𝑚,𝑡}+ 𝑇𝑖𝑚𝑒𝑊𝑒𝑖𝑔ℎ𝑡_{𝑟,𝑚,𝑡} × 𝑇𝑖𝑚𝑒𝑈𝑠𝑒_{𝑟,𝑚,𝑡} (5.5) Equation 5.5 presents two balancing parameters: 𝑘𝑟,𝑚,𝑡 is an adjustment factor for non-monetary differences in the total cost of different modes while 𝑇𝑖𝑚𝑒𝑊𝑒𝑖𝑔ℎ𝑡_{𝑟,𝑚,𝑡} describes the relative importance of time and cost. This factor is endogenous to the model: if the total travel time per capita exceeds the TTB (assumed equal to 1.2 hours/person/day), the time factor 𝑇𝑖𝑚𝑒𝑈𝑠𝑒𝑟,𝑚,𝑡 is awarded a greater weighting (Girod et al., 2012).

In the model MESSAGE-TRANSPORT (McCollum et al., 2016), mode switching decisions are taken via a logit-based algorithm. The passenger travel demand projections split by mode are endogenously determined as the product of the total regional travel demand by the modal share for each mode, region and time, through MNL probabilities. These are expressed as the sum of fuel price, non-fuel price and a time element.

Advantages and disadvantages of discrete choice models in representing modal choice are the same as those for including technology choice previously discussed. In particular, it is interesting to notice that the concept of TTB can be easily integrated in this methodology, as e.g. in the model TRAVEL (Girod et al., 2012).

5.4.3.3 Constant elasticities of substitution

As with technology choice, modal choice can be modelled through CES. Examples of models using such an approach are EPPA (Karplus et al., 2013), PRIMES-TREMOVE (E3MLab/ICCS, 2014) and ReMIND (Pietzcker et al., 2010). In the latter study, the different transport modes are formulated in a nested CES structure, while at the lowest level of the tree diagram the technologies in each transport mode are represented with linear production functions. CES functions first regulate the substitution between freight and passenger transport, then between on-land, maritime and aviation, and finally between rail, truck, urban cars, intercity cars and bus. This nested structure was

developed according to the level of linkage of the transport services and the ease of mode

replacement. The model UKTCM (Brand et al., 2012) endogenously determines modal shares using elasticities: modal choice is modelled by linking through dynamic elasticities travel demand for each mode to vehicle ownership and operating costs, as well as to GDP and number of households. As previously discussed, the CES methodology can be best applied within a top-down framework and the values for the CES functions are typically estimated.