Within-Day/Supply

The within-day/supply model can be viewed as the heart of SimMobility’s mid-term model. Here the daily activity schedule is carried out in the network.

The model takes in the attributes of the city’s road network and public trans-portation system, and upon them simulates the movement of vehicles. The attributes of the road segments include: directionality, number of lanes, capacity, and free-flow speed. For the public transportation system, the attributes include: routes, stop locations, frequency, vehicle capacity, and dwell time models.

Time progress through discreet time ticks, usually set to 5-second intervals. As time progresses, individuals are loaded into the network making trips in accordance with their activity schedule. When car trips are made, the vehicles are loaded into the network based on the individual’s stating point. When public transportation trips are made, individuals walk to the nearest transit stop, wait for the appropriate vehicle to pick them up, and board that vehicle if it indeed has the remaining capacity. When on-demand services are called, the individual waits at their origin node for a vehicle to pick them up. Walking is computed based on assigned average walking speed, multiplied by walking distance.

At the end of the simulation, SimMobility releases several output files that record the attributes of the movements throughout the day. These attributes include:

∙ Individual movements: start/end time, start/end node, mode, movement with-in/outside the CBDm waiting time

∙ Vehicle movement by trip: travel time, travel distance, vehicle powertrain, en-ergy consumed for the trip

∙ Link attributes: congestion level and flow speed by time of day

The inter-zonal travel times by mode and by time of day are then computed based on individuals’ actual experienced travel time. These computed travel times are then

be used multiple times until a certain convergence criteria as defined by the user is obtained.

4.2 Activity-Based Accessibility

Activity-based accessibility (ABA) is defined as the value for the individual from carrying out their daily activity schedule, expressed in terms of time or money. This measure of accessibility was developed in the ITS Lab by Dong et al. [2006], and was defined as:

Our method for computing ABA has been somewhat simplified, and had made the following assumptions:

∙ We use the base strategy and scenario for scaling ABA (the strategy that ap-pears in the denominator). The value 𝐴𝑐𝑐^𝑏_𝑖, or maximum expected utility from carrying out the activity schedule, also known as Daily Pattern Binary (DPB), is computed in its regular form under the base condition and computed again with a change in 𝑥 (or ∆𝑥).

∙ The appearance of 𝐴𝑐𝑐^𝑏_𝑖 in the numerator is replaced with 𝐴𝑐𝑐^𝑤_𝑖 , the expected maximum utility from carrying out all possible daily activity schedules when the only mode available is walking. This situation, which emulates a pre-industrial revolution world, allows us to quantify the benefits of any transportation system which provides additional modes other than walking. The difference between 𝐴𝑐𝑐^𝑎_𝑖 and 𝐴𝑐𝑐^𝑤_𝑖 becomes the benefit for the individual from putting a trans-portation network into place, or the benefit from having additional modes other than walking (walking representing the human natural state).

The reason this "policy" (of no motorized transport whatsoever) is not used in the denominator as well, is that this creates a situation of individuals who cannot access any zones at all, and whose expected maximum utility (𝐴𝑐𝑐^𝑤_𝑖 ) is 0. When 𝐴𝑐𝑐^𝑤_𝑖 is zero, the denominator is also 0, and 𝐴𝐵𝐴𝑖 goes to infinity.

Hence we choose to use a scaling factor that will scale more moderately and realistically.

∙ We use 2 forms for ∆𝑥: time and a monetary value. When ∆𝑥 represents change in time, it is replaced with 1 minute of travel time. When ∆𝑥 represents monetary value, it is replaced with 1 dollar of travel cost.

The addition of 1 minute of travel is applied to all modes. For modes which have different segments of travel, this additional minute is split proportionally among the expected travel time of each segment of travel. An example for this is when an individual uses public transportation: we compute their travel time as being made up of three segments: walking (access and egress to PT), waiting time, and in-vehicle time. Since these three segments of travel entail different levels of disutility, the additional minute is split between the segments of travel, so the effect of travel time on overall utility in each mode remains linear.

The additional dollar in travel cost is given to all modes except walk, which is free. All modes are assumed to have a single fare, even if multiple mechanized means are used.

For additional information on how travel time and travel cost were altered for the ABA computation, see the appendix, Appendix A.1.3.

From the assumptions, we get the following definition of ABA:

𝐴𝐵𝐴_𝑖 = (𝐴𝑐𝑐^𝑎_𝑖 − 𝐴𝑐𝑐^𝑤_𝑖 ) ∆𝑥

⃒

⃒

⃒𝐴𝑐𝑐^𝑏(Δ𝑥)_𝑖 − 𝐴𝑐𝑐^𝑏_𝑖⃒

⃒

⃒

(4.2)

Where:

𝐴𝑐𝑐^𝑎_𝑖 DPB for individual 𝑖 when strategy 𝑎 is in place.

𝐴𝑐𝑐^𝑤_𝑖 DPB for individual 𝑖 when only walking is available.

𝐴𝑐𝑐^𝑏_𝑖 DPB for individual 𝑖 under the base strategy and scenario.

From here on we refer to ABA computed with an increase in one minute in travel time as "ABA-time" and as ABA computed with an increase in one dollar in travel cost as "ABA-cost".