Value of Time Handling

The ABM represents Value of Time in both the travel model (trip/tour making) and in traffic assignment. The tour/trip making component breaks value of time out by income resulting in the following mean values of time:

• Household Income $0-$30k = $6.01/hr ($2010)
• Household Income $30-$60k = $8.81/hr ($2010)
• Household Income $60-$100k = $10.44/hr ($2010)
• Household Income >$100k = $12.86/hr ($2010)

These values and additional value of time related controls are found in the properties configuration file

A key aspect of implementation of value of time in the ABM is that the ABM assigns a unique value of time to each household based on a lognormal distribution. The above values are the mean values of time by income category. The following describes how value of time is assigned for each household, noting that a minimum value ($1/hr) and a maximum value of time ($50/hr) are also inputs that have been set.

The version of the SANDAG model from which the ABM was transferred uses a distributed value of time. The value of time is drawn from a set of lognormal distributions by income with mean values of time for each income group according to the values above in the properties file. There are four income groups with breakpoints as defined (the last income group breakpoint isn’t defined explicitly). The formula for a lognormal distribution is as follows:

fx(x;μ,σ)=1/(xσ√2π) e^(-〖ln⁡(x-μ)〗^2/〖2σ〗^2 ), x>0

Where: X = a log-normally distributed variable μ = the lognormal distribution location parameter; specifically, the mean of ln(x)[1] σ = the lognormal distribution scale parameter; specifically, the standard deviation of ln(x)[2]

The location parameter μ can be calculated by the following formula, where m is the non-logarithmic mean and v is the non-logarithmic variance of the distribution:

μ=ln(m/√(1+v/m^2 ))

The scale parameter σ can be calculated by the following formula:

σ=√(ln(1+ v/m^2 ) )

In this case mu is re-calculated as mean income * a multiplier for mu as defined below. So the code that creates the lognormal distribution looks like this:

double mu = Math.log(meanValueOfTime[i] * meanValueOfTimeMultiplierBeforeLogForMu);
valueOfTimeDistribution[i] = new LognormalDist(mu, valueOfTimeLognormalSigma); 

The value of time is set at the household level and everyone in the household gets the same VOT (could be improved as a future enhancement) except for persons under 18 which get a multiplier to generate a lower VOT (higher cost sensitivity) for them. The value of time is capped and there is a minimum value as well as per the properties link above, expressed in dollars per hour.

Then in mode choice the cost coefficient is calculated based on the in-vehicle time coefficient (in utiles/cent) and the value of time (in dollars/hour). Divide VOT by 60 to convert to dollars/minute, multiply by 100 to convert to cents/minute. Divide in-vehicle time coefficient by converted VOT to calculate the cost coefficient; (0.6*c_ivt)/vot. This calculation is done in the tour and trip mode choice UECs.

Value of Time from the assignment aspect of the ABM much less complex since it uses an aggregate equilibrium assignment algorithm in which a single global representations of value of time is applied to all travelers (segmented by auto and truck). Additional context on how value of time is set in traffic assignment can be found here.