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Envisioning an emission diet: application of travel demand mechanisms to facilitate policy decision making

Abstract

Emission reduction strategies are gaining attention as planning agencies work towards adherence to air quality conformity standards. Policymakers struggling to reduce greenhouse gases (GHG) must grapple with a growing number of travel demand policies. To consider any of these emerging demand mechanisms as a viable option to meet emission targets, planners and policymakers need tools to better understand the implications of such policies on travel behavior. In this paper we present an integrated multimodal travel demand and emission model of four policy strategies; presenting GHG and air pollutant reduction results at a very detailed level. Multiple policy outcomes are compared within a single modeling framework and study area. The results reveal that while no one demand mechanism is likely to reduce emissions to a level that meets policy-maker’s goals; a first-best pricing strategy that incorporates marginal social costs is the most effective emission reduction mechanism. Implementing such a mechanism may offer total emission reductions of up to 24 %. However, the efficacy of this strategy must be weighed against difficulties of establishing efficient pricing, a costly implementation, and substantial negative impacts to non-highway facilities. Decision makers must select a mixture of pricing and land use strategies to achieve emission goals on all road facilities.

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Abbreviations

C 1 :

The average commute cost from the commute optimization operation

C 1 :

Average commute before optimization

C 2 :

Average commute cost after optimization

C a :

The capacity for link a

C excess :

The excess commute derived from commute optimization

\(D_{ij}^{k}\) :

Various distance terms (linear, log, squared, cubed and square root)

e a :

Emission price

\(f_{ij}^{r}\) :

Flow on path r, connecting each origin–destination (O–D) pair (ij)

l a :

Distance for link a

q ij :

Demand between each origin–destination (O–D) pair (ij)

t a :

Travel time for link a

t a (x a ):

Travel cost on link a as a function of flow

t ij :

Travel cost between origin i and destination j

\(u_{a}^{I} \left( {x_{a} ,e_{a} ,} \right)\) :

Travel time function for Model-1 which incorporates emission pricing term e a

\(u_{a}^{II} \left( {x_{a} ,\theta_{a} ,} \right)\) :

Travel time function for Model-1 which incorporates VMT tax term θ a

\(u_{a}^{III} \left( {x_{a} ,\sigma } \right)\) :

Travel time function for Model-1 which incorporates gas tax term σ

u a :

User cost for link a

\(u_{ij}^{c}\) :

Least cost path between O–D pairs i–j

x a :

Flow for link a

α a :

Constant, varying by facility type (BPR function)

β a :

Constant, varying by facility type (BPR function)

β k :

Weights for each term in the size variable (S j )

γ c :

Value of time (VOT) for user class c

\(\delta_{a,ij}^{r}\) :

Flow on link a, a subset of path r, connecting each origin–destination (O–D) pair (ij)

τ a :

Toll value for link a

Φ a :

Emissions cap for each link a

ϕ a :

Total emissions for link a

c :

User class

d ij :

The number of commuter trips between i and j

n :

Assignment iteration number

T :

The total number of commuters

t o :

Free flow time on link a

φ :

Emissions charge per gram of emissions, in cents

ω :

A positive constant (exponential demand function)

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Correspondence to Timothy F. Welch.

Appendix

Appendix

Base-case

This principle is based on the fact that individuals choose a route in order to minimize their travel time or travel cost and such a behavior on the individual level creates an equilibrium at the system (or network) level over a long period of time (Sheffi 1985). Simply, for each origin–destination (O–D) demand pair, the travel-cost/travel-time on all used routes of the road network should be equal.

$$Minimize \mathop \sum \limits_{a} \mathop{\int}\limits_{0}^{{x_{a} }} \left( {t_{a} (x_{a} )} \right)$$
(1)

Subject to:

$$\mathop \sum \limits_{r} f_{ij}^{r} = q_{ij}$$
(2)
$$x_{a} = \mathop \sum \limits_{i} \mathop \sum \limits_{j} \mathop \sum \limits_{r} f_{ij}^{r} \delta_{a,ij}^{r}$$
(3)
$$f_{ij}^{r} ,q_{ij}^{r} \ge 0$$
(4)

Equation (1) represents that at equilibrium the network will satisfy the UE condition, i.e. travel time on all the used routes connecting any given i-j pair will be equal. The term, t a , is the travel time for link a, which is a function of link flow x a . Equation (2) is a flow conservation constraint to ensure that flow on all paths r, connecting each O–D pair (ij) is equal to the corresponding demand. In other words, all O–D trips must be assigned to the network. Equation (3) represents the definitional relationship of link flow from path flows. Equation (4) is a non-negativity constraint for flow and demand. The travel time function t a (.) is specific to a given link ‘a’ and the most widely used model is the Bureau of Public Roads function given by

$$t_{a} \left( {x_{a} } \right) = t_{o} \left( {1 + \alpha_{a} \left( {\frac{{x_{a} }}{{C_{a} }}} \right)} \right)^{{\beta_{a} }}$$
(5)

where to(.) is free flow time on link ‘a’, and α a and β a are constants (and vary by facility type). C a is the capacity for link a. In the base model the objective is minimization of TST.

First-best emission pricing

The emissions cap for each link is:

$$\Phi_{a} = \left[ {\frac{1}{N}\mathop \sum \limits_{a = 1}^{N} \left( {\frac{{\phi_{a} }}{{l_{a} }}} \right)} \right]*l_{a}$$
(6)

where ϕ a is the total emissions for link a calculated for each link in the base model and l a is the link distance. Once the cap is determined, the emission price (e a ) can be incorporated into the travel demand model. The emission price can be converted to travel time units with appropriate factor (γ c) representing VOT in monetary terms as cents per minute for travellers of five income categories c. The revised user cost function for link based emission is

$$u_{a}^{I} \left( {x_{a} ,e_{a} } \right) = t_{a} \left( {x_{a} } \right) + \frac{{\varphi e_{a} \left( {x_{a} } \right)}}{{\gamma^{c} }}$$
(7)

where \(u_{a}^{I} \left( {x_{a} ,e_{a} ,} \right)\) is the travel cost function for Model-1, which incorporates emission pricing term e a . The objective function for Model-1 is similar to base case with the exception that the third term from Eq. (7) \((\frac{{\varphi e_{a} \left( {x_{a} } \right)}}{{\gamma^{c} }})\) is added to Eq. (1) which is the total emissions e produced on link a, which is a function of link flow x a multiplied by charge per gram of emissions, φ.

Second-best emission pricing (VMT Tax)

Analytically, the user cost function can be stated as the following to incorporate the VMT based tax.

$$u_{a}^{II} \left( {x_{a} ,\theta_{a} } \right) = t_{a} \left( {x_{a} } \right) + \frac{{\theta_{a} l_{a} }}{{\gamma^{c} }}$$
(8)

where, θ a is the VMT tax in $/mile for link a, l a is the link length in miles, and γ c is the VOT in $/hour. In traffic assignment procedure, the user cost shown in Eq. (8) can be used in Eq. (1). The advantage of VMT based tax is to encourage travelers to use transit as an alternate mode if the tax appears too onerous. Equation (8) refers to VMT based tax associated with value of time (VOT).

Gas tax

The effect of gas price on user behavior can be implemented as follows:

$$u_{a}^{III} \left( {x_{a} ,\sigma } \right) = t_{a} \left( {x_{a} } \right) + \frac{{\sigma l_{a} }}{{\gamma^{c} \vartheta }}$$
(9)

where σ is the gas price in dollars per mile (as a ration of dollars per gallon and fleet-wide efficiency of 24.5 mpg), l a is the link length in miles, γ c is the VOT in $/hr, and ϑ is the automobile gasoline efficiency in miles per gallon. Auto Operating Cost (AOC) is another component which is considered in the mode choice model. A higher gas price will result in a higher AOC and therefore will make auto travel more expensive.

Commute efficiency

$$\mathop {Minimize}\limits_{{}} \mathop \sum \limits_{i} \mathop \sum \limits_{j} u_{ij} d_{ij}$$
(10)

where u ij  = t ij and t ij is the travel cost between origin i and destination j and d ij is the number of commuter trips between i and j. The constraints for the optimization problem are subject to

$$\mathop \sum \limits_{j} d_{ij} = O_{i}$$
(11)
$$\mathop \sum \limits_{i} d_{ij} = D_{j}$$
(12)
$$d_{ij} \ge 0$$
(13)

The average commute cost from the optimization can be interpreted as

$$C_{1} = \frac{1}{T}\mathop \sum \limits_{i} \mathop \sum \limits_{j} u_{ij} d_{ij}^{o}$$
(14)

where T is the total number of commuters, and \(d_{ij}^{o}\) is the optimal number of commuters between ij pair. Before optimization, the average commuter cost was:

$$C_{2} = \frac{1}{T}\mathop \sum \limits_{i} \mathop \sum \limits_{j} u_{ij} d_{ij}^{{}}$$
(15)

The excess commute can be defined as the percentage difference between cost before and after optimization. This can be represented as

$$C_{excess} = \frac{{\left( {C_{2} - C_{1} } \right)*100}}{{C_{1} }}$$
(16)

The excess commute can be considered as a dis-benefit from the planner’s viewpoint.

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Welch, T.F., Mishra, S. Envisioning an emission diet: application of travel demand mechanisms to facilitate policy decision making. Transportation 41, 611–631 (2014). https://doi.org/10.1007/s11116-013-9511-4

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Keywords

  • Emission reduction
  • Greenhouse gas
  • Multimodal travel demand
  • Pricing