Evaluating the Efficiency of Traffic Mitigation Fees
at the San Pedro Bay Ports in a
Congestion- Pricing Framework
Draft Final Report
METRANS Project 06- 07
June, 2007
Seiji S. C. Steimetz, Principal Investigator
Otto Chan
Agnes Ng
Sean Fergus
Department of Economics
California State University at Long Beach
i
Disclaimer
The contents of this report reflect the views of the authors, who are responsible for the
facts and the accuracy of the information presented herein. The document is
disseminated under the sponsorship of the Department of Transportation, University
Transportation Centers Program, and California Department of Transportation in the
interest of information exchange. The U. S. Government and California Department of
Transportation assume no liability for the contents or use thereof. The contents do not
necessarily reflect the official views or policies of the State of California or the
Department of Transportation. This report does not constitute a standard, specification,
or regulation.
ii
Abstract
This study develops an empirical framework for estimating a peak- period truck toll
designed to efficiently balance peak and off- peak truck traffic on the highway system
surrounding the San Pedro Bay port complex and at its terminal gates. Like the current
OffPeak program’s Traffic Mitigation Fee ( TMF), this congestion- pricing mechanism
operates under the constraints that a toll cannot be assessed during off- peak gate hours,
and that the toll is uniform across the peak period. Unlike the TMF, however, the toll
applies to all truck trips rather than only to a limited class of gate moves. The distinction
is drawn because the toll is aimed at correcting truck- generated congestion externalities,
and all port- bound truck trips generate congestion externalities regardless of purpose.
Methods for obtaining these cost estimates are also developed in this study and applied to
data on highway and terminal- gate traffic conditions.
Estimation results imply a peak- period truck toll of $ 18.25 per roundtrip, which is
expected to generate annual revenues of roughly $ 14 million at current trip volumes.
These revenues are comparable to current off- peak gate costs, suggesting that the
efficiency objectives of economic policymakers and cost- recovery objectives of marine
terminal operators can be simultaneously achieved.
The results also suggest that the external costs generated by trucks on the highway
network enveloping the ports dominate those generated at their terminal gates, motivating
a more holistic public discussion of truck congestion at the ports.
The $ 18.25 toll applied to all peak- period truck trips is small in comparison to the current
TMF of $ 50 per twenty- foot- equivalent container moved. A possible implication is that
the burden of relieving congestion and financing off- peak terminal operations can be
spread across a broader class of trip purposes while still adhering to efficiency and cost-recovery
concerns.
iii
Table of Contents
1. Introduction 8
2. Congestion- Pricing Framework 10
2.1 Congestion Tolls 10
2.2 Congestion Tolls with an Untolled Alternative 12
3. Congestion- Externality Framework 15
3.1 Bottleneck Model of Trip Delays 15
3.2 Accommodating Mixed Traffic 16
3.3 Value of Time 17
3.4 Passenger- Car Equivalents 18
3.5 Summary of Truck Congestion- Externality Measurement 19
4. Empirical Setting and Estimation 20
4.1 Empirical Setting and Estimation Overview 20
4.2 Highway External Cost Estimation 22
4.3 Time- Averaged Highway Externalities 28
4.4 Roundtrip Route Externalities 29
4.5 Route- Averaged Externalities 31
4.6 Terminal- Gate Externalities 33
5. Peak- Period Truck Tolls 36
6. Discussion Points 37
6.1 Levying Tolls on All Truck Trips 37
6.2 Congestion Externalities on Surrounding Highways 37
6.3 Revenue Requirements 38
6.4 Caveats 38
7. Summary 39
Bibliography 41
iv
Index of Tables and Figures
Tables
Table 1
Passenger- Vehicle Value of Time Estimates
18
Table 2
Commercial Value of Time Estimates
18
Table 3
Commercial Truck Passenger Car Equivalent Estimates
19
Table 4
Key Parameters for External Congestion Cost Estimates
19
Table 5
Inbound and Outbound Truck Routes
21
Table 6
Terminal Trip Travel- Time Intervals
22
Table 7
Average Travel Time Estimation Results for Northbound Interstate 110
24
Table 8
Truck- Generated External Congestion Cost Estimates by Highway Segment and Travel-
Time Interval
27
Table 9
Estimated Share of Terminal Truck Trips Taken During Each Travel- Time Interval
28
Table 10
Weighted Average of Truck- Generated External Costs Across Travel- Time Intervals by
Highway
29
Table 11
Truck- Generated External Costs on Inbound Routes
30
Table 12
Truck- Generated External Costs on Outbound Routes
30
Table 13
Combined Truck- Generated External Costs on Inbound and Outbound Routes
31
Table 14
Shares of Peak- Period Terminal Trips by Route
32
Table 15
Weighted- Average of External Costs Across Routes
32
Table 16
Peak- Period Terminal- Gate Truck Waiting Times and Arrival Rates by Time of Day
34
Table 17
Estimation Results for Truck Waiting Times at Terminal Gates
35
Table 18
Terminal- Gate External Costs by Peak- Period Travel- Time Interval
36
Table 19
Summary of Roundtrip External Cost Estimates
36
v
Figures
Figure 1
Aerial View of Surrounding Highway System and Truck Routes Considered
21
Figure 2
Aerial View of Interstate 110 Segment Leading to the Port of Los Angeles
23
Figure 3
Predicted and Actual Travel Times by Time of Day
25
Figure 4
Terminal- Gate Waiting Times and Truck Arrival Rates by Time of Day
34
Figure 5
Predicted and Actual Terminal- Gate Waiting Times by Time of Day
35
vi
Disclosure
This project was funded in its entirety under contract with the California Department of
Transportation.
vii
Acknowledgements
The project director gratefully acknowledges the outstanding research assistance
provided by project team members, Agnes Ng, Otto Chan, and Sean Fergus. The project
team also thanks Kenneth Small and Erik Verhoef for providing an advanced copy of
their most excellent text: “ Urban Transportation Economics”, and participants of the
METRANS 2007 National Urban Freight Conference for helpful comments and
suggestions. None of these people are responsible for any errors or omissions in this
report.
8
1. Introduction
In 2002, responding to growing concerns about truck queuing at marine terminal
gates and the resulting concentration of diesel emissions, the California State Assembly
passed Assembly Bill 2650 ( AB 2650). The bill offered terminal operators at the Los
Angeles and Long Beach ports a choice between two ways to reduce truck queuing: ( 1)
extending gate hours from 40 to at least 70 hours per week or ( 2) implementing a
terminal- gate appointment system. The bill also imposed a fine on operators of $ 250 for
each truck idling at their gates for more than 30 minutes. Terminal operators initially
opted for an appointment system. 1 Meanwhile, cargo movement at the ports continued to
grow dramatically, as did concerns about port capacity and traffic congestion on
surrounding freeways. This prompted the introduction of Assembly Bill ( AB 2041),
which mandated extended gate hours. Under the pressure of this proposed legislation, the
terminal operators formed a consortium known as “ PierPass” to implement the “ OffPeak”
program, which established a voluntary extension of full- service operations at all twelve
of the ports’ international container terminals. 2
The OffPeak program began in July 2005 and now divides gate operations into
peak and off- peak hours. Peak hours are Monday through Friday from 3: 00 a. m. to 6: 00
p. m.; off- peak hours are Monday through Thursday from 6: 00 p. m. to 3: 00 a. m., and
Saturday from 8: 00 a. m. to 6: 00 p. m. Allowing cargo movement during off- peak hours,
when the roads surrounding the port complex are relatively clear, offers the promise of
improving traffic conditions and air quality around the ports. A “ Traffic Mitigation Fee”
( TMF) is assessed on certain types of loaded containers entering or exiting marine
terminal gates by road during peak gate hours, with fee revenues earmarked to cover
increases in off- peak terminal operating costs. PierPass collects these fees from shippers
and consignees ( truck drivers are not responsible for paying the TMF) and distributes
them to terminal operators. When OffPeak first began, the TMF was set at $ 40 per
twenty- foot equivalent ( TEU) based on a per- TEU allocation of off- peak gate costs. In
April 2006, an independent review of these costs resulted in the current TMF of $ 50 per
TEU.
The TMF can be viewed as a form of “ congestion pricing”, where tolls are
assessed in an effort to improve the efficiency of congested facilities. There is a long and
rich economic literature on congestion pricing, which generally aims to correct the
negative externalities that result from congested travel. 3 In the context of truck
congestion in and around the ports, each truck trip generates negative externalities, for
example, by delaying the travel of others and exposing them to increased diesel
emissions. If the goal is to maximize the economic efficiency of road use then a toll
equal to the external cost generated by each trip would be warranted. The formulation of
the current TMF, however, does not consider the magnitudes of these externalities but,
instead, focuses solely on cost recovery. This does not imply that the TMF is “ wrong” in
1 See Giuliano et al. ( 2006)
2 Ibid.
3 Section 2 provides formal, economic definitions of “ efficiency” and “ negative externalities”.
9
any sense, but rather that it targets an objective that differs from that of maximizing
economic efficiency.
The purpose of the present study is to develop an empirical framework for pricing
access to marine terminals in a manner that maximizes the economic efficiency of traffic
on highways surrounding the port complex and at terminal gates. In particular, it
describes how to measure this toll when, like the current TMF, off- peak access cannot be
charged. The magnitude of the toll can then be compared to that of the current TMF in
order to gain a sense of how closely the objectives of efficiency- maximization and cost-recovery
coincide.
This framework relies heavily on estimating the external congestion costs
generated by each truck trip, comprising the bulk of this study’s empirical efforts. 4 In
short, the toll developed herein is designed to correct these externalities. This implies a
key distinction between the current TMF and the toll estimated in this study, where the
former only applies to moving a limited class of loaded ocean containers but the latter
applies to all truck trips. The rationale is that that all port- bound trucks, regardless of trip
purpose, generate congestion externalities when conditions are crowded, warranting a toll
on all truck trips. Yet, of particular interest to terminal operators, the revenues implied
by this congestion- pricing scheme can be compared to off- peak gate costs to determine if
the objectives of efficiency- maximization and cost- recovery from loaded ocean
containers can work hand- in- hand.
The results of this study suggest a peak- period toll of $ 18.25 per truck traveling
roundtrip to and from the port complex. This toll is based on optimally balancing peak
and off- peak truck traffic on the highway system surrounding the ports and at terminal
gates. For reasons discussed in the analysis that follows, the toll is calculated as the
difference between the external congestion cost that each truck trip generates during peak
and off- peak gate hours. The toll is small in comparison to the current TMF, but it must
be kept in mind that the current TMF only applies to trucks carrying certain types of
loaded ocean containers. In this sense the $ 18.25 toll suggests spreading the burden of
congestion relief across a wider class of port- related truck trips.
Of the estimated perk- period congestion externalities, about 10% are attributable
to queuing at terminal gates, while the remaining 90% can be attributed to highway
delays. This result illustrates the importance of considering the surrounding highway
network when devising port- related congestion- pricing policies. The analysis also shows
that the toll of $ 18.25 per peak- period trip could generate monthly toll revenues of
roughly $ 13.9 million per month. This level of revenue may be sufficient to reimburse
marine terminal operators for increases in their off- peak operating costs.
This report proceeds as follows. Section 2 formally describes the theoretical
framework used to calculate economically- efficient congestion tolls in general, and the
4 To keep the analysis tractable, only externalities attendant to delayed travel are considered. This does not
imply that pollution externalities are unimportant. The focus here is on travel- delay externalities because
they are typically considered to dominate other road externalities ( see Small 1992).
10
adjustments required when tolls cannot be charged during off- peak hours. Section 3
develops an empirical framework for estimating the external congestion costs that each
truck trip generates, which is needed to calculate the tolls discussed in Section 2. Section
4 describes the empirical setting and data used to obtain external cost estimates. Because
a single toll for all peak- period trips is called for, requiring a single external cost
estimate, the section also develops a procedure for averaging congestion externalities
across trip routes and travel periods. Externalities on highways surrounding the ports and
at terminal gates are considered in turn. Section 5 reports the uniform, peak- period truck
toll implied by these externalities. Section 6 offers a few discussion points, followed by
concluding remarks in Section 7.
2. Congestion- Pricing Framework
2.1 Congestion Tolls
Congestible facilities, such as highways and port terminals, suffer the classic
economic problem of negative externalities. To understand the problem requires an
understanding of the distinction between the private and social costs of using these
facilities. Consider, for example, the time costs of using a crowded highway. The
private cost to each user is simply the value of their time spent in transit – which we can
call their marginal private cost. Each additional user, however, consumes scarce road
capacity and forces existing travelers to reduce their speeds. In this sense the social cost
of an additional trip exceeds its private cost owing to the delay costs imposed upon
existing users. Because individual trip decisions are based solely on private costs, the
value of the delays imposed on other users is called an external congestion cost or
congestion externality. So the cost to all users resulting from each additional trip is the
sum of its marginal private cost and the congestion externality it generates. We can refer
to this sum as the marginal social cost of each trip.
The marginal benefit of a trip is the value that users place on making the trip. The
level of road use that maximizes the net benefits to its users occurs when the marginal
benefit of the last trip taken equals its marginal social cost; this condition describes an
economically efficient or optimal level of use. In equilibrium, however, users enter to the
road up to the point where marginal benefit equals marginal private cost. What results is
an inefficiently large amount of traffic because the marginal social cost of using the road
exceeds its marginal benefit. In other words, users ( rationally) ignore the congestion
externalities imposed on other users, resulting in excessive traffic congestion.
The challenge facing policymakers is to somehow reduce the facility’s use to an
economically efficient level. There is a rich history in the economics literature on using
pricing incentives to accomplish this. 5 The general idea is to charge each user a
congestion toll that would increase the private cost of each trip and reduce traffic to its
5 For an excellent overview, see Small ( 1992).
11
optimal level. This type of toll is often called a “ Pigovian” or “ first- best” toll. The
amount of the toll is equal to congestion externality generated at the efficient level of
traffic.
Formally, define the total benefit to road users during a given commute period as
= ∫
'
0
( )
v
B d v dv , where d( v) is the marginal benefit of road use and v represents traffic
volume, which serves as a measure of road use. 6 Denote the total cost of road use as
C( v) = v ⋅ c( v) , which equals marginal ( and average) private cost, c( v), multiplied by the
level of use, v. Marginal private cost naturally increases with use because the road is
congestible. 7 In equilibrium, users enter the road until marginal benefit equals marginal
private cost. If it were possible to levy a toll, τ, on each trip then users would enter the
road until marginal benefit equals the sum of marginal private cost and this toll. We can
refer to this sum as the generalized price of each trip, p, where p ≡ c( v) + τ . The
equilibrium condition then becomes d( v) = p.
If the policy goal is to induce an economically efficient level of traffic then the
objective is to maximize net benefits, B- C, with respect to traffic volume:
( ) ( )
'
0
Max d v dv v c v
v
v
∫ − ⋅ ( 1)
Maximizing ( 1) entails differentiating it with respect to v and setting the resulting
expression equal to zero; this expression is called a first- order condition of the
maximization problem. 8 From this first- order condition, it can be shown that
v
v
c v c v c v
∂
∂
( ) + τ = ( ) + ( ) ( 2)
Equation ( 2) shows that the optimal level of traffic is achieved where the generalized
price of road use ( on the left- hand side) equals its marginal social cost ( the right- hand
side). As described above, the marginal social cost has two components. The first, c( v),
is the addition to social cost privately faced by the marginal traveler. The second,
v
v
c v
∂
∂ ( ) , is the increased cost imposed on all existing users due the marginal traveler’s
further consumption of road capacity. This latter cost is the congestion externality
described above.
6 d( v) is typically called the demand curve for road use, and B measures the consumer surplus enjoyed by
users during the commute period. Note also that in the U. S. traffic volume, v, is often measured in vehicles
per hour.
7 Because road capacity is treated as fixed, the cost of the road itself is omitted from the total cost of use.
As such this cost function is often called short- run average variable cost.
8 At a maximum of any function ( if it exists), its derivative with respect to the relevant maximand equals
zero indicating that the “ top” of the function has been reached.
12
From ( 2) it is readily apparent that the optimal toll required to induce an
economically efficient level of traffic is
v
v
c v
∂
∂
τ = ( ) ( 3)
indicating that the toll equals the congestion externality generated by the marginal
traveler ( at the efficient level of road use). An analogous approach can be used to derive
optimal tolls for other congestible facilities, such as terminals at maritime ports.
2.2 Congestion Tolls with an Untolled Alternative
In many cases it is impossible or politically infeasible to always implement the
toll described in the previous section. For example, toll roads are often built with the
understanding that an alternative route is available at no charge. In the case of the TMF
at the San Pedro Bay ports, no fee is levied on trucks entering the port complex during
off- peak gate hours. As such it is not possible to achieve a “ first- best” level of truck
traffic at the terminal gates and the highways extending to them. 9 Instead, policymakers
must find a “ second- best” solution, where a toll is sought to maximize economic
efficiency under the constraint that tolls are not allowed during off- peak periods.
The approach proposed here is analogous to that derived in the literature on
“ second- best pricing” in the presence of an “ untolled alternative”. 10 In this setting, traffic
on a given road ( such as Interstate 710) can be divided between peak traffic, vP, and off-peak
traffic, vO. The goal is then to find a toll that optimizes the mix of peak and off-peak
truck traffic with the understanding that tolls cannot be charged during off- peak
hours. To this end let d( v) represent the marginal benefit of traveling during either
period, where overall traffic, v, is now defined as P O v = v + v . Implicit in this framework
is the assumption that peak and off- peak travel are “ perfect substitutes”. The marginal
( and average) private cost in each period for truckers, or those dispatching them, is
( ) P P c v for peak travel and ( ) O O c v for off- peak travel.
The objective is now a slightly more complicated version of equation ( 1):
( ) ( ) ( ) [ ( ) ( )] [ ( ) ( )]
0
, ,
Max d v dv v c v v c v c v d v c v d v O O O P P P O O O
v v
v v P P P
P O
P O
− ⋅ + − + ⋅ + ⋅ − ⋅ − ∫ +
λ τ λ
τ
( 4)
9 Note that the toll described in the previous section applies to cars and trucks alike. But it is currently
infeasible to levy tolls on cars traveling the highways leading to the port, representing yet another
constraint on achieving an efficient level of overall traffic.
10 Verhoef et al. ( 1995) is an important work in this area.
13
The λP and λO terms are referred to as “ shadow prices” reflecting the value of relaxing the
constraints associated with them in equation ( 4). These constraints are simply the
equilibrium conditions for peak travel, c ( v ) d( v) P P + τ = , and off- peak travel,
c ( v ) d( v) O O = , each stating that marginal benefit equals the “ generalized price” in each
period. If a toll could be charged during the off- peak period, then the net benefits to
travelers would increase by a positive amount equal to λO. If the toll is set optimally
during the peak period, then no gains can be exploited by changing the toll and we would
expect λP= 0.
A few caveats are worth pointing out at this point. First, it is understood that the
current TMF is designed to generate revenue sufficient to cover off- peak terminal
operations. Equation ( 4) can be modified to explicitly incorporate this constraint, though
the result would be a toll that divides off- peak operating costs by the number of trucks
traveling during peak gate hours. The relative efficiency of this toll would then depend
on the “ marginal cost of public funds”, a measure of how “ distortionary” raising revenue
with the TMF is relative to some other means of taxation. The objective here is instead is
to determine an optimal mix of truck traffic while setting aside revenue- generation
concerns; the revenues implied by this toll are discussed later in this report. Second, it is
understood that only certain trucks bearing loaded ocean containers are subject to the
current TMF. It is important to understand, however, that each truck traveling to the port
generates congestion externalities – loaded or not. 11 Moreover, attempting to gauge the
relative efficiency of offering preferential treatment to “ bobtails” and “ empties” would
require ad- hoc assumptions about the marginal benefit of each type of trip. Furthermore,
it can be shown that under the constraint of tolling only loaded containers, a congestion-externality
based toll would still prevail, but would reduce net benefits relative to more
inclusive tolling. In short, the framework developed herein can be viewed as starting
with a “ clean slate”, where the focus is on the efficient pricing of all peak- period truck
trips when off- peak trips cannot be tolled.
That said, the first- order conditions from the maximization problem in ( 4) can be
solved to yield the optimal ( second- best) peak- period toll:
v
d
v
c
v
d
v
v
v c
v
c
O
O
O
P
P
∂
∂ − ∂
∂
∂
− ∂
⋅
∂
∂
−
∂
∂
τ = ( 5)
Equation ( 5) looks daunting at first glance but has a simple interpretation. The first term
on the right- hand side of ( 5) is the peak- period congestion externality generated by the
marginal truck trip ( c. f. equation ( 3)). The last right- hand side term has two parts. The
11 In other words, trucks hauling empty containers or unloaded chassis are not distinguished from fully
loaded trucks ( or other large vehicles such as water carriers) because each consumes roughly the same
amount of road capacity. One might argue, however, that “ bobcats” should receive differential treatment.
There is not sufficient evidence, however, to suggest that the PCE for a bobcat is substantially less than that
of a laden truck. A notable exception, however, is that some terminals have dedicated bobcat lanes, which
would reduce the externalities that they generate at terminal gates. Data on bobcat- only gate moves is
fairly sparse, however, so the analysis proceeds by abstracting from this feature.
14
first part, O
O v
v
c
∂
∂
, is the congestion externality imposed on off- peak travelers, which
results from the switching of some trips into the off- peak period to avoid the toll. If the
toll is sufficiently large, it may also result in the “ cancelling” of some trips due to
shippers opting for alternative ports such as Oakland. The second part of the last right-hand
side term,
v
d
v
c
v
d
O ∂
∂ − ∂
∂
∂
− ∂
, is the fraction of the trips displaced from the peak period
that are moved to the off- peak period instead of cancelled entirely. So equation ( 5) can
be summarized as follows: the optimal peak- period toll charges the congestion externality
generated by each trip, less the congestion externality caused by switching to the off- peak
period, after accounting for trips to this port that are cancelled.
It may be reasonable, however, to assume that the toll would not be large enough
for shippers to switch to alternative ports. This can be characterized by assuming that the
overall demand for trips to the port complex, peak and off- peak, is “ perfectly inelastic”. 12
The assumption would be consistent with PierPass estimates on the impact of the current
TMF, where only switching between peak and off- peak trips is considered. 13 With a
perfectly- inelastic demand, note that the v
d
∂
∂ term in ( 5) equals infinity. The term
measures the slope of the demand curve for port trips, and this slope is infinite when
demand is perfectly inelastic. The fraction
v
d
v
c
v
d
O ∂
∂ − ∂
∂
∂
− ∂
thus equals one, resulting in
an optimal peak- period toll of
O
O
P
P v
v
v c
v
c
∂
∂
−
∂
∂
τ = ( 6)
Thus when overall demand is perfectly inelastic, the optimal peak- period toll is simply
the difference between the congestion externalities imposed on peak and off- peak
travelers. In this sense the toll optimally balances the congestion externalities in each
period, thereby balancing each period’s traffic flows. Note that the demand curve, d( v),
no longer appears in the toll expression so applying ( 6) primarily involves measuring the
congestion externalities generated in each period. Henceforth in this analysis, optimal
peak- period tolls are calculated using ( 6).
12 See Leachman & Associates ( 2005) for a discussion of port- elasticity estimates for the San Pedro Bay
Port Complex.
13 See http:// www. pierpass. org/.
15
3. Congestion- Externality Framework
3.1 Bottleneck Model of Trip Delays
Equation ( 6) shows that calculating peak- period tolls requires congestion-externality
estimates for each period. These estimates, in turn, depend on how user costs
in each period, cP and cO, respond to increased traffic flows (
v
c P
∂
∂
and
v
c O
∂
∂
). The
economics and engineering literatures on estimating such relationships are voluminous,
and several approaches are available. Each relies on some specific functional form
relating travel times to traffic flows. 14
The approach taken in this study is to assume that trip delays result from
“ bottlenecks” that form on various parts of the highway network surrounding the ports
when traffic exceeds “ free- flow” capacities. These bottlenecks create queues that users
must wait in before resuming free- flowing travel. Truck pedestals at terminal gates can
also be viewed as bottlenecks when the inflow of trucks exceeds the pedestal’s
processing capacity, resulting in gate queues. A bottleneck model is thus capable of
characterizing both highway delays and gate delays within a single estimation
framework.
Formally, let c( v) ≡ γ ⋅ T( v) define the marginal private cost for a given portion of
a peak or off- peak trip, where T( v) is travel time and γ is the value that users place on
that travel time; γ is often referred to as the “ value of time” ( VOT), which indicates the
dollar amount users are willing to pay for a marginal reduction in travel time. This value
differs for car and truck drivers because the latter are typically more averse to delays. For
example, truck delays can result in missed gate appointments and fewer “ turns”; Section
3.2 discusses how to accommodate different values of time for car and truck users. 15 To
summarize, the private cost of a given trip is the time it takes to make the trip, multiplied
by the monetary value placed on that travel time.
In a bottleneck framework, assuming a constant inflow of traffic, v, it can be
shown that the average travel time ( in minutes) for those encountering a bottleneck is
⎥⎦
⎤
⎢⎣
⎡
= + ⋅ − 1
2
( )
k
f v
T v T w v ( 7)
14 A comprehensive review of these literatures is beyond the scope of this study. It should be noted,
however, that a “ bottleneck” or “ queuing” approach is adopted here mainly due to ( i) concerns about
frequent “ hypercongestion” on surrounding highways and ( ii) a relatively strong statistical fit with traffic
data drawn from these highways.
15 For truck users, VOT is typically referred to as “ Commercial VOT”.
16
when traffic flow exceeds the highway’s ( or terminal gate’s) capacity, vk; w is the amount
of time that capacity is exceeded. 16 When capacity is not exceeded, travel time is simply
Tf, representing the time required to make a trip under free- flowing conditions ( or the
time required to complete a pedestal transaction without delay). Equation ( 7) thus
decomposes travel time into a free- flow time plus any time spent in a “ traffic jam”.
Using equation ( 7), marginal private cost can be expressed as
⎟ ⎟
⎠
⎞
⎜ ⎜
⎝
⎛
⎥⎦
⎤
⎢⎣
⎡
= ⋅ + ⋅ − 1
2
( )
k
f v
c v γ T w v ( 8).
Recall, however, that the external congestion cost is salient for calculating peak- period
tolls. Following the discussion in Section 2.1, the external cost, denoted EC, is given by
the difference between marginal social cost,
v
c v v
∂
∂( ( ) ⋅ ) , and marginal private cost, c( v) :
⎥⎦
⎤
⎢⎣
⎡
− = ⋅ ⋅
∂
∂ ⋅
=
k v
c v w v
v
EC c v v
2
( ( ) ) ( ) γ ( 9).
Because this congestion externality is derived from average travel times, it measures the
average external cost generated by each vehicle entering the highway ( or terminal- gate
queue) during congested travel. Note also that this external cost is zero when v< vk, i. e.
when traffic flows freely.
3.2 Accommodating Mixed Traffic
Equation ( 9) provides a general expression for the externality generated by an
increase in traffic flow, v, and suffered by users with value of time γ. This expression
does not, however, specify the type of vehicle that adds to traffic flow, nor does it
consider the different VOT’s associated with different types of vehicles. To consider a
mix of vehicles sharing a highway, let “ cars” denote passenger vehicles and “ trucks”
denote large commercial vehicles. This raises two immediate questions about the impact
of increased traffic flows: ( i) what are the external costs suffered by cars and truck
drivers together, and ( ii) how do the external costs generated by trucks entering the
highway compare to those generated by cars?
In this study the first question is addressed by assigning separate VOT’s for cars
and trucks, then applying them to the proportions of each vehicle type suffering
congestion externalities. For example, suppose a vehicle entering the highway creates a
one- minute travel delay. If 10% of the highway comprises trucks, then the value that
trucks place on this delay is applied to 10% of overall traffic volume, while the value that
16 For a complete derivation see Small ( 1992), pp. 72- 74. Note also that this formulation is consistent with
a “ piecewise- linear” model of the relationship between travel times and traffic flows.
17
cars place on the delay is applied to the remaining 90%. Formally, let γT denote truck
VOT and γC denote car VOT. Also, let αT and ( 1 ) C T α = − α represent the share of
overall traffic attributable to trucks and cars. For an increase in overall traffic flow, v, the
value of the external delay, i. e. the external congestion cost ( EC) is
⎥⎦
⎤
⎢⎣
⎡
= ⋅ + ⋅ ⋅ ⋅ ⋅
k
C C T T v
EC v w 1
2
( γ α γ α ) ( 10)
which is a simple extension of equation ( 9). 17
To address the second question, the impact of a truck entering a highway is
described in terms of its “ passenger- car equivalent” ( PCE). For example, suppose that an
entering truck has the same effect on highway travel times as two cars entering. The
truck is then said to have a PCE equal to two. The concept of truck PCE’s allows for
using a single empirical model of travel delays to analyze both car and truck entries. For
instance if overall traffic volume is measured in PCE’s then the externality generated by
an entering car would be given by equation ( 10). If an entering truck’s PCE is two, then
the resulting externality is simply two times equation ( 10).
3.3 Value of Time
Equation ( 10) shows that measuring congestion externalities requires information
on both truck and car values of time. There is an extensive literature on car VOT from
which to draw. The most recent, and arguably most reliable, studies are based on real-world
choices made by urban rush- hour commuters who can choose a tolled highway to
escape congested travel. 18 In short, the combination of tolls paid and travel times saved
reveals their value of time. For the handful of studies considered here, this value ranges
from $ 24 to $ 30 for each hour saved. Table 1 summarizes their findings ( after adjusting
for inflation).
17 Note that from equation ( 7), the external delay is
k v
w
v
T v 1
2
( ) = ⋅
∂
∂
. So equation ( 10) is essentially a
weighted average of this delay across cars and trucks, where C C γ ⋅ α and T T γ ⋅ α serve as weights.
18 See Brownstone and Small ( 2005) for a review of such studies.
18
Table 1
Passenger- Vehicle Value of Time Estimates
Study Value of Time ( VOT) a
Lam and Small ( 2001) $ 29.61
Small et al. ( 2005) $ 24.25
Steimetz and Brownstone ( 2005) $ 27.72b
Average $ 27.19
a Converted to 2007 U. S. Dollars ( Base = 1982- 1984).
b Estimate based on a sample of California Interstate 15 morning commuters, weighted by income and trip
distance to match the California State Route 91 sample of morning commuters used in Brownstone and
Small ( 2005).
To measure external costs using equation ( 10), the average of these values ($ 27.19) is
used for car VOT, γC.
The literature on truck VOT, often referred to as “ commercial VOT”, is less
extensive. Kawamura ( 1999), however, provides a comprehensive review of this
literature. Commercial VOT studies do not typically enjoy the same “ real- world” choice
data exploited by car VOT studies. Their estimates instead rely on survey data or a
method called “ switching- point analysis”. The findings of Kawamura ( 1999) and other
notable studies are summarized in Table 2.
Table 2
Commercial Value of Time Estimates
Study Value of Time ( VOT) a
Texas Transportation Institute ( 1997) $ 57.58
Kawamura ( 1999) $ 33.39 b
de Jong ( 2000) $ 50.09
Smalkoski and Levinson ( 2005) $ 55.15
Average $ 49.05
a Converted to 2007 U. S. Dollars ( Base = 1982- 1984).
b Estimate based on data from Truckload ( TL) and For- Hire operators only.
The average of the commercial VOT values in Table 2 ($ 49.05) is used for γT when
measuring external costs with equation ( 10).
3.4 Passenger- Car Equivalents
Section 3.2 briefly describes how passenger- car equivalents ( PCE’s) can be used
to estimate the externalities generated by truck inflows. This, of course, begs the
question of which PCE value to use for trucks heading to and from the ports. A given
truck’s PCE depends, inter alia, on prevailing traffic conditions and highway grade ( i. e.
how steep a highway is). Because the highways surrounding the port complex are
relatively flat, only PCE estimates based on zero- grade roads are considered here. A
19
handful of studies estimating PCE’s under these conditions, including the often- cited
2000 Highway Capacity Manual, is summarized in Table 3.
Table 3
Commercial Truck Passenger Car Equivalent Estimates
Study Passenger- Car Equivalent ( PCE)
Mingo and Zhuang ( 1994) 4.10
Webster and Elefteriadou ( 1999) 2.00
Highway Capacity Manual ( 2000) 2.00
Al- Kaisy et al. ( 2002) 2.79
Average 2.72
The average of these PCE estimates ( 2.72) is applied to equation ( 10) when estimating
the congestion externalities generated by port- bound trucks on highways surrounding the
port complex.
3.5 Summary of Truck Congestion- Externality Measurement
Equation ( 10) allows for estimating truck- generated congestion externalities when
combined with the VOT and PCE estimates discussed above. Equation ( 6) shows that
these estimates yield optimal peak- period truck tolls when ( 10) is applied separately to
peak and off- peak periods.
For estimation purposed, VOT and PCE values are drawn from existing studies
following the above discussion. This leaves other parameters to be estimated from data,
such as bottleneck duration, w, and free- flow capacity, vk. Terminal- gate delays are also
estimated using equation ( 10) by setting αC equal to zero ( because car traffic is negligible
at terminal gates). The particulars of estimating these parameters are discussed in
following sections. Table 4 provides a brief summary of key parameter values required
for external- cost estimation.
Table 4
Key Parameters for External Congestion Cost Estimates
Parameter Symbol Source
Passenger- Vehicle Value of Time γC Previous Studies
Commercial Value of Time γT Previous Studies
Overall Traffic Volume v Measured
Car Proportion of Overall Traffic Volume vC Measured
Truck Proportion of Overall Traffic Volume vT Measured
Highway / Terminal- Gate Bottleneck Duration w Estimated
Highway / Terminal- Gate Free- Flow Capacity vk Estimated
20
4. Empirical Setting and Estimation
4.1 Empirical Setting and Estimation Overview
Following the discussions in Sections 2 and 3, peak- period truck tolls are
calculated by first estimating the congestion externalities generated by trucks during peak
or off- peak trips using equation ( 10). These estimates are then applied to equation ( 6) to
yield optimal peak- period truck tolls under the constraint that off- peak trips cannot be
charged.
Presuming that multiple tolls within the peak- period are not allowed, the goal here
is to calculate a uniform toll that applies to all trucks traveling during peak gate hours.
Doing so is consistent with the current TMF in that tolls are not differentiated by exact
trip characteristics such as point of origin or arrival time within peak gate hours. To
develop a uniform peak- period toll, the notion of an “ average externality” generated
across peak or off- peak gate hours is introduced. For instance, a truck might depart at
noon from an Inland Empire warehouse, travel along Highway 91 West and encounter
traffic once in Los Angeles County, connect to Interstate 710 South, and arrive at 2: 00
p. m. to wait in a terminal gate queue; the reverse trip might be made at 3: 00 p. m. On
each leg the truck creates, and suffers, the sum of several congestion externalities: on
each highway during inbound travel, at the terminal gate, and on the same outbound
highways. These externalities would be different, however, if the trip began at 9: 00 a. m.
and the driver decided to connect to Interstate 710 via Interstate 605 and Interstate 105.
If it is assumed that either scenario is equally likely then the “ average” externality
generated by the complete trip can be viewed as the average of the externalities that
would have resulted from each possible route and departure- time combination.
The above scenario depicts the essence of this study’s approach to measuring
externalities across an entire peak or off- peak period. Each trip is treated as having some
probability of interacting with some portion of the surrounding highway network and
during a given travel- time interval. Externalities are then measured by the weighted-average
of the externalities created on each potential leg of a trip during each possible
travel- time time interval, including those generated at terminal gates.
Figure 1 provides an aerial view of the surrounding highway network that is
examined in this study, and Table 5 lists the possible inbound and outbound routes that
are considered. 19 Note that some truck trips originate from within the network, thus
requiring travel on fewer highways.
19 All of the aerial highway views provided in this study were generate using “ Google Earth” – an
application that can be downloaded at http:// earth. google. com/
21
Figure 1
Aerial View of Surrounding Highway System and Truck Routes Considereda
a Source: Google Earth.
Table 5
Inbound and Outbound Truck Routesa
Inbound Route Outbound Route
10W- 605S- 105W- 710S 710N- 105E- 605S- 10E
10W- 605S- 91W- 710S 710N- 91E- 605N- 10E
605S- 105W- 710S 710N- 105E- 605N
605S- 91W- 710S 710N- 91E- 605N
105W- 710S 710N- 105E
91W- 710S 710N- 91E
405N- 710S 710N- 405S
105W- 110S 110N- 105E
91W- 110S 110N- 91E
405S- 110S 110N- 405N
a Numbers denote highways within the network, letters indicate direction of travel, and dashes denote
interchanges. For example, “ 91W- 110S” means westbound travel on State Route 91, followed by
southbound travel on Interstate 110, ending at the Port of Los Angeles.
22
Three peak- period travel- time intervals are considered, which correspond to
periods when terminal- gate traffic is heaviest. One off- peak time interval is considered
under the assumption that highway and gate delays are negligible after 8: 00 p. m. Table 6
summarizes these time intervals.
Table 6
Terminal Trip Travel- Time Intervals ( Monday- Friday)
Peak or Off- Peak Gate Hours Travel- Time Interval
Peak 7: 00 a. m. – 9: 00 a. m.
Peak 1: 00 p. m. – 3: 00 p. m.
Peak 3: 00 p. m. – 6: 00 p. m.
Off- Peak 6: 00 p. m. – 8: 00 p. m.
4.2 Highway External Cost Estimation
Equation ( 7) serves as the starting point for estimating the congestion externalities
generated by port- bound trucks on the highway system surrounding the ports. The
external delay caused by adding a truck to a given highway in the system is estimated by
relating the average travel time, T, required to travel that highway to its overall traffic
volume, v. The estimated parameters of ( 7), w and vk, are then combined with
information car and truck VOT and traffic shares and applied to equation ( 10).
Data on vehicle speeds ( used to measure travel times), traffic volumes, and the
share of traffic volumes attributable to trucks were drawn from the Freeway Performance
Measurement Systems ( PeMS) – a traffic database maintained by a collaboration between
the University of California at Berkeley, the California Partners for Advanced Transit and
Highways ( PATH), and the California Department of Transportation ( Caltrans). 20 These
data were compiled in fifteen- minute intervals through August and September of 2006 for
each of the highways listed in Table 5 ( both directions). Only data from the segments of
these highways that exhibited systematic travel delays were included ( because travel
delays do not occur on free- flowing segments). The data were then divided into the time
intervals shown in Table 6 ( three intervals during peak gate hours, one during off- peak
hours).
The particulars of estimating external costs using these data with equations ( 7)
and ( 10) are best understood by focusing on a single highway segment. Consider a 20-
mile northbound segment of Interstate 110 leading from the Port of Los Angeles ( in this
case from Harbor Boulevard to Washington Boulevard). Figure 2 provides an aerial view
indicating the endpoints of this segment.
20 The PeMS data are available at https:// pems. eecs. berkeley. edu/
23
Figure 2
Aerial View of Interstate 110 Segment Leading to the Port of Los Angelesa
a Source: Google Earth
Looking at equation ( 7), travel time, T, is the dependent variable ( in minutes), whereas
overall traffic volume, v, is the independent variable ( in vehicles per hour); Tf, w, and vk
are parameters. 21 To keep matters simple, it is assumed that vehicles travel at 65 miles
per hour during free- flow conditions, implying that the free- flow travel time, Tf, is
60 18.5
65
20 ⋅ = minutes. This leaves two parameters to be estimated: the duration of each
bottleneck period, w, and the free- flow capacity of the highway segment, vk. The
resulting estimation equation is
21 More precisely, v is measured as the inflow of vehicles at the highway segment’s southern end in order to
keep consistent with bottleneck modeling.
24
⎥⎦
⎤
⎢⎣
⎡
= + ⋅ − 1
2
( ) 18.5
k v
T v w v ( 11).
Note that ( 11) is not linear in vk so non- linear estimation techniques are required. In this
study the method of Non- Linear Least Squares is employed. 22 Table 7 summarizes the
results from estimating equation ( 11) for this highway segment.
Table 7
Average Travel Time Estimation Results for Northbound Interstate 110
Parameter Estimate t- Statistic
Free- Flow Capacity ( vk) a 1479.92 29.46
Bottleneck Duration ( w) b 4.92 9.78
Adjusted R2 0.9981
a Measured in vehicles per hour.
b Measured in minutes.
The table shows that average travel times on northbound I- 110 are predicted quite well
from the bottleneck model in equation ( 11), where the adjusted coefficient of
determination ( R2) is 0.9981. The estimated parameters suggest that this segment of I-
110 is capable of carrying roughly 1,480 vehicles per hour without delayed travel. When
traffic exceeds this capacity, delays result from bottlenecks that last for roughly five
minutes. Figure 3 plots actual travel times and those predicted by the model in ( 11) by
time of day, illustrating how faithfully the model tracks travel delays.
22 Specifically, the data are loaded into STATA SE 9.1 statistical software and the parameters of ( 11) are
estimated using STATA’s “ nl” command.
25
Figure 3
Predicted and Actual Travel Times by Time of Day
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
5: 15 AM
6: 30 AM
7: 45 AM
9: 00 AM
10: 15 AM
11: 30 AM
12: 45 PM
2: 00 PM
3: 15 PM
4: 30 PM
5: 45 PM
7: 00 PM
8: 15 PM
9: 30 PM
Time of Day
Travel Time ( minutes)
Predicted
Actual
The estimates for w and vk can now be applied to equation ( 10), along with the
values in Tables 1 and 2 for γC and γT ( the VOT measures for cars and trucks, each
converted to dollars per minute). What remains are the shares of overall traffic belonging
to cars and trucks, αC and αT, during a given time interval. During the 7: 00- 9: 00 a. m.
interval, the average overall traffic volume is 2,693 vehicles per hour, 229 of which
represent trucks. This implies that the share of volume belonging to trucks during this
interval is 9% ( αT= 0.09), whereas cars comprise the remaining share ( αC= 0.91).
Applying all of this information to equation ( 10), and multiplying the results by
the passenger- car equivalent given in Table 3, yields the external congestion cost
imposed on existing cars and trucks by a truck entering this segment of northbound I- 110
during the 7: 00- 9: 00 a. m. interval:
2.72 $ 5.90
1,479
1
2
92 . 4 693 , 2 ) 09 . 0 82 . 0 $ 91 . 0 45 . 0 ($ = ⋅ ⎥⎦
⎤
⎢⎣
⎡
EC = ⋅ + ⋅ ⋅ ⋅ ⋅ ( 12)
The calculation in ( 12) shows that each truck entering during this period generates, on
average, an external congestion cost of $ 5.90. Note that the product
2.72 12.19
1,479
1
2
92 . 4 = ⋅ ⎥⎦
⎤
⎢⎣ ⎡
⋅ gives the external delay caused by each entering truck –
12.19 minutes in this case – and the remaining terms in ( 12) place a dollar value on this
26
delay. This does not imply that each entering truck causes a delay of 12.19 minutes to
each existing traveler. It instead shows that an entering truck delays each existing
traveler by a small amount, and the sum of these small delays adds up to 12.19 minutes.
The value of this overall delay to existing cars and trucks, i. e. the external congestion
cost, is $ 5.90.
The above steps are repeated for each highway segment and during each time
interval ( including during off- peak gate hours) to estimate a set of external congestion
costs generated by trucks on the highway system surrounding the ports. Table 8
summarizes these externality measures. 23
23 Complete estimation results from applying equation ( 7) to each highway segment are available from the
authors by request.
27
Table 8
Truck- Generated External Congestion Cost Estimates by Highway Segment and Travel- Time Interval
Highway Direction Peak or Off- Peak Travel- Time Interval External Costa
710 North Peak 7: 00 a. m. – 9: 00 a. m. $ 3.25
710 North Peak 1: 00 p. m. – 3: 00 p. m. $ 3.33
710 North Peak 3: 00 p. m. – 6: 00 p. m. $ 3.92
710 North Off- Peak 6: 00 p. m. – 8: 00 p. m. $ 3.11
710 South Peak 7: 00 a. m. – 9: 00 a. m. $ 3.90
710 South Peak 1: 00 p. m. – 3: 00 p. m. $ 3.53
710 South Peak 3: 00 p. m. – 6: 00 p. m. $ 3.47
710 South Off- Peak 6: 00 p. m. – 8: 00 p. m. $ 0.00
605 North Peak 7: 00 a. m. – 9: 00 a. m. $ 5.37
605 North Peak 1: 00 p. m. – 3: 00 p. m. $ 4.83
605 North Peak 3: 00 p. m. – 6: 00 p. m. $ 5.04
605 North Off- Peak 6: 00 p. m. – 8: 00 p. m. $ 4.63
605 South Peak 7: 00 a. m. – 9: 00 a. m. $ 5.37
605 South Peak 1: 00 p. m. – 3: 00 p. m. $ 4.63
605 South Peak 3: 00 p. m. – 6: 00 p. m. $ 4.54
605 South Off- Peak 6: 00 p. m. – 8: 00 p. m. $ 3.84
405 North Peak 7: 00 a. m. – 9: 00 a. m. $ 2.20
405 North Peak 1: 00 p. m. – 3: 00 p. m. $ 2.01
405 North Peak 3: 00 p. m. – 6: 00 p. m. $ 2.12
405 North Off- Peak 6: 00 p. m. – 8: 00 p. m. $ 1.92
405 South Peak 7: 00 a. m. – 9: 00 a. m. $ 3.24
405 South Peak 1: 00 p. m. – 3: 00 p. m. $ 3.20
405 South Peak 3: 00 p. m. – 6: 00 p. m. $ 3.08
405 South Off- Peak 6: 00 p. m. – 8: 00 p. m. $ 2.97
110 North Peak 7: 00 a. m. – 9: 00 a. m. $ 5.90
110 North Peak 1: 00 p. m. – 3: 00 p. m. $ 4.52
110 North Peak 3: 00 p. m. – 6: 00 p. m. $ 4.97
110 North Off- Peak 6: 00 p. m. – 8: 00 p. m. $ 0.00
110 South Peak 7: 00 a. m. – 9: 00 a. m. $ 3.37
110 South Peak 1: 00 p. m. – 3: 00 p. m. $ 3.57
110 South Peak 3: 00 p. m. – 6: 00 p. m. $ 3.45
110 South Off- Peak 6: 00 p. m. – 8: 00 p. m. $ 3.12
105 East Peak 7: 00 a. m. – 9: 00 a. m. $ 1.89
105 East Peak 1: 00 p. m. – 3: 00 p. m. $ 2.07
105 East Peak 3: 00 p. m. – 6: 00 p. m. $ 1.92
105 East Off- Peak 6: 00 p. m. – 8: 00 p. m. $ 1.93
105 West Peak 7: 00 a. m. – 9: 00 a. m. $ 2.69
105 West Peak 1: 00 p. m. – 3: 00 p. m. $ 3.04
105 West Peak 3: 00 p. m. – 6: 00 p. m. $ 3.05
105 West Off- Peak 6: 00 p. m. – 8: 00 p. m. $ 2.83
91 East Peak 7: 00 a. m. – 9: 00 a. m. $ 5.43
91 East Peak 1: 00 p. m. – 3: 00 p. m. $ 5.23
91 East Peak 3: 00 p. m. – 6: 00 p. m. $ 5.33
91 East Off- Peak 6: 00 p. m. – 8: 00 p. m. $ 4.85
91 West Peak 7: 00 a. m. – 9: 00 a. m. $ 7.49
91 West Peak 1: 00 p. m. – 3: 00 p. m. $ 7.14
91 West Peak 3: 00 p. m. – 6: 00 p. m. $ 7.52
91 West Off- Peak 6: 00 p. m. – 8: 00 p. m. $ 6.66
10 East Peak 7: 00 a. m. – 9: 00 a. m. $ 3.03
10 East Peak 1: 00 p. m. – 3: 00 p. m. $ 3.44
10 East Peak 3: 00 p. m. – 6: 00 p. m. $ 3.28
10 East Off- Peak 6: 00 p. m. – 8: 00 p. m. $ 3.23
10 West Peak 7: 00 a. m. – 9: 00 a. m. $ 3.20
10 West Peak 1: 00 p. m. – 3: 00 p. m. $ 3.11
10 West Peak 3: 00 p. m. – 6: 00 p. m. $ 3.33
10 West Off- Peak 6: 00 p. m. – 8: 00 p. m. $ 2.85
a Measured in 2007 U. S. dollars per trip.
28
4.3 Time- Averaged Highway Externalities
Table 8 shows that the externality generated by each truck trip varies by time of
day for each highway. Because the objective here is to develop a uniform toll,
aggregation over time ( and space) is required. The approach taken here is to first average
these external costs by time interval; Section 4.5 discusses averaging across trip routes.
The basic idea is to construct a weighted average of the externalities generated during
each of these intervals using the share of truck trips taken in each interval as weights.
Meyer, Mohaddes Associates, Inc. ( 2004) provides estimates on the share of
terminal truck trips taken during each of the peak- period time intervals listed in Table 6.24
Table 9 summarizes the share of overall trips taken during each peak- period interval.
Table 9
Estimated Share of Terminal Truck Trips Taken During Each Travel- Time Interval
Travel- Time Interval Peak or Off- Peak Share of Total Peak or Off- Peak Tripsa
7: 00 a. m. – 9: 00 a. m. Peak 29%
1: 00 p. m. – 3: 00 p. m. Peak 44%
3: 00 p. m. – 6: 00 p. m. Peak 27%
6: 00 p. m. – 8: 00 p. m. Off- Peak 22% b
a Source: Meyer, Mohaddes Associates, Inc. ( 2004), Table 5, p. 27
b Assumes a uniform arrival rate throughout the off- peak period.
Also reported in the table is the assumed share of trips taken from 6: 00- 8: 00 p. m. during
off- peak gate hours. The underlying assumption is that truck trips are roughly uniform
over the nine- hour off- peak period, implying that 22% of all off- peak trips occur during
these two hours. This is an admittedly strong assumption, but a paucity of data on off-peak
gate moves necessitates it. Note also that trips taken after 8: 00 p. m. are not
considered because it is assumed that off- peak externalities are negligible during late-evening
trips.
Table 10 reports the weighted- average externality generated during peak and off-peak
gate hours for each of the highway segments belonging to the routes listed in Table
8 ( both directions).
24 See Meyer, Mohaddes Associates, Inc. ( 2004), Table 5, p. 27. The actual time intervals reported in their
table are 8: 00- 9: 00 a. m. (“ AM Peak”), 2: 00- 3: 00 p. m. (“ Mid- day Peak”), and 4: 00- 5: 00 p. m. (“ PM Peak).
Their estimates are used to approximate the distribution of peak- period trips for the travel- time intervals in
Table 6.
29
Table 10
Weighted Average of Truck- Generated External Costs Across Travel- Time Intervals by Highway
Highway Direction Weighted- Average
Peak- Period External Costa
Weighted- Average
Off- Peak- Period External Costa
710 North $ 3.47 $ 0.69
710 South $ 3.62 $ 0.00
605 North $ 5.04 $ 1.03
605 South $ 4.82 $ 0.85
405 North $ 2.10 $ 0.43
405 South $ 3.18 $ 0.66
110 North $ 5.05 $ 0.00
110 South $ 3.48 $ 0.69
105 East $ 1.98 $ 0.43
105 West $ 2.94 $ 0.63
91 East $ 5.32 $ 1.08
91 West $ 7.35 $ 1.48
10 East $ 3.28 $ 0.72
10 West $ 3.20 $ 0.63
a Measured in 2007 U. S. dollars per trip.
For example, a truck traveling from the Port of Los Angeles on northbound Interstate 110
during the peak- period generates an external cost of $ 5.05. According to Table 9,
however, the externality would be greater ($ 5.90) if travel occurred between 7: 00 a. m.
and 9: 00 a. m., and smaller ($ 4.52) for travel between 1: 00 p. m. and 3: 00 p. m. In
averaging across these intervals, more weight is given to the mid- day interval because a
greater share of peak- period trips ( 44%) is taken mid day. The resulting externality
measure, including the 3: 00- 6: 00 p. m. interval, is
$ 5.90⋅ 0.29 + $ 4.52⋅ 0.44 + $ 4.97 ⋅ 0.27 = $ 5.05 . For an off- peak trip on I- 110N, no
externality is generated because traffic typically flows freely from 6: 00- 8: 00 p. m. in that
direction. 25 Southbound off- peak truck trips, however, generate a weighted- average
externality of $ 3.12⋅ 0.22 = $ 0.69 because trucks interact with other highway commuters
heading to the San Pedro area between 6: 00 p. m. and 8: 00 p. m.
4.4 Roundtrip Route Externalities
Table 10 provides a measure of the external cost generated by each truck traveling
the individual highways surrounding the port complex. The total externality generated by
each truck, however, depends on which of these highways are traveled. For example, a
peak- period trip to the Port of Long Beach from east of Los Angeles might entail
traveling westbound on Highway 91then southbound on Interstate 710. Adding the
externalities on these highways, according to Table 10, yields a combined externality of
$ 7.35 + 3.62 = $ 10.97 for the inbound trip. Assuming that the outbound trip follows the
reverse of this route ( 710N to 91E), the combined outbound externality is
25 Note that northbound I- 110 is a “ reverse commute” for residents of the San Pedro area.
30
$ 3.47 + $ 5.32 = $ 8.79 . The total externality for the truck’s roundtrip peak- period travel
is thus $ 10.97 + $ 8.79 = $ 19.75 .
The same can be done for each of the routes proposed in Table 5. Tables 11
through 13 report the peak and off- peak average externalities generated on these routes
for inbound, outbound, and roundtrip truck travel.
Table 11
Truck- Generated External Costs on Inbound Routes
Route Peak- Period
External Costa
Off- Peak Period
External Costa
10W- 605S- 105W- 710S $ 14.59 $ 2.12
10W- 605S- 91W- 710S $ 18.99 $ 2.53
605S- 105W- 710S $ 11.39 $ 2.99
605S- 91W- 710S $ 15.79 $ 1.14
105W- 710S $ 6.57 $ 1.99
91W- 710S $ 10.97 $ 0.43
405N- 710S $ 5.72 $ 1.32
105W- 110S $ 6.43 $ 2.11
91W- 110S $ 10.83 $ 1.80
405S- 110S $ 6.66 $ 2.11
a Measured in 2007 U. S. dollars per trip.
Table 12
Truck- Generated External Costs on Outbound Routes
Route Peak- Period
External Costa
Off- Peak Period
External Costa
710N- 105E- 605S- 10E $ 13.77 $ 2.87
710N- 91E- 605N- 10E $ 17.11 $ 2.12
710N- 105E- 605N $ 10.49 $ 2.53
710N- 91E- 605N $ 13.83 $ 2.99
710N- 105E $ 5.45 $ 1.14
710N- 91E $ 8.79 $ 1.99
710N- 405S $ 6.65 $ 0.43
110N- 105E $ 7.02 $ 1.51
110N- 91E $ 10.36 $ 2.11
110N- 405N $ 7.14 $ 1.80
a Measured in 2007 U. S. dollars per trip.
31
Table 13
Combined Truck- Generated External Costs on Inbound and Outbound Routes
Inbound Route Peak- Period
External Costa
Off- Peak Period
External Costa
10W- 605S- 105W- 710S $ 28.36 $ 4.98
10W- 605S- 91W- 710S $ 36.10 $ 4.65
605S- 105W- 710S $ 21.88 $ 5.53
605S- 91W- 710S $ 29.62 $ 4.14
105W- 710S $ 12.02 $ 3.13
91W- 710S $ 19.76 $ 2.41
405N- 710S $ 12.37 $ 1.75
105W- 110S $ 13.45 $ 3.61
91W- 110S $ 21.19 $ 3.90
405S- 110S $ 13.80 $ 3.91
a Measured in 2007 U. S. dollars per roundtrip.
4.5 Route- Averaged Externalities
The above table shows that the external cost generated by roundtrip travel to and
from the port complex depends, in part, on the route taken. To calculate a uniform toll,
averaging across these routes is required. The general procedure is to construct a
weighted- average roundtrip external cost using the share of truck trips taken on each
route as weights. It is assumed that outbound trips follow the reverse of inbound trips. 26
There is very little information available on the exact distribution of port- bound
trips across routes. However, Meyer, Mohaddes Associates, Inc. ( 2004) complied data
on the number of trucks traveling each highway around the port complex from a
comprehensive survey of local truckers; the data are limited to trips taken during the mid-day
interval of the peak period. 27 Because this is the only known information of its kind,
it is used here to impute the share of trips taken on each route for all travel- time intervals.
Assuming that the mid- day trip distribution can be extrapolated to all travel periods is
somewhat heroic, but it is presumably superior to constructing a “ simple average” across
route costs. Table 14 reports the ( imputed) share of port- bound trips taken on each route.
26 An implicit assumption is that peak and off- peak trips do not overlap. For instance, a truck may enter the
port complex during peak gate hours and exit during the off- peak period. This possibility is omitted from
the analysis due to a lack of data on the frequency of such occurrences.
27 See Meyer, Mohaddes Associates, Inc. ( 2004), Exhibit 21, p. 40.
32
Table 14
Shares of Peak- Period Terminal Trips by Route
Inbound Route Share of Peak- Period Trips
10W- 605S- 105W- 710S 8.2%
10W- 605S- 91W- 710S 8.2%
605S- 105W- 710S 7.8%
605S- 91W- 710S 7.8%
105W- 710S 13.7%
91W- 710S 14.7%
405N- 710S 10.6%
105W- 110S 8.1%
91W- 110S 8.2%
405S- 110S 12.7%
a Source: Imputed from Meyer, Mohaddes Associates, Inc. ( 2004), Exhibit 21, p. 40.
For example, the table suggests that 14.7% of all inbound trips occur on westbound
Highway 91, connecting to southbound Interstate 710, representing trips from east of Los
Angeles to the Port of Long Beach.
Using these route shares as weights, a weighted- average, roundtrip external cost is
constructed across these routes for peak and off- peak travel. Of course, the routes listed
are by no means exhaustive; it is assumed that these routes are the most heavily traveled
by port- bound trucks and that the externalities generated on omitted routes are small by
comparison. Table 15 reports the peak and off- peak roundtrip external costs for each
route and the route shares used as weights for each route.
Table 15
Weighted- Average of External Costs Across Routesa
Inbound
Route
Peak
External
Cost
Off- Peak
External
Cost
Route
Share
Share- Weighted
Peak
Externality
Share- Weighted
Off- Peak
Externality
10W- 605S- 105W- 710S $ 28.36 $ 4.98 8.2% $ 2.32 $ 0.41
10W- 605S- 91W- 710S $ 36.10 $ 4.65 8.2% $ 2.96 $ 0.38
605S- 105W- 710S $ 21.88 $ 5.53 7.8% $ 1.71 $ 0.43
605S- 91W- 710S $ 29.62 $ 4.14 7.8% $ 2.32 $ 0.32
105W- 710S $ 12.02 $ 3.13 13.7% $ 1.64 $ 0.43
91W- 710S $ 19.76 $ 2.41 14.7% $ 2.90 $ 0.35
405N- 710S $ 12.37 $ 1.75 10.6% $ 1.32 $ 0.19
105W- 110S $ 13.45 $ 3.61 8.1% $ 1.09 $ 0.29
91W- 110S $ 21.19 $ 3.90 8.2% $ 1.74 $ 0.32
405S- 110S $ 13.80 $ 3.91 12.7% $ 1.75 $ 0.50
Weighted Average $ 19.75 $ 3.63
a Measured in 2007 U. S. Dollars per roundtrip.
33
The sum of the weighted route costs gives the weighted- average external cost for peak
and off- peak trips. The table shows that, on average, each truck making a roundtrip
during the peak period generates an externality of $ 19.75; an average externality of $ 3.62
is generated during each off- peak trip.
4.6 Terminal- Gate Externalities
Table 15 above only provides estimates for the external congestion costs
generated along the Los Angeles highways leading to and from the port complex.
External delays are also suffered, however, upon arrival by trucks waiting to be processed
at terminal gates. It is also quite likely that trucks suffer external delays inside the
terminals as well. The externalities suffered on terminal property, however, are beyond
the scope of the present study. Instead, the external costs at terminal gates are measured
from arrival at the terminal to departure from the gate pedestal. 28
Equation ( 7) is particularly useful for estimating external delays at terminal gates
because these gates exhibit classic bottleneck behavior. When the arrival rate of trucks
( v) exceeds the pedestal’s processing capacity ( vk), the pedestal acts as a bottleneck and
delays are generated in the form of truck queues. The external cost caused by an
additional truck arrival is given by equation ( 9), noting that only truck VOT and inflows
are relevant ( γ and v). So the analysis proceeds similarly to that conducted for highways
in previous sections. In this case, truck waiting times ( T) are related to truck arrival rates
in order to estimate the parameters of equation ( 7).
Only a handful of studies provide information on waiting times and arrival rates at
the San Pedro Bay port complex, most notably Ioannou et al. ( 2006), Giuliano et al.
( 2006), and Lam et al. ( 2006). Data for the present analysis are drawn from Ioannu et al.
( 2006), however, because waiting times and arrival rates are available by peak- period
time of day. This also provides enough data points to estimate ( 7) and allows for
separating the resulting externality estimates into the time intervals given in Table 6.
Table 16 and Figure 4 depict the relationship between waiting times ( in minutes) and
truck inflows ( in arrivals per minute) for a single day at an undisclosed terminal gate. 29
28 A gate pedestal is where truck transactions are processed. For example, a truck dropping off a load
requires a “ ticket” issued at the pedestal before entry into the terminal is permitted. At busy terminal gates,
truck queues typically form behind each pedestal.
29 See Ioannu et al. ( 2006), Figure 41, p. 76.
34
Table 16
Peak- Period Terminal- Gate Truck Waiting Times and Arrival Rates by Time of Daya
Time of Day Waiting Timeb Arrival Ratec
8: 45 3.0 1.80
9: 15 6.0 2.00
9: 45 14.0 2.20
10: 15 6.0 1.60
10: 45 3.0 1.20
11: 15 6.5 0.90
11: 45 5.0 1.30
12: 15 7.5 1.10
12: 45 6.5 1.50
13: 15 3.0 1.30
13: 45 4.0 1.40
14: 15 3.5 1.90
14: 45 4.5 1.75
15: 15 8.0 1.90
15: 45 3.5 1.70
16: 15 2.0 0.90
a Source: Ioannu et al. ( 2006), Figure 41, p. 76.
b Measured in minutes.
c Measured in trucks per minute.
Figure 4
Terminal- Gate Waiting Times and Truck Arrival Rates by Time of Daya
0
2
4
6
8
10
12
14
16
8: 45
9: 15
9: 45
10: 15
10: 45
11: 15
11: 45
12: 15
12: 45
13: 15
13: 45
14: 15
14: 45
15: 15
15: 45
16: 15
Time of Day
Waiting Time ( minutes)
0
0.5
1
1.5
2
2.5
Arrival Rate ( trucks/ min.)
Wait Time
Arrival Rate
a Source: Ioannu et al. ( 2006), Figure 41, p. 76.
The shortest waiting time given in Table 16 ( the last entry) is two minutes. This value is
used for the “ free- flow” parameter, Tf, in equation ( 7), which implicitly assumes that
pedestals can process one truck every two minutes without creating queues.
35
The results from estimating ( 7) are provided in Table 17. Figure 5 plots the
actual waiting times and those predicted from ( 7) by time of day. The figure shows that
predicted waiting times follow actual waiting times somewhat closely. 30
Table 17
Estimation Results for Truck Waiting Times at Terminal Gates
Parameter Estimate t- Statistic
Pedestal Processing Capacity ( vk) a 0.3031 4.20
Bottleneck Duration ( w) b 0.9587 3.40
Adjusted R2 0.7981
a Measured in trucks processed per minute.
b Measured in minutes.
Figure 5
Predicted and Actual Terminal- Gate Waiting Times by Time of Day
0
3
6
9
12
15
8: 45
9: 15
9: 45
10: 15
10: 45
11: 15
11: 45
12: 15
12: 45
13: 15
13: 45
14: 15
14: 45
15: 15
15: 45
16: 15
Time of Day
Waiting Time ( minutes)
Predicted
Actual
Using equation ( 9), Table 18 reports the external costs produced at terminal gates
by each additional truck arrival. These costs are separated into those generated during
the three peak- period intervals in Table 6, based on the average arrival rates during those
intervals. By assumption, terminal- gate externalities are negligible during off- peak gate
hours. The table also reports the share of peak- period trips taken during each of these
intervals based on the information in Table 9.
30 The model underestimates one large waiting time, which could bias the resulting externality estimates
slightly downward.
36
Table 18
Terminal- Gate External Costs by Peak- Period Travel- Time Interval
Travel- Time Interval Truck Arrival Ratea External Costb Share of Peak- Period Trips
7: 00 a. m. – 9: 00 a. m. 1.90 $ 2.49 29%
1: 00 p. m. – 3: 00 p. m. 1.53 $ 1.99 44%
3: 00 p. m. – 6: 00 p. m. 1.53 $ 1.99 27%
Weighted Average $ 2.13
a Measured in trucks per minute.
b Measured in 2007 U. S. Dollars per trip.
Table 18 also reports a weighted- average external cost across these intervals, where the
trip shares reported in Table 18 serve as weights. This represents the average external
cost generated by each truck arriving at a terminal gate during peak gate hours and
facilitates the construction of a uniform peak- period truck toll.
5. Peak- Period Truck Tolls
Table 19 summarizes the external costs implied by the all of the estimates
developed in Section 4.
Table 19
Summary of Roundtrip External Cost Estimatesa
Peak Gate Hours Off- Peak Gate Hours
Average Highway External Cost $ 19.75 $ 3.63
Average Terminal- Gate External Cost $ 2.13 -
Sum of External Costs $ 21.88 $ 3.63
a Measured in 2007 U. S. Dollars per roundtrip.
The optimal peak- period truck toll is given by the difference between the peak and off-peak
congestion externalities generated by truck trips to and from the port complex,
including those generated at terminal gates during peak gate hours. With the constraint
that no tolls can be levied during the off- peak period, and assuming that the toll is not
large enough to divert shipments to competing ports, equation ( 6) prescribes the optimal
toll. Because a single, uniform toll is desired, the external- cost measures applied to ( 6)
represent weighted- average costs, where averaging is performed across time and routes. 31
31 Given that off- peak tolls are prohibited, “ optimal” is used here in a “ second- best” context. Moreover, the
averaging of external costs across routes and travel- time intervals may reduce the relative efficiency of this
toll.
37
The results in Table 19 suggest levying a toll of $ 18.25 ( i. e.
$ 19.75 + $ 2.13 − $ 3.63) for each round- trip taken by all trucks during peak gate hours.
Of this toll, $ 16.12 ( i. e. $ 19.75 − $ 3.63) is attributable to congestion on the highway
system surrounding the port complex, and $ 2.13 is attributable to congestion at terminal
gates.
6. Discussion Points
6.1 Levying Tolls on All Truck Trips
A key distinction between the current Traffic Mitigation Fee and the toll
estimated herein is that the latter does not discriminate by trip purpose. The TMF applies
to loaded ocean containers, but does not apply to bobcats, empty chassis, domestic
containers, or containers designated for transshipment to other ports. Intermodal
containers that depart or arrive via the Alameda Corridor for import or export are also not
subject to the TMF. However, the above estimates demonstrate that all port trips
regardless of purpose generate congestion externalities, which must be considered if tolls
are aimed at correcting highway and terminal congestion externalities. The $ 18.25 toll is
small in comparison to the current fee of $ 50 per TEU, which often amounts to $ 100 per
loaded truck. 32 From the standpoint of alleviating congestion externalities, it might be
argued that shippers and consignees subject to the current TMF are paying “ too much”
while those dispatching trucks for other purposes are paying “ too little”. Of course, there
may be political or institutional objections to levying tolls on all truck trips. But the
sizeable discrepancy between the current TMF and the optimal toll might warrant further
discussion on why the burden of relieving congestion and financing off- peak operations
falls squarely on those conducting a limited class of gate moves.
6.2 Congestion Externalities on Surrounding Highways
Much of the public discussion on congestion at the San Pedro Bay ports revolves
around traffic along the two major highways leading to the ports, Interstates 710 and 110,
and at terminal gates. The results presented here emphasize, however, that port- bound
trucks also interact with non- port traffic throughout the surrounding highway system.
For instance, Table 13 shows that peak- period roundtrip travel using Interstates 10, 605,
91, and 710 generates a congestion externality of $ 36.10. This is mainly attributable to
trucks interacting with large volumes of regular commuters on each of these heavily-traveled
highways. By comparison, the peak- period congestion externality suffered at
terminal gates is $ 2.13. Although adding one truck to a gate queue delays all trucks
further back in the queue, the sum of these delays is small in comparison to summing the
delays imposed by the same truck on a large number of highway users. As such, traffic
solely along I- 710, I- 110, and at terminal gates is only responsible for a relatively small
32 The most common container size encountered at the port complex is 40 feet or 2 TEU’s.
38
portion of the congestion costs created by port traffic. This portion becomes smaller if
considering a larger area of the highway system than depicted in Figure 1. A more
holistic view of port- related congestion may thus be warranted when prescribing truck
tolls to manage this congestion.
6.3 Revenue Requirements
A critical concern for terminal operators is ensuring enough revenue to cover the
increased gate costs resulting from off- peak operations. The current TMF of $ 50 per
TEU is calculated strictly on the basis of cost recovery. The salient question is whether
or not the revenues generated by the $ 18.25 toll determined above, which is estimated
without any revenue- requirement constraint, would be sufficient to cover these increased
gate costs.
According to PierPass ( 2006), the net increase in gate costs resulting from the
current OffPeak program is roughly $ 12.6 million per month. A monthly volume of
roughly 263,000 twenty- foot- equivalent containers are subject to the TMF. Dividing the
increased gate cost by this volume yields a cost per TEU of about $ 48. Adding $ 2 for
overhead costs yields the current TMF of $ 50 per TEU. Total TMF revenue is about $ 13
million per month, or $ 657,000 per day.
Based on estimates from Port of Long Beach ( 2004) and Meyer, Mohaddes
Associates, Inc. ( 2004), about 30,000 trucks per month passed through terminal gates
during peak hours in 2005.33 Assuming an annual growth rate in trip volume of 7.6%
( Fischer 2005), roughly 38,000 trucks per month will make peak- period trips in 2008.
Applying a toll of $ 18.25 to this volume of trips yields $ 693,500 in daily toll revenue, or
roughly $ 13.9 million per month. 34
The toll will induce some non- loaded truck trips into the off- peak period, but will
also shift some loaded truck trips back into the peak period. The net effect is not known
as the OffPeak program is relatively new and the data required for estimating peak- period
trip demand is quite scarce. The point to be taken from the above discussion, however, is
that the revenue generated by an $ 18.25 toll on all truck trips may be sufficient to cover
increases in off- peak gate costs. 35
6.4 Caveats
The analysis in this study attempts to gauge the magnitude of an economically
efficient peak- period truck toll, and how it compares to the current TMF. The toll
estimated herein is based entirely on external costs attendant to delayed travel. Several
strong assumptions are required to achieve this estimate and, as such, it should be viewed
33 See Meyer, Mohaddes Associates, Inc. ( 2004), Table 5, p. 27.
34 The monthly figure assumes twenty peak periods per month.
35 Note that a reduction in off- peak trips will also reduce off- peak gate costs.
39
more as a useful starting point rather than a toll that warrants immediate implementation.
Ultimately, this study’s primary contribution is the development of a framework for
pricing port- related traffic, not necessarily the price itself. To implement this framework,
further consideration must be given to each of the key assumptions and estimated
parameters discussed throughout this study.
Note also that the idea of pricing externalities extends beyond those attendant to
travel delays. For example, a major policy concern is the external pollution costs
generated by trucks idling inside terminal gates. Further study on the per- trip magnitude
of environmental externalities would be most useful for expanding the scope of the tolls
discussed here.
Also warranted is comprehensive research on estimating the overall demand for
trips to the port complex. This would allow for a more through analysis of toll revenues
and for estimating tolls without assuming that overall demand is perfectly inelastic. Data
limitations impede current efforts to do so, but observable changes in trip prices and
volumes in the future, perhaps due to changes in future TMF levels, may bear fruit for
further research.
7. Summary
The OffPeak program can be viewed as an investment in capacity expansion,
where revenues from the program’s Traffic Mitigation Fee pay for this investment.
However, fully exploiting the economic efficiency of this expansion, taking into account
the congestion externalities generated by truck travel to and from the ports, requires a
congestion- pricing mechanism that looks beyond cost recovery.
This study develops an empirical framework for estimating a peak- period truck
toll designed to efficiently balance peak and off- peak truck traffic on the surrounding
highway system and at terminal gates. Like the current TMF, this pricing mechanism
operates under the constraints that a toll cannot be assessed during off- peak gate hours,
and that the toll is uniform across the peak period. Unlike the TMF, however, the toll
developed herein applies to all truck trips rather than only to a limited class of container
moves. This distinction is drawn because the toll is designed to correct congestion
externalities, and all port- bound truck trips generate these congestion externalities
regardless of purpose.
Estimation results suggest that the bulk of the congestion externalities generated
by trucks during the peak period occur on the highway network enveloping the ports –
beyond more- often discussed facilities such as Interstates 110 and 710 and terminal gates.
The intuition is that trucks typically interact with thousands of vehicles on several
crowded highways during each leg of their inbound and outbound trips. As such, using
tolls to correct these externalities may warrant a more holistic public discussion of port-related
congestion.
40
The peak- period truck toll estimated herein is $ 18.25 per roundtrip and is
expected to generate roughly $ 14 million in monthly toll revenues during the coming
year. These revenues are on the same order as the current net increase in off- peak
terminal operating costs, suggesting that an efficiency- maximizing toll may be
compatible with the cost- recovery goal of the current TMF.
Compared to the current TMF, which often amounts to $ 100 per loaded- container
move, the toll of $ 18.25 is small. A possible interpretation of this result is that the burden
of relieving congestion and financing the OffPeak program may be focused to narrowly
on a limited class of container moves. By assessing the $ 18.25 toll on all truck trips,
including the movement of empties, domestic containers, intermodal containers, and
containers designated for transshipment, this burden can be spread to a broader class of
trip purposes while still meeting the objectives of economic policymakers and terminal
operators.
Overall, this study aims to guide further research on managing congestion at the
San Pedro Bay port complex. Although its empirical results are informative, they can be
dramatically affected by modifying their underlying assumptions or adopting alternative
estimation methods. Moreover, the empirical framework developed in this study can be
greatly improved, for instance, by broadening its scope to include other externalities such
as air pollution, and by incorporating detailed information on the overall demand for port
traffic. Efforts to improve this framework would greatly benefit from cooperation and
data sharing between policymakers, analysts, port authorities, trucking firms, and marine
terminal operators.
41
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