Transport Policy 41 (2015) 68–79

Contents lists available at ScienceDirect

Transport Policy journal homepage: www.elsevier.com/locate/tranpol

Policy lessons for regulating public–private partnership tolling schemes in urban environments Omid M. Rouhani a, H. Oliver Gao a,b,n, R. Richard Geddes c a

School of Civil and Environmental Engineering, Cornell University, Hollister Hall, Ithaca, NY 14853, USA Shanghai Oriental Scholar, Sino–US Global Logistics Institute, Antai College of Economics and Management, Shanghai Jiaotong University, Shanghai 200030, PR China c Department of Policy Analysis and Management, Cornell University, 251 Martha Van Rensselaer Hall, Ithaca, NY 14853, USA b

art ic l e i nf o

a b s t r a c t

Available online 15 April 2015

Public–private partnerships (P3s) are likely to impact entire transportation systems in fundamental ways. However, few studies have examined the potential impact of P3s on large-scale transportation networks. These studies have focused on modeling rather than on policy analysis. The literature thus does not offer guidance for designing and administering P3s to improve transportation system performance while maintaining profitability. Using Fresno, California's transportation network as a laboratory, we consider the effects of alternative P3 tolling approaches on profit maximization and system performance optimization at full urban transportation network scale. Based on system modeling results, we offer the following recommendations for policy makers to design and promote successful P3s in urban settings: (i) to promote a profitable and a socially beneficial system, toll rates should be set examining both profitmaximizing and system-optimal rates; (ii) even though tolls (i.e., higher travel costs) on a few roads help reduce travel demand they may, counter-intuitively, lead to higher total travel cost for the overall transportation system because of users’ decision to travel longer distances to avoid tolls, especially when high toll rates are applied; (iii) lower limit(s) on tolls (in addition to upper limits) may be required to enforce system-optimal tolling and avoid undercutting by private owners; (iv) a variable tolling approach (i.e., temporally- and spatially-varying tolls) significantly reduces congestion and increases profits relative to flat tolls; and (v) public officials should provide a comprehensive plan regarding past, current, and future P3 projects along with a detailed system-wide impact analysis to promote a more sustainable transportation system. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Public–private partnership Road pricing Transportation networks Tolling regulation System performance

1. Introduction Sharp declines in funding from traditional sources combined with large, ongoing investment needs suggest that a major change in transportation policy is required. The main transportation infrastructure funding source—fuel tax revenue—is falling as vehicular fuel efficiency rises and as annual vehicle miles travelled in the United States declines (American Society of Civil Engineers, ASCE, 2013). Many segments of the U.S. transportation are old and in poor condition (The Road Information Project TRIP, 2011). Moreover, fuel taxes cannot provide the flexibility necessary to incentivize efficient use of transportation resources (Kim et al., 2008; Rouhani, 2009). Public–private partnerships (P3s) have been viewed by many experts as an alternative mechanism that can help address such problems. To tackle the intensifying challenges n Corresponding author at: School of Civil and Environmental Engineering, Cornell University, Hollister Hall, Ithaca, NY 14853, USA.

http://dx.doi.org/10.1016/j.tranpol.2015.03.006 0967-070X/& 2015 Elsevier Ltd. All rights reserved.

faced by the U.S. transportation system, both the public and private sectors should search for more innovative yet measured P3 models and accompanying legislation (Zhang, 2005; Chung et al., 2010; de Jong et al., 2010). Our knowledge of P3’s system-wide effects is limited. Generally, previous research has relied on a project-specific approach. Overall P3 success, however, hinges on more than project-specific financial analysis. Therefore, it is critical to develop better insights into the range and types of regulatory processes that successfully support P3s in transportation networks (see e.g., Chen and Subprasom, 2007; Rouhani and Niemeier, 2011; Rouhani, 2012). Several studies have examined private participation in largescale transport networks. Zhang and Levinson (2009) evaluated short-run and long-run network performance under alternative ownership structures (private/public and centralized/decentralized). Zhang (2008) analyzed the combination of pricing, investment, and ownership to study the welfare impacts of road privatization on a large-scale network (the Twin Cities). Dimitriou et al. (2009) developed a game-theoretic formulation for the joint

O.M. Rouhani et al. / Transport Policy 41 (2015) 68–79

optimization of capacity investments and toll charges, examining practical issues such as the regulation of tolls on privately-operated highways. Rouhani et al. (2013) used demand analysis and game theory concepts to model the effects of including several concession projects on a number of system performance measures. Existing studies have focused either on model development (see above) or on real-life P3 projects analysis only without a systems perspective (e.g., Evenhuis and Vickerman, 2010). Key policy insights about how the implementation of P3 projects affects a transportation system as a whole and how the P3 contracts should be regulated in urban transportation systems are absent in the literature. We attempt to fill that gap and generate policy recommendations by simulating recurrent traffic congestion under various P3 approaches, using the Fresno, California road network as a mid-size urban system case study. We focus mainly on regulating P3s that grant a private developer (usually a consortium of firms) the right to collect tolls from an existing facility under a long-term concession contract. Public-sector project sponsors retain monitoring and enforcement responsibilities (Reason Foundation, 2009). Our goal is to offer insights into the following fundamental issues: (i) the distinction between profit/revenue-maximizing and system performance-optimizing road pricing; (ii) the merits of providing spatially- and temporally-variable tolling as compared to flat-rate tolling; (iii) the impact of toll collection costs; and (iv) the effect of P3s on system-wide travel costs, including emissions and fuel consumption. We conclude by suggesting a list of major factors that the public sector should take into account when planning for the use of P3s on toll roads in an urban setting.

2. Methodology and case study 2.1. Modeling The basic mathematical approaches borrow from our previous studies, including modified traffic assignment (Rouhani and Niemeier, 2011), profit maximization (Rouhani et al., 2013), general system cost minimization (Rouhani and Niemeier, 2014a), and spatial variation in tolls (Rouhani and Niemeier, 2014b). To model different problems, we employ a bi-level programming framework. At the higher level, policy makers/private operators pursue two basic objectives for system operation: transportation system performance optimization and toll-profit maximization. At the lower level, travelers react to the application of various toll schedules and modify their travel choices. We provide a brief description of the two major higher-level problems we consider: (1) the transportation system general cost minimization (SGCM) problem in order to optimize system performance; and (2) the profit-maximization problem (PMP). The SGCM problem minimizes a monetary combination of total travel time, fuel consumption, and emissions costs over a transportation system, excluding toll costs since tolls are transfers between two groups and do not affect system performance. SGCM accounts for the social welfare loss resulting from reduced travel demand as well (Rouhani and Niemeier, 2011). The problem’s decision variables are the toll rate on each of the candidate roads. Policy makers might use the resulting system-optimal rates from SGCM as the basis for limiting private firm’s toll rates. The PMP simulates a different problem: private firms solve for the profit (or revenue minus toll collection cost) maximization problem and find the corresponding optimal toll rate. However, the toll rate might be constrained (i.e., capped) by P3 contracts, which could affect the optimal toll rate and the optimal profit from toll collection. To account for the impact of toll collection costs, we solve two versions of the PMP problem: (1) revenue maximization

69

by ignoring toll collection costs; and (2) profit maximization taking toll collection costs into account. An important extension of the PMP and SGCM models, called a “spatial variation model,” allows tolls to vary across different segments of the tolled road (Rouhani and Niemeier, 2014b). Spatial variation in tolls can induce a more-profitable or a system-improving efficient traffic flow pattern. The problems discussed above all use a modified user-equilibrium (UE) model as the underlying (lower-level) model to simulate users’ behavior. The modified UE assumes that users account for general costs of travel rather than travel time only. The modified model updates origin/ destination (O/D) demand iteratively, considering the updated (higher) general costs of travel.1 2.2. Assumptions For simplicity and because of modeling constraints, we make several basic assumptions. We have divided our assumptions into three categories 2.3. Transportation planning model (1) The transportation planning model is a static deterministic user-equilibrium model (Sheffi, 1984); (2) neither the city of Fresno nor its planning model has a strong public transportation system. Therefore, we do not consider potential switching to a public transportation mode; and (3) the planning model is a single-user equilibrium model. Because of variations in the value of time (VOT) for different user classes, a single-user equilibrium model is inadequate for a comprehensive analysis of impacts across user classes. However, city-size models generally do not cover multi-class user equilibrium features, as for our transportation planning model. Hence, we focus mainly on the aggregate impacts on average users.

2.4. General travel costs (1) Using a slightly lower rate than the average wage of $16.79 per hour for Fresno (Schrank et al., 2012), we assume that an average user values time at $14/hour. Considering the load factor of 1.4 persons/vehicle, the value of time for each vehicle is estimated at $20/hour (14
1.4); (2) based on California Air Resources Board’s (CARB’s) EMFAC (2011) model for mobile emissions inventory calculation, the emission factors are calculated using the VMT-weighted averages for different vehicle classes at different speeds (Rouhani and Gao, 2014); and (3) to calculate transportation system emissions and fuel costs, we use the following parameters: $25/ton of CO2, $250/ton of CO, $7000/ton of NOx, $3000/ton of TOG, $30,000/ton of PM10, $300,000/ton of PM2.5. 2

2.5. Tolling (1) For flat tolls, tolling agencies apply a constant mileage-based toll rate on all toll road segments. For variable tolls, the toll rate is different for each road segment (spatial variation) and/ 1 See Appendix for detailed information about the mathematical models used in this study. 2 These criteria-pollutant health-related cost rates are the average estimates of the following studies: Wang et al. (1994), McCubbin and Delucchi (1999), and AEA Technology Environment (2005). We also assume $4 per gallon of gasoline.

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or for each time period (temporal variation or peak versus offpeak); (2) The operating cost of toll collection is assumed to be $0.2 per transaction, based on the operating costs of various tolling agencies in practice (Balducci et al., 2011): the operating costs of Toronto 407 and Dulles Greenway (both run by private agencies) averaged around $0.3 per transaction in 2007, and operating costs for urban and multi-road agencies, with a higher number of transactions, averaged around $0.16 per transaction; and (3) For the capital cost of toll collection, we base our calculation on the average capital cost of Toronto 407 and Dulles Greenway (Balducci et al., 2011). Using a 30-year payback period and a 5% discount rate, we estimate the annual average capital cost for these roads to be $1.2 million per mile. Accordingly, we assume capital costs of $1.2 million per mile for highways and $1.5 million per mile for arterials since arterials have a higher number of access points (i.e., more tracking devices). In addition to the above basic assumptions, we ran a sensitivity analysis on the major parameters in the Results section. Sensitivity analysis clarifies the effect of deviations from the basic values assumed for the parameters. 2.6. Case study

Table 1 Main characteristics of the candidate roads. (Source: transportation planning model, city of Fresno—2030 forecasts) Name Length-private (Mile)

HW-1 SR168 4.92 HW-2 SR180 5.23 Arterial-1 Shaw 8.47

Freeflow speed (MPH)

AM Peak VMT (basehourly)

Off-peak VMT (basehourly)

65 58 40

70,265 68,701 44,163

28,009 30,138 14,710

We do not necessarily suggest Fresno as the suitable place to implement P3 toll roads. However, our goal is to estimate the impact of alternative P3 tolling approaches on a large metropolitan transportation system, using a travel demand model. The Fresno network consists of 20,865 links and 1852 traffic analysis zones. As shown in Fig. 1, we selected three segments of roads as candidate P3 concession toll projects, including two highways (SR168 and SR180); and one arterial (Shaw). This choice leaves the majority of the system toll free. Table 1 presents the main features of the selected roads for the do-nothing case (where no tolling scheme is applied). The roads were selected on the basis of profit potential to encourage private participation and congestion reduction to reduce overall travel costs.

We study the City of Fresno and use its transportation planning model with a calibrated base year of 2003 and future year of 2030.

Fig. 1. Road network of Fresno, California with P3 candidate roads. Source: transportation planning model, city of Fresno.

O.M. Rouhani et al. / Transport Policy 41 (2015) 68–79

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Table 2 Comparison of toll rates: our estimated rates versus rates in practice (for passenger cars). Our study

Real cases

System optimal

Peak rate (Cents/mile) Off-peak rate (Cents/mile)

Profit optimal

Revenue optimal

HW1

HW2

Art1

HW1

HW2

Art 1

HW1

HW2

Art1

25 32

27 25

22 12

47 31

73 59

77 127

33 20

44 17

41 18

3. Results To generate policy insights into best P3 practices in urban environments, we solve for the SGCM and PMP problems under various conditions and calculate the general outcomes under alternative toll rates. We begin the results section with a detailed examination of how toll rates should be designed to satisfy different objectives (Section 3.1), and follow with a discussion of the benefits of temporal and spatial variation in tolling (Section 3.2). Finally, we conduct a sensitivity analysis on some key parameters of the model to verify our results (Section 3.3). 3.1. Toll rates Toll rates play an important role in the analysis of P3s. To provide a general vision about the level of toll rates, we start by comparing our estimated toll rates for the three candidate roads (solving the problems in Section 2.1) to the actual toll rates implemented on U.S. toll roads. As shown in Table 2, our estimated profit-maximizing tolls (the solutions of PMP) range from 47 to 77 cents per mile for morning peak hours and 31–127 cents per mile for off-peak hours. These rates are generally higher than the rates of 46 cents per passenger car (PC)-mile for the Chicago Skyway and 3 cents per PC-mile for the Indiana Toll Road, which is mainly a rural road (FHWA, 2011). Our calculated profit-maximizing rates are also higher than Dulles Greenway tolls–37 cents per mile for peak and 31 cents/mile for off-peak hours (Dulles Greenway, 2012), and definitely higher than value-added tolling–15 cents per mile for peak and 5 cents for off-peak hours (Poole, 2011). The fact that profit-making rates are higher than the actual rates suggests that for U.S. toll facilities, toll ceilings effectively limit toll rates. However, our calculated revenue-optimal rates (33–44 cents per mile for peak and 17–20 cents per mile for off-peak) are mostly lower than toll rates employed in practice. Therefore, for cases where toll collection costs are sunk (e.g., when toll collection infrastructure already exists, so road owners maximize revenue rather than profit), much lower toll rates are expected. On the other hand, our system-optimal rates3 (from solving SGCM problems) are in the range of 12–32 cents per PC-mile, which are mostly lower than real rates applied on U.S. toll facilities. In fact, it appears that U.S. toll rates are set between the profit-maximizing and system-optimal levels, possibly to address a combination of profit-making and congestion-reduction objectives. A side note is that toll rates vary from one case to another and should be set differently for alternative transportation network configurations, for different travel demand levels, and for different user characteristics. In fact, our estimated profit-optimal and system-optimal rates dramatically differ from one candidate road to another and from one time period to another. Therefore, 3 System-optimal rates minimize the total system travel costs including time, fuel, and emissions costs (excluding tolls since tolls could be viewed as money transfers between two groups and they do not affect system performance). These travel cost components are summed converting all these costs into monetary terms.

Chicago Skyway

Indiana Toll Road

Dulles Greenway

46 

3 

37 31

this simple comparison between the toll rates might not be valid for some cases. One important policy insight about implementing various toll rates relates to their general effects on revenue, profit, and system performance. Fig. 2 shows total hourly toll revenue, toll profit (revenue minus cost), and system-wide travel costs as functions of toll rates applied to Highway no.1–SR 168. These hourly values are estimated for morning peak hours (Fig. 2-a1 and a2) and for offpeak hours (Fig. 2-b1 and b2) applying different toll rates (in dollars-per-PC-mile) on the highway. The revenue and profit are estimated using two versions of the PMP problem: without toll collection costs (revenue maximization) and with toll collection costs (profit maximization), respectively. The system cost is estimated using the SGCM objective function value. Note that tolls on only one road (or one road segment) can impact the performance of the whole transportation network via changing traffic patterns. The first observation in both Fig. 2-a1 and b1 is that the tolls that optimize revenue and profit are substantially different from the tolls that optimize system performance. That difference induces different user behavior and different traffic flow patterns. As a result, it creates a difference in total system travel costs across system-optimal tolls and profit- and revenue-optimal tolls. As can be seen in Fig. 2-a1, profit-optimal and even revenue-optimal tolls increase total system travel costs (system cost is the dotted line) relative to the do-nothing scenario (where the toll rate is zero). This suggests that allowing unconstrained tolls with a profitmaximization goal might diminish system performance. For instance, the profit-optimal toll rate on Highway no.1 increases system-wide social costs of travel by equivalent to $50,000 hourly (or about 2% increase relative to the no-toll case), resulting in a $75 million annual increase in system travel costs, including time, fuel, and emissions costs. The increase in system travel costs (excluding toll costs) occurs despite the fact that implementing tolls increases private costs of driving and thus decreases travel demand. Our analysis also suggests that, under certain conditions, the profit- and revenue-maximizing tolls can be lower than systemoptimal tolls (see for example for Highway no.1 in off-peak hours, as shown in Fig. 2-b1). In fact, a profit-maximizing operator may rationally charge a toll rate lower than the system-optimum (which should be set as the price cap in a P3 contract). Therefore, from a systems perspective, not only should policy makers place an upper limit (i.e., a cap) on tolls for each time period, they should also set a lower limit on tolls which stops road operators from undercutting the applied upper toll limit(s). To better understand the above-mentioned results in terms of changes in travel demand, we examine the impact of different toll rates on the transportation system under two categories: (i) effects on the tolled road; and (ii) effects on all other parts of the network. Fig. 2-a2 and b2 shows how VMT on the tolled (own) road, total VMT on all other roads of the transportation system, and total number of trips change as the toll rate on Highway No.1 increases. Fig. 2-a2 shows an interesting result for peak hours: although VMT on the tolled highway decreases as tolls increase, VMT on all other roads increases even more. As a result, total system VMT increases with tolls. Despite the decrease in total trips, high tolls

2,700 2,660

8,000

2,620

6,000 4,000

2,580

2,000 -2,000

2,540 0

0.3

0.6

0.9

Tolls ($/mile)

2,500

60

0

50

-50

40

VMT decreaseOwn VMT increaseOthers Vehicle trips change

30 20

-150 -200 -250

10 0

-100

0

0.3

0.6

-300 0.9

Tolls ($/mile)

2,000

Revenue

917

Profit

907

Total cost

897 887

1,000

877 0

0

0.3

0.6

-1,000 -2,000

0.9

867 857 847

Tolls ($/mile)

837

60

0

50

-50

40

-100

VMT decreaseOwn VMT increaseOthers Vehicle trips change

30 20

-150 -200 -250

10 0

0

0.3

0.6

Vehicle trips change (hourly)

10,000

Total cost

Revenue ($/hour)

Profits

3,000

Changes in VMT (1000s hourly)

12,000

0

Changes in VMT (1000s hourly)

2,740

Revenue

Total system cost ($1000/hour)

Revenue ($/hour)

14,000

Total system cost ($1000/hour)

O.M. Rouhani et al. / Transport Policy 41 (2015) 68–79

Vehicle trips change (hourly)

72

-300 0.9

Tolls ($/mile)

Fig. 2. Total revenue, total profit, total system costs (1), and travel demand (2) when pricing Highway no. 1 for (a) peak and (b) off-peak hours.

could increase overall VMT since some users might decide to travel longer distances to avoid tolls. However, for low toll rates, such changes in VMT would lead to a lower system travel cost (as can be seen on Fig. 2-a1, total system costs first decreases with toll rates). That is because candidate roads are initially highly congested, and the switch to other less-congested roads could reduce total travel costs as long as the marginal decrease in congestion on the tolled road is significant. For off-peak hours (Fig. 2-b2), however, the decrease in toll-road VMT outpaces the VMT increase on other roads, since travel demand is more elastic during off-peak hours (i.e., users are more willing to choose not to travel during off-peak than during peak periods). For both peak and off-peak hours, the own-demand elasticities for revenue-optimal and profit-optimal toll rates are about –1 and lower than –1 (more than 1 in absolute terms), respectively. For system-optimal toll rates, however, peak demand elasticities are quite different from off-peak elasticities. Although own-elasticity could be an appropriate factor to calculate profits and revenues4, it is not the only factor for calculating system-optimal rates since those rates are also affected by network and spillover effects. Based on our results, system-optimal rates for a road could result in inelastic demand (–0.51 in peak hours, Fig. 2-a1), and they could also result in elastic demand (–1.30 in off-peak hours, Fig. 2-b1) for the same road but under different travel demand patterns (peak versus off-peak). 4 A profit maximizing firm sets its toll to maximize profit (π = p. q (p) ). The first order condition of the maximization with respect to own toll (p ) is q + p (∂q/∂p) ¼0 or q. (1 + (∂q/q)/∂p/p ) ¼ 0. So, when toll collection cost is zero, the firm maximizes revenues (profits) by setting a toll that results in an elasticity of –1, if there is no limit on tolls. When we add an increasing toll collection cost function with respect to q (decreasing with respect to the toll rate) to the analysis, the first order condition leads to a toll that induces demand elasticity lower than –1 (higher than 1 in absolute terms).

Fig. 3 shows total hourly revenue, profit, and the system-wide travel costs as functions of the toll applied to the Arterial (i.e., Shaw). The difference between the system, revenue, and profitoptimal tolls can be observed for the arterial, similar to Highway no.1 in Fig. 2. Another observation is that tolling a road may provide positive profits under one level of demand (Fig. 3-a1 for peak hours), but tolling the same road does not always provide positive profits under another level of demand (Fig. 3-b1 for off-peak hours), even when tolls are set at profit-maximizing levels. This result has an important policy implication: a profit-maximizing firm might only charge at peak hours, and set the toll rates at zero for off-peak hours, especially when the operating cost of toll collection is high relative to revenue, as could be the case for arterials with a larger number of entry and exit points and relatively low average VMT. As shown in Fig. 3, a profit-maximizing road owner might rationally set the off-peak prices at zero despite of the sunk capital costs of toll collection, and still make a positive profit with peak-hour pricing only. This result is specifically valid for arterials. Estimated toll collection costs (shown by the differences between revenue and profit for each toll rate) are substantial relative to their corresponding toll revenues (which can result in negative profits) due to the high transaction costs associated with the numerous entry and exit points specific to many urban systems. Hence, policy makers should favor less expensive toll collection systems in urban settings. Privately-operated systems might provide such low-cost systems because of scale or learning economies that cannot be obtained by government (De Bettignies and Ross, 2004). In general, the arterial’s travel demand trends with respect to tolls (Fig. 3-a2 and b2) are similar to the highway’s travel demand trends (Fig. 2-a2 and b2), but on a smaller scale, since an individual arterial’s effect on a system is generally less significant. To account for changes in various system cost components under alternative toll rates, we take travel time, fuel consumption,

2,570

0

2,520

0

0.3

0.6

1.2

Revenue

-3,000

2,470

Profits Total cost

-6,000

Changes in VMT (1000s hourly)

0.9

2,420

Tolls ($/mile)

0

45 40 35

-50

30 25

-100

20 15

VMT decreaseOwn VMT increaseOthers Vehicle trips change

10 5 0

0

0.3

0.6

-150

-200

0.9

897

1,000 0 -1,000

887

0

0.3

0.6

0.9

1.2

877 867 857

-2,000

847

Revenue

-3,000

Profit

837

Total cost

-4,000

827

Tolls ($/mile)

45

0

40 35

-50

30

VMT decrease-Own

25

VMT increaseOthers

20

-100

Vehicle trips change

15

-150

10 5 0

Tolls ($/mile)

0

0.3

-200

0.6

Total system cost ($1000/hour)

3,000

907

Vehicle trips change (hourly)

2,620

Revenue ($/hour)

6,000

73

2,000

Changes in VMT (1000s hourly)

2,670

Total system cost ($1000/hour)

9,000

Vehicle trips change (hourly)

Revenue ($/hour)

O.M. Rouhani et al. / Transport Policy 41 (2015) 68–79

0.9

Tolls ($/mile)

(1)

96.7

Total fuel cons. (1000 gal/hr)

Total travel time (1000 Veh.hr)

Fig. 3. Total revenue, total profit, total system costs (1), and travel demand (2) when pricing Arterial no.1 for (a) peak and (b) off-peak hours.

Arterial

95.7

Highway1 Highway2

94.7

Optimal : 21.9 cents

93.7 92.7

Optimal : 25.4 cents

91.7 90.7

Optimal : 10.9 cents

0

0.3

0.6

0.9

(2)

176 Arterial

175

Highway1 Highway2

174 173

Optimal : 20.9 cents

172 171

Optimal : 27.5 cents

170 169

Optimal : 25.4 cents

0

0.6

0.9

(3)

6.80

Total PM2.5 (1000grams/hr)

0.3

Tolls ($/mile)

Tolls ($/mile)

Arterial Highway1

6.70

Highway2

6.60 Optimal : 10.9 cents 6.50

Optimal : 21.9 cents Optimal : 13.7 cents

6.40

0

0.3 0.6 Tolls ($/mile)

0.9

Fig. 4. System-wide cost of (1) travel time (2) fuel consumption, and (3) PM2.5 emissions when pricing Highway no.1 and Arterial no.1 during peak hours.

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the optimal rates are usually very close for different cost components. The difference is particularly important for a city or region in a non-attainment area which requires conforming to a specific level of emissions in order to be eligible to receive a (federal) budget allocation (Gauna, 1995). In that case, we need a separate analysis on the optimal tolls to minimize emissions. Differences in optimal rates shrink further if weights (monetary costs) of the cost components are added since travel time is the dominant monetary factor. However, the tolls that minimize total travel time are not necessarily the same as the toll rate that minimizes total system travel costs. For example, the corresponding system-optimal rate for Highway No.2 (i.e., the rate that minimizes the combination of time, fuel, and emissions costs) is 21.7 cents per mile while the rate that minimizes total travel time is 10.9 cents/mile. In general, taking fuel consumption and emissions costs into account, in addition to commonly-considered travel time costs, is likely to have minor effects on system-optimal tolls since time is the main cost component. However, the magnitude of travel costs and the relevant system-wide benefits or costs of employing P3 projects would be greatly affected by adding fuel and emissions costs. Fig. 5 shows off-peak system cost trends, which are fundamentally different from those for peak hours (Fig. 4). Almost all toll schedules considered for off-peak periods would improve system performance (decrease travel cost components) relative to the do-nothing case (where tolls are zero), in contrast to what we found for peak periods. The reductions in fuel consumption are greater than the reductions in other cost components, and contribute more to improvements in system performance. For off-peak hours, the hockey-stick-shaped curves observed for peak hours change into sine-shape curves (especially for

(1)

31.7

(2) Total fuel cons. (1000 gal//hr)

Total travel time (1000 Veh.hr)

GHG emissions, and the criteria pollutant emissions to be the major travel cost factors in our analysis. For peak hours, Fig. 4 shows how total travel time (Fig. 4-(1)), total fuel consumption (Fig. 4-(2)), and total PM2.5 emissions (Fig. 4-(3)) change as tolls on the candidate roads increase. These figures do not include GHG emissions based on the rationale that GHG emissions are linearly related to fuel consumption. For peak hours (Fig. 4), the general trend for all cost components is that first, as tolls increase, system travel costs decrease. Once travel costs hit their minimum, system travel costs increase with toll rates. This is typical for tolling both highways and arterials. This result is counter-intuitive since higher toll rates are expected to decrease travel demand, and as a result, reduce system travel costs. However, traffic volume spillovers (intensifying congestion and increasing VMT on un-tolled roads, as shown in Figs. 2-a2 and 3a2) have adverse effects on the system during peak periods. For all cost components, the spillover effects are greater than the effects of lowering travel demand for peak hours when toll rates are high (more than $0.3/mile for all roads), as shown in Fig. 4 by higher total costs of these toll rates relative to the costs of no-tolling. Therefore, for high toll rates, the spillover effects dominate the congestion-reducing effect, thus diminishing overall system performance. Another important observation in Fig. 4 is that the toll rates that minimize different travel cost components generally differ. For example, the optimal rate to minimize total travel time on Arterial no.1 is 21.9 cents per mile (Fig. 4-(1)) while the optimal rate to minimize total fuel consumption is 20.9 cents per mile (Fig. 4-(2)). Although in some cases the difference is substantial (13.7 cents/mile minimizing total PM2.5 versus 25.4 cents/mile minimizing total time or total fuel consumption for the arterial),

Arterial

31.5

Highway1

Optimal : 12.3 cents

Highway2

31.3 31.1

Optimal : 24.7 cents

30.9

Optimal : 31.7 cents

30.7 30.5

0

0.3

0.6

0.9

65

Optimal : 12.3 cents

Arterial Highway1

64.5

Highway2

64 Optimal : 24.7 cents 63.5 63

Optimal : 31.7 cents

0

Tolls ($/mile)

0.3

0.6

0.9

Tolls ($/mile)

Total PM2.5 (1000 grams/hr)

(3) 2.20

Arterial

2.18 Optimal : 13.3 cents

Highway1 Highway2

2.16 2.14 Optimal : 24.7 cents

2.12

Optimal : 31.7 cents 2.10

0

0.3

0.6

0.9

Tolls ($/mile) Fig. 5. Off-peak total system-wide cost of (1) travel time (2) fuel consumption, and (3) PM2.5 emissions when pricing Highway No.1 and Arterial No.1.

O.M. Rouhani et al. / Transport Policy 41 (2015) 68–79

75

Fig. 6. System-optimal prices for (a) off-peak; and (b) AM peak.

highways) where travel costs rise and then fall as tolls increase (Fig. 5). These changes stem from the cumulative effects of travel demand reduction and spillover. Although travel demand reduction is the prevalent factor for off-peak hours, spillover effects can increase travel costs over a small range of toll rates. Note that the irregularity in some of the functions in Fig. 5 (for off-peak) stems from the fact that the model is sensitive to very small changes in travel costs. These small changes can shift users’ route choices, and consequently significantly distort resulting system travel costs. On the other hand, travel costs in off-peak hours are generally lower than those of peak hours. Therefore, even small changes in toll rates lead to large impacts on users’ estimated travel costs and, as a result, off-peak hours’ results are less regular than peak hours’ results. However, although our model is sensitive to these small changes, these small changes might not be fully perceived by users in practice since users usually do not have complete information about travel costs.

For system cost-minimization cases, temporally-variable tolls increase the average total travel time saved, compared to flat tolls, by 19.5% and 131.1% for the studied arterial and highway, respectively. In addition to temporally-variable tolling, the spatial variation for revenue-maximizing cases further increase total revenues further by 23.4% for the arterial and by 5.9% for the highway, and the spatial variation for system-optimal cases further reduces total travel time of the whole system by 65.7% for tolling the arterial and 167% for tolling Highway no.1, relative to corresponding spatially-flat tolls (additional to what temporal variation offers). This has important policy implications: variable tolling of highways is more effective in improving system performance (systemoptimal cases) than in raising revenues. This policy insight explains why private sponsors might not be interested in variable tolls although such tolls could generate large social benefits.

3.2. Spatially- and temporally-varying tolls

To examine the robustness of our results, we conducted sensitivity analysis on several key parameters of our model. Our analysis estimates changes in results when a parameter is allowed to deviate from its base level (determined in Section 2.2). Fig. 8 displays changes in profit-optimal tolls and optimal profits as the unit operating cost of toll collection (per transaction) increases for Highway no.1 (Fig. 8-(a)) and for Arterial no.1 (Fig. 8-(b)), and for peak (Fig. 8-(1)) and off-peak (Fig. 8-(2)) periods. In all cases, as unit operating cost increases, optimal tolls increase and the optimal profit level declines. Both results are intuitive. In fact, a high unit operating cost incentivizes road owners (operators) to transfer their toll collection cost burden to road users; road owners would increase tolls to reduce travel demand and consequently to reduce their total operating costs. Value of time (VOT) is one of the major elements in analyzing P3 projects. By varying VOT, a specific time-equivalent cost of tolling is translated into different monetary costs of tolls, i.e., a 10min-equivalent toll corresponds to $5 using a $30/hour VOT and corresponds to $10 using a $60/hour.5 Under the revenue-optimal flow patterns (holding time costs constant), a higher average VOT will result in a higher toll rate (monetary) and consequently a higher revenue by a constant ratio. Fig. 9 shows the linear relationship between optimal revenue and VOT, as explained above. However, the impact of VOT on profit-optimal tolls and optimal profits is more complicated. Optimal tolls might decrease with VOT (Fig. 9-a2) since private owners may find it more profitable to decrease tolls in order to increase demand on their tolled road. This counterintuitive result

Several studies have shown the effectiveness of temporallyvarying tolls (somtimes called value pricing) in improving the transportation system performance, especially for reducing congestion (Burris and Sullivan, 2006; Lou et al., 2011). As shown above, we divide the analysis into morning peak and off-peak hours and estimate the corresponding results for each period. Fig. 6 depicts the estimated difference in system-optimal prices between peak and off-peak periods for candidate roads. This significant difference suggests that in order to reach system/profitoriented optimal flow patterns, a temporally-variable pricing scheme should be included in P3 contracts, i.e., toll schedule should allow for variations over time. In addition to temporal variation, road owners or public officials could distort traffic flows along a corridor by setting different toll rates on different segments of the toll road (spatial variation), in order to reduce congestion, raise more revenue, or to satisfy a combination of the two goals (Rouhani and Niemeier, 2014b). Fig. 7 shows the estimated optimal spatial variation in toll rates along Highway No. 2. As can be seen in the figure, the off-peak tolling pattern (dotted lines) is different from the peak hour pattern (solid lines). In addition, the optimal tolling pattern to achieve profit maximization (Fig. 7-a) is quite different from the systemoptimal pattern (Fig. 7-b). Irregular variations of optimal toll rates along different road segments indicate how complex the implementation of optimal variable tolls could be. Table 3 shows that flexible tolls can have a significant impact on the analysis. For the profit maximization cases, temporal variations in tolls (peak versus off-peak) increase total revenues by 10% for the arterial and 1.5% for the highway, relative to flat tolls.

3.3. Sensitivity analysis

5 The time cost of tolls is the major driver of users’ travel behavior and consequently is the major driver of changes in travel demand and traffic flow patterns.

76

O.M. Rouhani et al. / Transport Policy 41 (2015) 68–79

1.3 0.82

AM-Direction1 off-peak-Direction1 off-peak-Direction2

AM-Direction1 off-peak-Direction1

X

off-peak-Direction2

Toll ($/mile)

Toll ($/mile)

AM-Direction2

X

AM-Direction2

-0.42 -1.03 Fig. 7. Toll patterns along Highway No. 2 for (a) profit maximization and (b) system-optimal problems.

is more likely during off-peak hours, due to more-elastic travel demand during those periods. However, the addition of heterogeneous users in terms of VOT (considering a multi-user equilibrium) could dramatically impact the results.

4. Policy recommendations Based on our above discussions, we provide policy makers with several new insights into how to design P3 contracts and how to evaluate P3 tolling approaches. We offer specific recommendations to which the public sector can refer in order to promote successful P3 projects. Recommendation #1: To promote a profitable and more efficient transportation system, toll rates should be set by assessing both profit-maximizing rates and system-optimal rates and carefully considering their potential effects. System optimization and profit maximization solutions usually fall short of satisfying the contradictory goals of raising profits and improving system performance, respectively. A successful P3 project should raise a significant amount of profits while simultaneously improving transportation system performance.

Therefore, neither profit maximization nor system performance optimization should be policy makers’ sole target. Rather, a combination of congestion reduction and profit-making goals should be the criteria for choosing among P3 projects and for setting toll rates. Recommendation #2: Tolls (i.e., higher travel costs) on a few roads do not lead to lower total travel costs for a transportation system as a whole. The opposite could be true for unconstrained profit-maximizing tolls. As shown in Figs. 2-a1 and 3-a1, for peak hours, total system travel costs (including time, fuel, and emissions costs and excluding toll costs) initially decreases when toll rates increase and then generally increases with toll rates. The increasing system cost with tolls is specific to high toll rates in peak periods since users’ decision to travel on longer paths to avoid tolls could diminish system performance. As an extreme case in Fig. 2-a1, the profitoptimal rate on Highway no.1, where only one road is priced, increases the total system travel cost by 2% leading to an immense $75 million dollar increase in total travel costs (as a measure for system performance) annually. As some congestion pricing studies assume, the simple assumption that tolls will reduce congestion is wrong. Instead, the public sector should deliberately search for the

Table 3 Results of applying temporally- and spatially-variable tolls. Case no. Cases

Type of variation

Optimum toll (cents/mi)

Improved travel time (pc equ-hour)

Total revenue ($)

Flat Ave. var Max var Min var % decrease from Flat to Var % change from flat to var Profit max

1 2 3 4

System Optimal

5 6 7 8

a

Throughput (VMT)

% change from flat to var

Art. no.1 Temporal HW no.1 Temporal Art. no.1 Spatial and temporal HW no.1 Spatial and temporal

25 32 25

26 26 29

41a 33a 183

17a 21a 18

  

10.0% 1.5% 23.4%

 1% 25% 0%

32

34

65

23



5.9%

15%

Art. no.1 Temporal HW no.1 Temporal Art. no.1 Spatial and temporal HW no.1 Spatial and temporal

13 11 13

17 16 10

22a 26a 120

14a 8a 0

19.5% 131.1% 65.7%

  

 6%  4%  8%

11

14

34

10

167.0%



2%

For temporal variation, only two toll rates have been applied: one for peak and one for off-peak.

0.5 0.4 0.3 0.2 0.1 0.1

Optimal toll

1.2 0.9

2,000

0.6

1,000 0 -1,000

0

0.1

0.2

-2,000

0.9

7,000

Optimal Profit

0.8

6,000

Optimal Profit

Optimal toll

0.7

5,000

Optimal toll

0.3

0.4

0.5

0.6

0.4 0.3 0.2 0.1 0.2

0.3

0.4

0.5

0.6

Optimal profit ($/hour)

0.5

0.70.0

0.3

0.4

Unit operating cost ($/transaction)

1.2

3,000

0.9

2,000

0.6

1,000 0

0.0

1.5

4,000

-1,000

0.5 0.3

1.8

0

-2,000

Unit operating cost ($/transaction)

1.5

3,000

0.7 0.0

0.2

0.6

0.1

5,000 4,000

Unit operating cost ($/transaction)

11,000 10,000 9,000 8,000 7,000 6,000 5,000 4,000 3,000 2,000 1,000 0 -1,000 0

6,000

Optimal toll ($/VMT)

0.6

1.8 Optimal Profit

0.1

0.2

0.3

0.4

Unit operating cost ($/transaction)

0.50.3

Optimal toll ($/VMT)

0.7

Optimal profit ($/hour)

0.8

Optimal toll

77

7,000

0.9 Optimal Profit

Optimal toll ($/VMT)

11,000 10,000 9,000 8,000 7,000 6,000 5,000 4,000 3,000 2,000 1,000 0 -1,000 0

Optimal toll ($/VMT)

Optimal profit ($/hour)

Optimal profit ($/hour)

O.M. Rouhani et al. / Transport Policy 41 (2015) 68–79

0.0

Fig. 8. Sensitivity of the profit and toll with respect to unit operating cost for (a) Highway No.1 and (b) Arterial No.1 and for (1) peak vs. (2) off-peak.

implementing high profit-maximizing toll rates. User choice is less restricted in an urban system than in a rural system. Incentivizing the use of less-costly public transportation would promote a more efficient and sustainable transportation system (e.g., the increase

Optimal profit

18,000

Toll profit

1.5 1.2

14,000

0.9

10,000

0.6

6,000 2,000

0.3

-2,000

0.0

31,000 27,000 23,000 15,000

1.8 1.5 1.2 0.9

0

0.6 0.3

-2,000

VOT($/veh.hour)

0.6

11,000 7,000

0.3

3,000 0.0

11,000

2.1

0.0

Revenue /profit ($/hour)

2,000

0.9

-1,000

2.4 Optimal revenue Optimal profit Toll profit

1.2

VOT($/veh.hour)

Optimal toll ($/VMT)

Revenue /profit ($/hour)

4,000

Optimal revenue Optimal profit Toll-profit

19,000

VOT($/veh.hour)

6,000

1.5

35,000

9,000 7,000

1.5 Optimal revenue Optimal profit

1.2

Toll-profit 0.9

5,000 0.6

3,000

0.3

1,000 -1,000

Optimal toll ($/VMT)

22,000

1.8

Revenue /profit ($/hour)

Optimal revenue

Optimal toll ($/VMT)

Revenue /profit ($/hour)

26,000

Optimal toll ($/VMT)

candidate toll roads and the toll rates that could reduce systemwide congestion, not to manage congestion on P3 (i.e., tolled) roads only. However, the existence of alternative modes to private cars (which was not presented in our case study) might justify

0.0

VOT($/veh.hour)

Fig. 9. Sensitivity of the revenue, profit, and toll with respect to the average VOT for (a) Highway no.1, (b) Arterial no.1, and for (1) peak vs. (2) off-peak periods.

78

O.M. Rouhani et al. / Transport Policy 41 (2015) 68–79

in share of public transports in London as a result of the London congestion charging scheme, Leape, 2006). Recommendation #3: A lower limit(s) along with an upper limit(s) might be required for enforcing the application of the system-optimal or a system-improving toll rate by the private operator. As discussed in the results section, system-optimal rates are not related to elasticities (they are mostly determined by the network effects), therefore, they could be either lower or higher than profitoptimal rates, which are mainly determined by elasticity. Particularly in an urban environment with many alternatives to P3 toll roads, system-optimal rates could be associated with elastic demand. Not only should policy makers put a cap on toll rates based on system-optimal rates, they should also set a lower limit on toll rates in P3 contracts, which prevents road operators from undercutting the applied upper toll limit(s). Recommendation #4: To increase profits and manage travel costs, policy makers could provide a flexible (temporal and spatial) tolling scheme for the private sector. Spatially- and temporally-varying tolls could be significantly effective in increasing profits, and specifically in improving system performance (Table 3). Rules #3 and #4 are not contradictory, rather these rules should be considered together. Although we recommend setting a limited range in which toll rates could change, this range should vary for different time periods (peak versus off-peak) and for different segments of the toll road. For instance, our results show that a profit-maximizing operator might charge at peak hours only, and set the toll rate at zero for off-peak hours, especially when the toll collection operating cost is high relative to the toll revenue, as could be the case for urban roads with many control points. One important finding from our analysis is that flexible tolling is more effective in reducing social costs of travel than it is in raising revenue. This finding explains why private sponsors might not be interested in flexible tolling but also explains why the public sector should include such flexibility in P3 contracts. However, applying variable tolls might favor a publicly-run tolling scheme where tolls could be set with more flexibility without the restrictions commonly imposed by P3 contracts. Recommendation #5: A detailed system-wide impact analysis of P3 projects is a must. Many lessons can be learned from a systems analysis of P3 projects. Examining a toll road only, or even a toll road and its major competing roads, is not sufficient. The possible spillover effects to other parts of the transportation system could lead to millions of dollars of travel costs, as is the case with some unlimited pricing scenarios in our study. In fact, without a systems analysis, a policy maker tends to choose P3s that can bring more money to the table while these more profitable cases could be disastrous for transportation system performance. On the other hand, running a pure congestion pricing scheme (only to improve system performance) could become an economic failure (Prud’homme and Bocarejo, 2005).

5. Caveat The transportation planning model used in this study was employed only for research purposes, and not for developing regional transportation plans or transportation improvement programs.

Acknowledgment The authors express their special gratitude to anonymous

reviewers for reviewing the paper, sharing thoughts, and insightful comments on the paper. We acknowledge the partial funding support from University Transportation Research Center of Region 2 (UTRC) project on "Evaluating the Role of Private Investment in Life Cycle Management of New York State's Infrastructure Assets". The second author also acknowledges partial support by a Grant from the National Natural Science Foundation of China (Project no. 71428001).

Appendix We rely on the basic mathematical approach developed in previous studies and only provide a brief description of four major problems as below: modified traffic assignment (Rouhani and Niemeier, 2011), profit maximization (Rouhani et al., 2013), general system cost minimization (Rouhani and Niemeier, 2014a), and spatial variation in tolls (Rouhani and Niemeier, 2014b). 2.1. Profit maximization problem (PMP) Using a bi-level programming framework, we consider the profit maximizing problems of project owners to be the higherlevel model and travelers’ behavior to be the lower-level model (a Stackelberg game). Road owners (operators) attempt to maximize their profit (πn ), which is the sum of the tolls gathered from the segments or the links of their road (or tolls on link i-j multiplied by the link’s equilibrium flows for all the roads owned by private firm n that comprise the Fn set, (i, j)∈Fn ), minus its costs (CFn, ij (τ¯ )) for firm n (¼ 1 to 3, assuming that each road is priced separately)

(Max profit) Max πn = τij

∑

τij . xij⁎ (τ¯) − CFn, ij (τ¯))

(i, j) ∈ Fn

s . t . τij ≤ τij‵

(1) (2)

where τ¯ is the vector of tolls (both own and cross tolls) comprising of τij ’s or tolls on each link (i,j), capped by τij′ ’s. x⁎ is the modified user equilibrium (UE) flow assuming general travel costs rather than time only, and the travel demand for each k-s Origin-Destination (O/D) pair (dks ) will be modified iteratively to reflect changes in the general cost of travel for the O/D, and is the solution of the following mathematical problem (Sheffi, 1984):

(UE) Min ∑ x

s. t.

∑

(i, j)

∫0

xij

Cij (u). du (3)

x pks = d ks , ∀ (k, s) ∈ P (4)

p ∈ Pks

x pks ≥ 0, ∀ p ∈ Pks , ∀ (k, s) ∈ P

xij =

∑ ∑

(5)

x pks . δijks,p, ∀ (i, j) ∈ A

(k, s) ∈ p p ∈ Pks

(6)

This model also uses Wardrop (1952)'s principle, with Cij as the generalized cost associated with traveling on link i–j rather than just the travel time tij (by replacing tij with Cij in the UE problem):

Cij = tij (xij ) + βij . τij

(7)

where τij (the charge for using link i–j) is determined by the link (road) owner from the higher level problem—Eq. 1–(Nagurney, 2000), and βij is the value of time coefficient which converts the charges in dollars (or cents) to costs in terms of time. Since the value of time varies for different users, we need a multi-user equilibrium to address the resulting difference in behavior. However, the Fresno transportation planning model is only designed

O.M. Rouhani et al. / Transport Policy 41 (2015) 68–79

for an average user. Therefore, our models only cover an average user, as well. Note that the toll collection cost for firm/road n (CFn, ij in Eq. 1) consists of two components: (1) the capital costs of providing the toll collection system which is fixed with respect to traffic volumes; and (2) the operating cost which is a function of the number of transactions (traffic volumes). 2.2. System general cost minimization (SGCM) The previous formulation only simulates the profit maximizing behavior of road operators. However, policy makers might also be interested in system cost pricing that maximizes transportation system performance. In that case, the higher-level formulation can be replaced with the system general cost minimization (SGCM) problem, which minimizes the total general costs of travel:

(

L

ij ) ∑ ∑ γk . λk ( tij (x ⁎ ) ). Lij . xij⁎

(GSCM) Min ∑ tij (xij⁎ ). xij⁎ + τij

i−j

k

i−j

ij

(8)

where the first term is the total travel time, and the second term is the total fuel and emissions cost. k denotes the cost component (e.g., fuel, CO2 emissions, CO emissions, etc.), and λk is the fuel consumption or emissions factor (gallons or grams per mile), which is a function of speed level ((Lij )/(tij (x ij⁎ )) ). To find the total emissions from each link, λk should be multiplied by the length of the link (Lij ) and its volume (x ij⁎ ). The total fuel consumption or emissions (in gallons or grams) and travel time cannot be summed because of the difference in units. γk has been added to convert the units from gallon or grams to timeequivalent travel cost (hours). So γk is a combination of two factors: the prices of each cost component ($/gallon or $/ton) and a general VOT measure ( β in $/hour). The addition of emissions and fuel consumption can present a more general social cost pricing scheme.

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