This paper provides a brief overview of the concept of value of time (VOT), in the context of toll road schemes. VOT analysis determines the tradeoffs travelers make between time and tolls. The analysis is very important when considering the choice between tolled and un-tolled alternatives. Using travel demand model of Fresno, CA, I provide a sensitivity analysis showing how the outcomes of tolling schemes can change with varying VOT levels

M. Rouhani, Omid

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Impact of Value of Time (VOT) on toll
roads
Omid M. Rouhani
Cornell University
16. June 2015
Online at http://mpra.ub.uni-muenchen.de/65087/
MPRA Paper No. 65087, posted 16. June 2015 20:14 UTC
Impact of Value of Time (VOT) on toll roads 
 
Omid M. Rouhani1 
1 School of Civil and Environmental Engineering, Cornell University, Hollister Hall, Ithaca, NY 14853, USA; Email: 
om67@cornell.edu Tel: +1 530 204 8576 
 
Abstract 
This paper provides a brief overview of the concept of value of time (VOT), in the context of toll 
road schemes. VOT analysis determines the tradeoffs travelers make between time and tolls. The 
analysis is very important when considering the choice between tolled and un-tolled alternatives. 
Using travel demand model of Fresno, CA, I provide a sensitivity analysis showing how the 
outcomes of tolling schemes can change with varying VOT levels. 
Keyword- Value of time, Road pricing, Congestion pricing, Optimal toll, Profits, System-wide 
costs.  
 
Introduction and Summary 
Value of time (VOT) is a measure that transportation practitioners employ in order to estimate 
how users of toll roads (or other facilities) make choices between a cost component and a time 
component of each trip (Rouhani and Niemeier, 2014a,b; Rouhani et al., 2014b; Rouhani et al., 
2015a,b). In fact, VOT explains the tradeoff between time and money (Brownstone and Small, 
2005; Small, 2012).  
We can explain the application of VOT concept using a simple example. Assume that a 
user have to options to reach its destination: 
 - Path 1: time: 0.5 hour, no tolls 
 - Path 2: time: 0.3 hour, $4 of tolls  
The question is which path would be the choice of the user? Without any toll, all users 
would generally choose Path 2 since it is faster (lower travel time). However, with a toll on Path 
2, some users might want to avoid Path 2 now since they have to pay money out of their pocket. 
Rich users or those ones that have urgent needs may want to pay more to save time. In other 
words, users should determine how they perceive these cost components relative to each other. 
Assuming a value of time measure, user can calculate a general costs instead of time cost only 
when roads are priced. For example, with a value of time of $10/hour, Path 1 has a general cost 
of $5 (0.5*10) and Path 2 has a general cost of $7 (0.3*10+4). With such calculation, users can 
choose their paths.  
VOT determines how users value time spent driving (travelling) and how they calculate a 
more general cost of travel (Rouhani and Niemeier, 2011; Rouhani, 2012; Rouhani et al., 2014a). 
For user i and each alternative mode j, GCi is the general cost of travel and can be calculated as 
follows: 
GCi = VOTi .tj (vj) + Cj         (1) 
where tj is the travel time spent and Cj is the price or the toll paid by each user. Travel time is a 
function of traffic volume (vj) or congestion level. VOTi is the value of time ($/hour) which 
transforms time (in hours) into a monetary measure ($). Note that a more general cost could 
include fuel costs (Rouhani and Zarei, 2014; Rouhani and Gao, 2014), especially considering 
huge environmental and energy footprints of the fossil fuel burning from transportation 
(McCubbin and Delucchi, 1999; Lin et al., 2009; Rouhani et al., 2010; Madani et al., 2011; 
Mirchi et al, 2012; Rouhani, 2013).  
Using different VOTs, a specific time cost of tolling (VOTi .tj (vj) in Equation 1) will be 
translated in different monetary costs of tolls, i.e., a 10 minute–equivalent toll equals to $5 using 
a $30/hour VOT and equals to $10 using a $60/hour1. Under the same flow pattern, a higher 
average VOT will result in a higher toll rate (monetary) and consequently a higher revenue by a 
constant ratio. Note that to do a thorough analysis, we need to use the Multi-user concept since 
users have perception about their VOT’s. Users are different in the way they incur tolls. When 
evaluating tolling schemes, a multi-user feature (Yang and Huang, 2004; Chen and Bernstein, 
2004; Rouhani and Niemeier, 2011) is necessary for any equity analysis (Levinson, 2010). 
VOT depend on so many factors such as income, type of trip, the quality of alternative 
paths/modes, etc (Hess et al., 2005). To estimate VOT, consider that traveler i chooses to 
maximize a random utility function (Lam and Small, 2011):  
Uitj ≡ θij+βiXitj+εitj          (2) 
where X
itj
 is the vector of variables affecting utility gained the time t of the choice. The vector 
include the toll C
itj
, travel-time T
itj
, and (un)reliability R
itj
, etc. Therefore, the value of travel time 
is defined as: 
 
itjitj
itj itj
/
/i
U T
VOT
U C
 

 
          (3) 
 
                                                          
1 The time cost of tolls is the main driver of the difference in users’ travel behavior. 
The derivatives in the above equation allow VOT to depend not only on the individual 
traveler i but also on the alternative j or choice of time t. VOT is a very important measure in 
evaluating road pricing (Rouhani, 2009; Rouhani, 2014), congestion pricing (Prud’homme and 
Bocarejo, 2005; de Palma and Lindsey, 2011; Rouhani et al., 2014b), and public-private 
partnership tolling schemes (de Bettignies and Ross, 2004; Boardman and Vining, 2012; 
Rouhani et al., 2015a), and in calculating social and private costs of driving (Rouhani et al., 
2013b). 
In this paper, I analyze the impact of VOT on several measures related to toll collection 
revenues and costs and their associated system-wide travel costs (system performance). The 
analysis is conducted using the travel demand model of the City of Fresno, California. The 
assumptions made for the calculation is available from Rouhani et al. (2013a), Rouhani and Gao 
(2014), and Rouhani and Gao (2015b). 
  
Results 
It is essential to run a sensitivity analysis on several key parameters of any model (Rouhani et al., 
2013b; Rouhani et al., 2014b) that impact outcomes of a tolling scheme. One of the most 
important variables is VOT. As we discussed, Value of time (VOT) is one of the major elements 
in analyzing P3 projects (Rouhani et al., 2015a). Considering several base parameters, we can 
calculate the effects of various VOT rates on the tolling schemes’ outcomes. Note that my 
analysis takes into account the effects on the whole network of a metropolitan area, not only the 
effects on the facility of concern (Safirvoa et al., 2007). Figure 1 shows the changes in optimal 
profit, optimal revenue, and profit-optimal toll rate as VOT level increases. The optimal toll and 
profit are shown for one typical highway (Figures 1–a) and one typical arterial (Figures 1–b) and 
for peak (Figures 1–1) and off-peak (Figures 1–2) periods. The method used to for calculating 
revenues, profits, and optimal tolls can be found in Rouhani et al. (2015a).   
Although highly effective on the results, an average VOT (not a detailed classified VOT 
study) only affects the tradeoffs between money (tolls) and time. Figure 1 displays that optimal 
revenue is linearly related to VOT (constant ratio). However, the effects of VOT on the optimal-
profit toll and optimal profit are not as simple. Even optimal toll may decrease with VOT (Figure 
1–a–2) since private owners might find it more profitable to decrease tolls and attract more 
demand even with higher tolls. We find that this counterintuitive result has higher chances of 
occurrence in off-peak hours, due to a more elastic demand. However, the addition of 
heterogeneous users in terms of VOT could drastically impact the results. Finally, VOT 
sensitivity analysis should be combined with the analysis on demand risk (Chen and Subprasom, 
2007), other risks associated with tolling (Jin and Zhang, 2011), operating costs (Rouhani et al., 
2014c), etc.      
  
  
Figure 1. Sensitivity of the revenue, profit, toll with respect to average VOT for (a) a 
typical Highway and (b) a typical Arterial No.1 and for (1) peak vs. (2) off-peak. 
 
For Highway and in peak periods, the sensitivity of system-optimal toll rates to changes 
in average VOT and fuel prices is shown in Figure 2. System-optimal rates are found using a 
very complex optimization problem (Poorzahedy and Rouhani, 2007; Madani et al., 2014) 
Although system-optimal rates minimize the total system travel costs including time, fuel, and 
emissions costs in monetary terms (Rouhani et al., 2015a), the dominance of travel time cost 
relative to other travel cost components (Rouhani et al., 2013c) leads to a rate that minimizes 
total travel time only (Yang, 1999). Unless the VOT is very low or the fuel prices are very high, 
the system–optimal rate remains the same. Even when the rate changes, the change is very small 
($0.25 to $0.26/mi). This result holds true for almost all other tolling systems (on all other 
roads). Although taking the fuel consumption and emissions costs into account have negligible 
effects in determining system-optimal rates, the magnitude of travel costs and the related system-
wide benefits or costs could be greatly affected by taking them into account.  
  
 
 
 
 
 
 
 
Figure 2. Sensitivity of the system-optimal tolls to average VOT and fuel price for a typical 
highway in peak hours. 
 
 
Copyright Note  
The author certifies that he has the right to deposit the contribution with MPRA.   
References 
Boardman, A. E., & Vining, A. R., (2012). The political economy of public-private partnerships and 
analysis of their social value. Annals of Public and Cooperative Economics, 83(2), 117–141.  
 
Brownstone, D., & Small, K. A., (2005). Valuing time and reliability: assessing the evidence from road 
pricing demonstrations. Transportation Research Part A: Policy and Practice, 39(4), 279-293. 
 
Chen, M., & Bernstein, D. H., (2004). Solving the toll design problem with multiple user 
groups. Transportation Research Part B: Methodological, 38(1), 61-79. 
 
Chen, A., & Subprasom, K., (2007). Analysis of regulation and policy of private toll roads in a build-
operate-transfer scheme under demand uncertainty. Transportation Research Part A, 41(6), 537-558. 
 
de Bettignies, J. E., & Ross, T. W., (2004).The economics of public-private partnerships. Canadian 
Public Policy/Analyse de Politiques, (2004), 135-154. 
 
de Palma, A., & Lindsey, R., (2011). Traffic congestion pricing methodologies and technologies. 
Transportation Research Part C, 19(6), 1377–1399. 
 
Hess, S., Bierlaire, M., & Polak, J. W. (2005). Estimation of value of travel-time savings using mixed 
logit models. Transportation Research Part A: Policy and Practice, 39(2), 221-236. 
 
Jin, X. H., & Zhang, G., (2011). Modelling optimal risk allocation in PPP Projects using artificial neural 
networks. International journal of project management, 29(5), 591–603. 
 
Lam, T. C., & Small, K. A. (2001). The value of time and reliability: measurement from a value pricing 
experiment. Transportation Research Part E: Logistics and Transportation Review, 37(2), 231-251. 
 
Levinson, D., (2010). Equity effects of road pricing: A review. Transport Reviews, 30(1), 33-57. 
 
Lin, C. Y., Zhang, W., Rouhani, O., & Prince, L. (2009). The implications of an E10 ethanol-blend policy 
for California. California State Controller John Chiang Statement of General Fund Cash Receipts and 
Disbursements, 5(5), 6-7. 
 
Madani, K., Rouhani, O. M., Mirchi, A., & Gholizadeh, S., (2014). A negotiation support system for 
resolving an international trans-boundary natural resource conflict. Environmental Modelling & 
Software, 51, 240-249. 
 
Madani, K., Rouhani, O. M., Pournazeri, S., Moradi, M., & Sheikhmohammady, M. (2011, May). Can we 
rely on renewable energy sources to overcome global warming. In Proceedings of the 2011 World 
Environmental and Water Resources Congress, ASCE (pp. 3319-3326). 
 
McCubbin, D. R., & Delucchi, M. A., (1999). The health costs of motor-vehicle related air pollution. 
Journal of Transport Economics and Policy, 33(3), 253–286. 
 
Mirchi, A., Hadian, S., Madani, K., Rouhani, O. M., & Rouhani, A. M. (2012). World energy balance 
outlook and OPEC production capacity: implications for global oil security. Energies, 5(8), 2626-2651. 
 Poorzahedy, H., & Rouhani, O. M., (2007). Hybrid meta-heuristic algorithms for solving transportation 
network design. European Journal of Operational Research, 182(2), 578–596. 
 
Prud’homme, R., & Bocarejo, J. P., (2005). The London congestion charge: A tentative economic 
appraisal. Transport Policy, 12(3), 279–287. 
 
Rouhani O. M., (2009). Road privatization and sustainability. MIT Journal of Planning, 6, 82-105. 
 
Rouhani, O. M., (2012). Frameworks for Public-Private Partnerships. Ph.D. dissertation, University Of 
California, Davis. 
 
Rouhani, O. M., (2013). Clean Development Mechanism: An appropriate Approach to reduce Greenhouse 
Gas Emissions from Transportation? Transportation Research Board 2013 92, No. 13-3195. 
 
Rouhani, O. M. (2014). Road pricing: An overview. http://mpra.ub.uni-muenchen.de/59662/ 
 
Rouhani, O.M., & Niemeier, D., (2011). Urban network privatization: A small network example. 
Transportation Research Record, 2221, 46–56.  
 
Rouhani, O. M., & Gao, H. O., (2014). An advanced traveler general information system for Fresno, 
California. Transportation Research Part A: Policy and Practice, 67, 254-267. 
 
Rouhani, O.M., & Niemeier, D., (2014a). Flat versus spatially variable tolling: A case study of Fresno, 
California. Journal of Transport Geography, 37, 10–18. 
 
Rouhani, O. M., & Niemeier, D., (2014b). Resolving the property right of transportation emissions 
through public–private partnerships. Transportation Research Part D, 31, 48–60. 
 
Rouhani, O. M., & Zarei, H., (2014). Gas Consumption Information: A Substitute for Congestion 
Pricing? Road and Transport Research 23 (3), 52. 
 
Rouhani, O. M., Madani, K., & Gholizadeh, S., (2010). Caspian Sea negotiation support system. 
In Proceeding of the 2010 world environmental and water resources congress, ASCE, Providence, Rhode 
Island (pp. 2694-2702). 
 
Rouhani, O.M., Niemeier, D., Knittel, C. R., & Madani, K., (2013a). Integrated modeling framework for 
leasing urban roads: A case study of Fresno, California. Transportation Research Part B, 48(1), 17–30.  
 
Rouhani, O. M., Kandel, A., & Christian, M. (2013b). The Renewable Portfolio Standard’s Impacts on 
the California’s Electricity Sector. International Journal of Power and Energy Systems, 33(3), 130-134. 
 
Rouhani, O.M.; Gao, O.; Beheshtian, A. (2013c). Social and Private Costs of Driving. Lecture 
presentation at the 2013 Annual Conference of the International Transportation Economics Association, 
Northwestern University, Evanston, Illinois. 
 
Rouhani, OM, Gao, HO, Geddes, R, Bel, G, & Zarei, H, (2014a). Social Welfare Analysis for Alternative 
Investment Public-Private Partnership Approaches. Lecture presentation in the 2014 Transportation 
Research Board conference, Washington D.C. 
 
Rouhani, O.M., Knittel, C., & Niemeier, D., (2014b). Road Supply in London: Addition of an Ignored 
Social Cost. Journal of Transportation Research Forum, 53 (1), 49–64. 
 
Rouhani, O.M., Gao, O., & Geddes, R. R., (2015a). Policy lessons for regulating public-private 
partnership tolling schemes in urban environments. Forthcoming in Transport Policy, DOI: 
doi:10.1016/j.tranpol.2015.03.006  
 
Rouhani, O. M., Gao, H. O., Zarei, H., & Beheshtian, A. (2015b). Implications of Fuel and Emissions 
Externalities, Spillovers to the Outside, and Temporal Variations on Zonal Congestion Pricing Schemes. 
In Transportation Research Board 94th Annual Meeting (No. 15-0905). 
 
Safirova, E., Gillingham, K., & Houde, S., (2007). Measuring marginal congestion costs of urban 
transportation: Do networks matter? Transportation Research Part A, 41, 734–749. 
 
Small, K., (2012). Valuation of travel time. Economics of Transportation, 1(1-2), 2–14. 
 
Yang, H., (1999). System optimum, stochastic user equilibrium, and optimal link tolls. Transportation 
Science, 33(4), 354-360. 
 
Yang, H., & Huang, H. J., (2004). The multi-class, multi-criteria traffic network equilibrium and systems 
optimum problem. Transportation Research Part B, 38(1), 1–15. 
 


Impact of Value of Time (VOT) on toll roads

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Impact of Value of Time (VOT) on toll roads

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