Revenue management based modelfor the dynamic definition of toll price for
freight vehicles
S. Schreiner & T. Hyodo
The Regional Planning Laboratory, Tokyo University of Marine Scienceand Technology, Japan.

Abstract
This study proposes a dynamic tolling method for a private toll network based onrevenue management, taking into account the daily dynamics of freighttransportation demand. The first part of this study assessed a sample of freightvehicles’ routes, using maximum route overlapping methodology to obtain arelation between network attributes and the route choice of such vehicles. In thesecond part, also using route overlapping methodology, the individual value oftime for each vehicle was estimated and incorporated to the route information as
an attribute of the trip. The third part of this study uses the results obtained
previously to model the dynamic tolling system. Discrete choice techniques areused to evaluate purchase probability during the day in relation to a set of
possible toll prices, identifying the efficient prices that achieve revenue
maximization. Finally, the model is tested by comparing the total daily toll
revenue results of the current static price strategy and the dynamic pricing
strategy. The data from the person trip survey conducted in 1999 in Tokyo isused as demand input data for the model.
Keywords: revenue management, toll road, route choice model

1Introduction

The long-term implications of the definition of a tolling scheme from the point ofview of Revenue Management were introduced by Nagae & Akamatsu [1].
Although the focus of that work concentrated on showing that the long-term
operation and day-to-day demand dynamics should be considered more dominantthan the demand dynamics within a day, the study presented in this paper focus
on the complementary objective of maximizing the expressway utilization by
applying revenue management techniques to hourly control the toll fee.
The route choice is possibly the most critical issue when modeling a
dynamic tolling system. The reason is certainly the heterogeneity of the demandand its variable perception of travel cost. This study focuses on the considerationof these both factors regarding freight transportation, which is far less affectedby personal impressions of the way to be traveled than the passenger traffic.
Even so, several attributes of the road network still affect the route choice.
Schreiner et al [2] examined the influence of some of these attributes on theroute choice of freight vehicles, showing that the influence of network attributes
depends directly on the value of time. Based on that result, it is assumed that theuser will take a route decision that considers exclusively the total perceived
travel cost of each of the available routes. Naturally, it is also assumed that theuser has knowledge of the network and its general level of service during theperiod when the trip takes place.

2Modelling methodologyThis study uses a Logit model to the calculation of the probability of a freightvehicle route use the tolled links. The utility is based on the generalized trip cost,which considers the influence of cognitive parameters in the length of the links
and an empirical distribution of values of time. The obtained probability of using
tolled links is then used in a revenue management model as single product caseto estimate the demand rate according to a set of possible toll prices.
Let the set of links L = {l1,…,lNOL} and nodes N = {n1,…,nNON} define thenetwork. Each link l is represented by a vector of attributes such as length,
number of lanes, lane width, type of link (tolled or non-tolled), toll price, etc.
The model is based on a discrete set of time intervals t, going from t0 to T. A
trip is defined by the vector r = {Or,Dr,VOTr}. The vector includes the origin
node, destination node, and individual value of time. The probability of arrival isgiven by λ. Let the path used by the demand route be defined as the set of links
leading to the destination Dr, from the origin Or, which incurs in the minimum
total cost for the trip r, considering the cost for each link l as
(1)
β kzlkGCl = (Fuel × Eff × Lengthl + VOTr × TTl + Tolll )×∏

where:
GCl: generalized cost of link l;
Fuel: fuel cost [JPY/liter];
Eff: engine efficiency [liters/km];
Lengthl: lenth of link l [km];VOTr: value of time for the trip r [JPY/min];TTl: travel time on link l;
Tolll: Toll price on lin k l.
zlk is the k-th attribute (e.g. road width) for the l-th link of the r-th trip;
β k is an estimated parameter for the k-th attribute.

The single product case is used in this model. The product is the use of
tolled links for the trip r. The probability that the trip r will include tolled links
P(tolled) is obtained by considering the binary Logit model defined as

eutolledeutolled + eunon−tolled(2)u = −0.01× Cost path(3)

P(tolled ) =where the utility u is defined as

The Costpath is the total cost of the set of links used between one given
origin-destination pair. The trip cost is calculated as described in eqn. (1). For
the computation of utolled, all tolled and non-tolled links are used. The
computation of unon-tolled considers exclusively non-tolled links. The possibility ofnon-travel was not considered.
For each time interval, the model considers the maximization of the toll
revenue, based on the discrete demand probabilities of purchase. Let p(t) denotethe price at time interval t, which is in fact the price to be decided. Each pricep(t) induces a unique demand rate P(tolled). The price p(t) must be present in theset of allowable prices P = {pmin,…,pmax}.
The demand rate d(t) is then defined asd(t) = λ P(tolled)(4)
which represents the probability of demand at the time interval t by a price p.
The revenue rate r(t) for a price p is then(5)r (t ) = p × d (t )Given the discrete nature of the price set, the model identifies the efficient(revenue maximizing) prices to define the optimal price set.
Once the arrival probability and purchase probability are correctlycomputed, the definition of the efficient set of toll prices can be easily obtained.

3Data set and sample description

The model is applied to the freight transportation demand identified by the 1999
Person Trip Survey in Tokyo Metropolitan Area. The network used in this casestudy is originally from the DRM (Digital Road Map) database, and is composedof 9,231 nodes and 25,062 links. The links present 25 attributes. From those, thefollowing are used in this model: Length: length of the link (in meters); Toll1: aflag indicating whether the link is tolled or not; Toll2: a flag indicating whether
the toll price of the link is “flat rate” or “length based”; Toll3: the toll price ofthe link; Assignment travel time: average travel time at the peak hour.
The case study network is presented in Figure 2, where the tolled links arehighlighted in black. This area comprises different tolled networks with different
toll price strategies. The model is applied exclusively to the access links of theShuto-Expressway system, which uses a flat toll price scheme. The otherexpressway networks use different toll schemes, e.g. length based price, andwere not included in the dynamic system.

Figure 1. Tokyo Metropolitan Area network
3.1 Estimation of value of time
Maximum route overlapping method was used for the estimation of the value oftime (VOT). An important characteristic of this methodology is the possibility toestimate the VOT individually for each trip. The use of individual VOTs implies
in a more detailed computation of individual choice behavior, as discussed by
Schreiner [3].
This method is based on the maximization of the overlapping links
between the calculated path and the observed path. This maximization isobtained through the variation of perception parameters which may be related tothe network (e.g. number of lanes, restrictions to height and weight, etc.) or to
the user (value of time, in this case).
These perception parameters are included in the model as link length
modifying parameters [Eqn (6)] in the case of network attributes, and as
generalized cost modifying parameter [Eqn (1)] in the case of the value of time.
The length modification is given by(6)L*an ( β ) = La ∏ β kz akk

Where:L ( β ) is the perceived length of the a-th link at the n-th trip sample;
zak is the k-th attribute (e.g. number of lanes) for the a-th link of the n-th trip
sample;*anβ k is the unknown parameter for the k-th attribute of the network.

The objective function of the maximization procedure is defined asD( β , ω ) =∑ ∑ δ × δ (β ,ω ) ×L
∑X
*nanana(7)annWhere:
δ na* ( β , ω ) : is equal to 1 if the n-th trip’s perceived minimum cost paths (fornetwork parameters β and value of time parameter ω ) include the a-th link,otherwise it is equal to 0.
The maximization procedure considered values of time between 0 and 100
JPY/min. The results are shown in Figure 2.
In the model, these values of time were converted into trip attributes.
(Entire sample)
100
90

Estimated VOT (JPY/min)

80
70
60
50
40
30
20
1001

9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161 169 177 185
Route Number

Figure 2. The estimated individual value of time
The results in the modelling of value of time show a very heterogeneous
distribution, indicating that a demand-wide generalization of value of time
probably result in loss of accuracy on the route choice (specially whether use
tolled routes or not).

4Model estimation results

The probability of arrival is obtained from the analysis of the departure time of
the trips surveyed in 1999. The model considers the peak hours volume asmaximum possible probability of arrival and, proportionally, to the off-peakvolumes. This distribution is presented in Fig. 3.
The estimation of the probability of purchase requires the use of moredetailed information, specifically the value of time distribution for the freighttrips. This data is given by a set of freight vehicle trips that include the observedroute. This set was used by Schreiner et al [2] to the evaluation of attributes
influencing the route choice behavior, and, also, by Schreiner [3] to evaluate theindividual value of time for each trip. The set of trips is composed by 597
observed routes of freight vehicles, including container-trailers and medium andsmall size trucks.

Probability of arrival

100.00%80.00%
60.00%
40.00%
20.00%
0.00%
012

3

4

567891011121314151617181920212223

Hour of the day

Figure 3. Estimated probability of arrival for tolled
network demand in Tokyo by hour
For each possible toll price p, the probability of using tolled links P(tolled)
was calculated for each trip and globally for the entire trip sample.
In the case study, the minimum and maximum toll price are set as pmin = 100
JPY and pmax = 2,000 JPY. A practical increment of inc = 100 JPY is used.
Figure 4 shows the obtained results for the global P(tolled).
The results show an stabilization of P(tolled) around 62% for toll prices over
JPY 1,700. This behavior was caused by the migration of the demand to theother tolled networks (where the RM model was not applied).
The demand rate d(t) with relation to each possible toll price, calculated basedon the sample of freight vehicle trips, is shown in Figure 5.

1.00
0.90
0.80

Average P(tolled)

0.70
0.60
0.50
0.40
0.30
0.20
0.10

1900

1700

1500

1300

1100

90
070
050
030
010
00.00

Toll Price

Figure 4. Average P(tolled) in relation with the toll
price for the entire trip sample

1900
1700
1500
1300
1100

Toll price

900
700
500

100

2219161310741300

Hour of the day
0%-20%

20%-40%40%-60%60%-80%80%-100%

Figure 5. Demand rate in relation with the priceand hour of the day
Similar to the definition of portfolio investment composition used in financial
economics, the key factor in the decision of the toll price is the respective risk, inthis case, with respect to the demand. Taking in consideration that the current toll

price is JPY 1,400 for large vehicles, it is possible assess the current demand rate,e.g., between 8a.m. and 9a.m. the demand rate is currently in the interval 60 to80%. The tactical advantage of the use of revenue management for the definitionof the toll price can be observed in the hypothetical situation of increasing thetoll price in this same time interval (8a.m. to 9a.m.) by JPY 100. The new price(JPY 1,500) would take the demand rate to the next lower interval of 40% to60%, possibly resulting in reduction of revenue on the long run.

5Model results

The demand rate estimations presented in the previous section permit thecomparison, in terms of revenue performance, between the current toll pricescheme and a hypothetical new price scheme.
The normal toll price for freight vehicles in the Tokyo Expressway System is
JPY 1,400 (approximately 14.00 USD). The company operating the system has
introduced some discount schemes including even the peak time. Currently, thetoll prices are as presented in Table 1 (Source: Metropolitan Expressway Co.,
Ltd. Web-site). Additional discounts are eventually offered in special occasions,such as prolonged holidays, however they are not considered here.
Table 1:

NormalPeak discountOff peak discountNight discountCurrent price scheme inTokyo Expressway
Systemall day
6am-11am
3pm-6pm
11am-3pm
6pm-10pm
10pm-6am

1400 JPY (aprox 14 USD)
1360 JPY (aprox 13.60 USD)
1260 JPY (aprox 12.60 USD)
1120 JPY (aprox 11.20 USD)

In order to perform the comparative analysis of the revenue performance ofboth schemes, the alternative prices presented in Table 2 were used. This pricescheme represents the toll price that induces a demand rate 1% over the demandrate of the current price scheme.
Table 2:Peak discountOff peak discountNight discount

Alternative prices basedon the model results

6am-11am
3pm-6pm
11am-3pm
6pm-10pm
10pm-6am

1280 JPY (aprox 12.80 USD)
1100 JPY (aprox 11.00 USD)
820 JPY (aprox 820 USD)The difference in total revenue at the interchanges where the new toll pricescheme was implemented is presented in Table 3.
Table 3:Operations hours
Peak discountOff peak discountNight discountResults of model
implementation
Revenue+ 2.82 %- 0.84 %- 25.57 %Veh.km
+ 0.52 %+ 1.94 %+ 2.96 %The results showed positive revenue modifications exclusively in the peaktime period, when the increase in traffic using the interchanges within the study
area compensate the reduction in the marginal revenue. For the off-peak andnight time periods, the reduction in the marginal revenue had a major impact inthe total revenue.
More detailed analyses of these results show a significant variation ofrevenue results within each time period, which suggests that the revenue
management model will produce better results if applied to a different timetablewith shorter time periods.

6Conclusions

The analyses permit to reach conclusions on the issues: potentiality andapplicability of the model; impacts in revenue and traffic volume; andrecommendations for further research.
The model showed a potential use for revenue management in themaximization of toll revenue. The requirements in terms of data management,
which historically impose a barrier for revenue management implementation, arenow available in several cities through electronic toll collection.
The proposed model showed positive results in increasing the total
revenue during the peak time period. During other periods the model resulted inconsiderably decrease in total revenue. Based on the behaviour of the demandrate, it is concluded that a price-time framework with shorter intervals wouldimprove the efficiency of the price scheme.
The changes in departure time are considered in the dynamic stochastic
assignment method used for the model testing as temporal utility; however they
are considered in the proposed model. As next step, it is recommended that theimpact in departure time be included in the modelling process, which incurs in
the development of a detailed assignment algorithm that considers variations in
the value of time at OD pair level and variations in temporal utility.
The assessment of the impact of demand heterogeneity was possible throughusing average values of value of time for a larger number of demand subsegments within the freight vehicle segment. It is recommended that in futuredata collections, the type of truck and type of cargo are also included, in order topossibly include these parameters in the model.
Finally, it was concluded that a variable toll price system may optimize therevenue collection, depending on the correct definition of the intervals for pricechange and definition of more specific vehicle classes for toll pricing.

References[1] Nagae, T. & Akamatsu, T., Dynamic Revenue Management of a Toll Road
Project under Transportation Demand Uncertainty, Networks and SpatialEconomics Vol.6, pp.345-357, 2006.
[2] Schreiner, S., Hyodo, T. & Takahashi, Y., A Study on the Influence of
Network Attributes on the Route Choice Behavior, Eastern Asia Society ofTransportation Studies, Vol. 7, pp. 642-653, 2007.
[3] Schreiner, S. & Hyodo, T., A Study on the Estimation of Value of Time
based on Truck Route Samples and Its Applications in Assignment
Procedures, Japan Society of Traffic Engineers, Proceedings of the 27th
Annual Meeting, 2007.