DIEPENBEEK, 2010.
STEUNPUNT MOBILITEIT & OPENBARE WERKEN SPOOR VERKEERSVEILIGHEID
Time valuation in traffic
Congestion costs, value of time & lost vehicle hours.
RA-MOW-2011-001
K. Van Raemdonck, C. Macharis
Documentbeschrijving
Rapportnummer: RA-MOW-2011-001
Titel: Time valuation in traffic
Ondertitel: Congestion costs, value of time & lost vehicle hours.
Auteur(s): K. Van Raemdonck, C. Macharis
Promotor: Prof. dr. Cathy Macharis
Onderzoekslijn: Evaluatietechnieken
Partner: Vrije Universiteit Brussel – MOSI T
Aantal pagina’s: 35
Projectnummer Steunpunt: 5.1-5.2
Projectinhoud: Evaluatietechnieken
Uitgave: Steunpunt Mobiliteit & Openbare Werken – Spoor Verkeersveiligheid, december 2010.
Steunpunt Mobiliteit & Openbare Werken Spoor Verkeersveiligheid Wetenschapspark 5 B 3590 Diepenbeek T 011 26 91 12 F 011 26 91 99 E [email protected] I www.steunpuntmowverkeersveiligheid.be
Samenvatting
In dit rapport wordt een methode voorgesteld om de congestiekosten ten gevolge van een ongeval te berekenen. Alle kosten die verbonden zijn met een ongeval worden overlopen. Het gaat enerzijds over slachtoffergebonden kosten zoals medische kosten, kosten door productieverlies en immateriële kosten. Anderzijds zijn er ook de ongevalgebonden kosten, zijnde de materiële kosten, afhandelingskosten en de congestiekosten.
Bij deze laatste blijkt dat enerzijds de voertuigverliesuren een belangrijke component zijn, langs de andere kant is ook de waarde van reistijd van fundamenteel belang voor de berekening ervan. Er wordt dan ook dieper ingegaan op de waarde van tijd. Het probleem van de variatie in deze reistijdwaardering wordt aangekaart en de verschillen tussen de waarderingen voor goederenvervoer, woon-werkverkeer, zakelijk verkeer en overig verkeer komen aan bod. Deze verschillen uiten zich in het feit dat goederenvervoer en zakelijk verkeer (verkeer tijdens betaalde uren) een hogere waarde van reistijd hebben dan woon-werkverkeer of overig verkeer zoals verkeer voor boodschappen of recreatie.
Vervolgens wordt er nog dieper ingegaan op de voertuigverliesuren. Het bleek dat er voor België of Vlaanderen nog geen volledig redundant systeem met gesloten wegsegmenten en dubbele inductielussen om snelheden en intensiteiten te meten bestaat (de uitbouw hiervan is echter wel gepland tegen 2012). Hierdoor is ook de betrouwbaarheid van de gegevens niet altijd even groot, waardoor er door middel van een literatuurstudie wat dieper ingegaan is op de verschillende methoden voor het berekenen van voertuigverliesuren. Hieruit werd dan, op basis van de voordelen van de verschillende methoden, een nieuw framework opgesteld. Op basis van de leerpunten uit dit rapport kan dan in verder onderzoek, na verzameling van de nodige gegevens, een meer betrouwbare berekening van de voertuigverliesuren uitgevoerd kan worden.
Tenslotte worden de congestiekosten besproken. Deze worden opgesplitst in kosten door uitwijkgedrag, kosten door de onbetrouwbaarheid van reistijden en kosten door gemiddelde extra reistijd. Onder uitwijkgedrag verstaan we onder andere het vertrekken op een ander tijdstip, met een andere transportmodus reizen, een andere route kiezen, of zelfs helemaal van de verplaatsing afzien. Van onbetrouwbaarheid van de reistijd is er sprake als de voorspelbaarheid van de reistijd klein is én wanneer de variatie in de reistijd groot is. De kosten door gemiddelde extra reistijd zijn alle kosten door tijdsverliezen opgelopen door weggebruikers op het wegennet gesommeerd over een bepaalde tijdshorizon, uitgedrukt in geld. Ze vertegenwoordigen slechts het tijdsverlies onderweg, en dekken dus niet de totale economische impact van congestie en vertragingen, noch de maximale voordelen die worden verkregen door het oplossen van een file. Deze kosten voor gemiddelde extra reistijd worden vervolgens berekend, gevolgd door een grondige bespreking van de beperkingen van deze berekening en de gebruikte data.
English summary
Title: Time valution in traffic
Subtitle: Congestion costs, value of travel time & lost vehicle hours. Abstract
In this report a method to calculate the congestion costs as a result of a road accident is presented. First, all the costs associated with an accident are discussed. On the one hand there are the injury-related costs like the medical costs, the costs because of production losses and the intangible costs. On the other hand there are the accident-related costs, being the tangible or material costs, the handling costs and the congestion costs.
With these last costs the lost vehicle hours seem to play an important role. On the other hand, the value of travel time is of great importance in the calculation of the congestion costs. This is why the value of travel time is studied in more detail. The problem of the variation in travel time valuation is raised, as well as the differences in the valuation of time of freight transport, commuting, business-related traffic and other traffic. These differences manifest themselves in the fact that freight transport and business-related traffic (traffic during paid working hours) have a much higher value of travel time compared to commuting or other traffic such as traffic for shopping or recreation.
Thereafter, the lost vehicle hours are studied in more detail. It appeared that for Belgium or Flanders a fully redundant system with closed road segments and double induction loops to measure vehicle speeds and intensities does not yet exists (the extension of the current network to such a network however, is planned for 2012). Because of this, the data is not always as reliable as needed, which is why the different methods for calculating the lost vehicle hours are studied in a literature review. On the basis of this literature study, a new framework was derived, so that in further research, after collecting the necessary data, a more reliable calculation of the lost vehicle hours can be performed.
Finally, the costs of congestion are being discussed. Congestion costs are divided into costs by alternative behavior, costs incurred by the unreliability of travel times and costs for the average extra travel time. Among alternative behavior we mean leaving at a different time, travelling with a different transport mode, using a different route, or even completely renouncing from the journey. Unreliability of travel time is present when the predictability of travel time is small and the variation in travel time is high. The costs for extra travel time include all costs by time losses incurred by road users summed over a certain time horizon, expressed in money. They only represent the waste of time while underway and do not cover the total economic impact of congestion and delays, nor the maximal benefits that could be obtained by solving a traffic jam. These costs for the average extra travel time are calculated, followed by a thorough discussion on the restrictions of this calculation and the used data. Conclusion finalizes the report.
Table of content
1.
I
NTRODUCTION... 6
2.
E
CONOMIC COST OF ROAD ACCIDENTS... 8
3.
V
ALUE OF TRAVEL TIME... 11
4.
L
OST VEHICLE HOURS... 13
4.1 1st method: The Netherlands (AVV, 2004) 13 4.1.1 Before 1999 ...13
4.1.2 After 1999 ...14
4.2 2nd method: Method of Tampère et al (2007) 15 4.3 3th method: Method of Morales (1986) 17 4.4 New Framework 19
5.
R
ELATION BETWEEN ACCIDENT COSTS AND THE VALUE OF TIME:
CONGESTION COSTS21
5.1 Incidental traffic jams 21 5.2 Congestion due to road accidents 21 5.3 Costs of congestion 22 5.3.1 Alternative behavior ...225.3.2 Costs by the unreliability of travel times ...24
5.3.3 The cost for average extra travel time ...25
5.3.4 Discussion ...30
6.
C
ONCLUSION... 32
6.1 Policy Recommendations 32 6.2 Future Research 33
7.
R
EFERENCES... 34
1 .
I
N T R O D U C T I O N
Being stuck in traffic has a cost to the society that might not be underestimated. This cost depends, among others, on the travel motif of those who are stuck in traffic. For example, for a truck driver who has to deliver a just-in-time delivery it is very important to remain on schedule. Someone who is stuck in traffic during paid working hours also causes a major cost for the company and indirectly the community. However, recreational traffic has a much lower cost. If you are, for example, visiting a friend or on your way to do some shopping, then lost time in a traffic jam is estimated to be less costly compared to on-the-job lost travel time.
According to De Brabander (2006) congestion costs in Belgium in 2002 were € 13,282,770. This, however, is an underestimation because it does not take the costs of alternative behavior and unreliability of travel time into account. The variation in the valuation of time and the unreliability of the data related to the lost vehicle hours should also be taken into account.
As can be concluded from a previous report in Work Package 5.1, “The stakeholders and their criteria in road safety measures: The next step in the development of the MAMCA”, one of the most important criteria of road users concerning road safety measures is travel time. In every of the three types of measures that can be taken to improve road safety, i.e. user related measures, vehicle related measures and infrastructure related measures, travel time plays a major role (Van Raemdonck et al., 2010). Congestion costs could be a good indicator of this criterion. This is why it is important to have a good estimation of these congestion costs. This report examines the congestion costs, how they are composed and especially how they can be calculated reliably. The last topic appears to be a problem. First, there are many different figures for the value of time, even if the travel motif is the same. There is also a lot of variation between different individuals and how they experience a loss of time while travelling. Not only the travel motif is important, but also the circumstances in which the journey happens and the type of transport mode can have a major impact. On the other hand, the calculation of the lost vehicle hours seems to be a problem as well. Lost vehicle hours are annually reported for Belgium and Flanders, but these reported figures are not always that reliable. To obtain correct and reliable data for the calculation of the lost vehicle hours it is important that the network is well equipped with accurate measurement systems, i.e. double induction loops to calculate vehicle speeds and intensities. In Flanders, such a quality network of measurement systems is being installed on the main roads since 2005. The density of the network however, is only high enough on the Ring of Antwerp and the E313. The extension of a fully redundant quality network of double induction loops, which is dense enough for reliable calculations of the lost vehicle hours, is planned for 2012. For secondary roads there is no data available at all, but the development of a measurement system for these roads is also planned. However, this will be a lot more complex than it is for the main road network. This is why, in this report, some methods for the calculation of the lost vehicle hours are being discussed. Based on these theories a new framework to estimate the lost vehicle hours will then be derived. Further research will exist out of the collection of the necessary data, with which the lost vehicle hours can be calculated more accurately. Afterwards, a better figure for the congestion costs can be estimated.
The next chapter of this report will deal with the costs resulting from a road accident in general. Next, the value of travel time will be examined in chapter 3. The fourth chapter will consist of a brief literature study about the methodology for the calculation of the lost vehicle hours. Based on this literature study a new framework will be set up in which the different advantages of the various discussed methods will be implemented. Finally, the
congestion costs and the calculation of these costs are studied, followed by a thorough discussion on the limitations of these calculations and the used data. Conclusion finalizes the report.
2 .
E
C O N O M I C C O S T O F R O A D A C C I D E N T S
The quantification of the costs of road accidents is a very important step in the efficient spending of resources to improve road safety. It offers an insight in the size of the problem and makes it comparable with other societal problems. Even more relevant, it reflects the magnitude of the benefits to be obtained if road accidents can be avoided (De Brabander, 2006). In other words, it is important for policy makers to take the costs resulting from road accidents into account when deciding on road safety measures. The social costs caused by road accidents include all costs for the compensation and recovery from any injuries and damages and all costs relating to the settlement of damages caused by an accident, but also all other costs resulting from the accident that occurred including production losses, congestion costs (of congestion created by an accident) and intangible suffering (SWOV, 2006). This definition proves that many different types of costs originate from road accidents. The aim of this chapter is to give a brief overview of the different costs resulting from accidents and how they are composed. Costs caused by traffic accidents can be divided into two groups. First there are the injury-related costs such as medical costs, production losses and intangible costs. Second, there are the accident-related costs, which are the tangible costs, handling costs and congestion costs. A schematic representation of the costs incurred by road accidents is shown in figure 1.
Figure 1: Classification of the costs resulting from road accidents
Source: SWOV, 2006
The injury-related costs are composed of medical costs, costs of production losses and intangible costs. Below, a short explanation of each of these components will be given.
• Medical costs
Medical costs cover the expenses necessary for the transportation to the hospital and care of the victims of an accident. It includes the cost to bring the ambulance to the scene of the accident, the medical care for the wounded, the cost of rehabilitation, etc. Also visiting costs, what visitors must pay to visit a victim in the hospital, and accelerated funeral expenses, which of course only occur in the case of a fatal accident, are considered as medical costs. The medical costs cover about 2% of the total road accident costs in Belgium (De Brabander, 2006).
• Production losses
Victims of accidents will sometimes be incapable to work for while. Some will even never work again, or will work less after their accident. This of course, next to the victim himself and his surroundings, is a cost for the society. These costs are called the "cold-blooded component of an accident" (Lindberg et al, 1999). So, production loss is the loss of output because of getting injured or dying prematurely as the result of a road accident. The future loss should also be charged here. This approach for defining production losses is also called the Human Capital Approach (Connelly & Suspangan, 2006). According to the estimates of De Brabander (2006) for 2002 the temporary and permanent production losses account for about 35% of the total costs resulting by road accidents in Belgium.
• Intangible costs
This is, in contrast to the previous, called the "warm-blooded component of an accident" (Lindberg et al, 1999). They are also called human or intangible costs and a previous report about these costs was written by Van Lier et al. in 2009 (RA-MOW-2009-002). The premise is that because of all the suffering and pain resulting from an accident, people want to avoid it, even without considering the financial consequences of the accident. These costs are usually calculated based on the value of a statistical life. The value of a statistical life is in fact a return, because by the rescue of a human life, and thus avoiding a fatality, much suffering and pain is avoided. The question to be asked is what road users want to pay to reduce or avoid accident risks. In other words, the willingness to pay for a reduction of the risk for a traffic accident is estimated (De Brabander & Vereeck, 2005; Van Lier et al, 2009). The intangible costs represent the biggest part of the traffic accident costs and covered 41% of the accident costs in Belgium in 2002 (De Brabander, 2006).
The accident-related costs are composed of tangible costs, handling costs and congestion costs. Again, a short explanation of these costs is given below.
• Tangible costs
These costs include the total material damage caused by an accident. Both damage to private property, including damage to vehicles, houses, cargo, etc. and damage to public property such as roads and other transport infrastructure are included. These costs accounted for about 19% of the total road accident costs in Belgium in 2002 (De Brabander, 2006).
• Handling costs
These are the costs resulting from the handling of road accidents. They include the costs of the fire departments, police and justice, but also cover the administering costs of insurance companies due to medical and material damage (SWOV, 2006). According to the estimates of De Brabander (2006) for 2002 handling costs covered a little more than 2% of the accident costs in Belgium.
• Congestion costs
These are the costs resulting from the time lost in traffic jams caused by road accidents. To determine these costs, the total congestion costs are divided by the share of the total congestion caused by road accidents. There are three types of congestion costs: costs resulting from direct travel time losses, costs resulting from unreliable travel times and the costs of alternative behavior. Direct travel time losses refer to the economical damage that occurs because within a certain amount of time fewer destinations can be reached and thus people cannot travel as far as they want to. Unreliable travel times arise from the fact that because of traffic jams as a result of road accidents the travel time is difficult to estimate. Arriving too early or too late because of this creates additional costs. Finally, alternative behavior arises because people want to avoid congestion by choosing a different route, leaving sooner or later, choosing another transport mode or even completely renouncing from their journey. According to estimates for 2002, congestion costs are the smallest part of the accident costs in Belgium. They only represent 0.11% of the total costs resulting by traffic accidents (De Brabander, 2006).
However, calculating congestion costs often results in an underestimation. Usually only the costs resulting from direct travel time losses are charged, and costs resulting from unreliable travel times and alternative behavior are not taken into account. Besides, data for the lost vehicle hours are often used in the estimation of these costs, but these data are not always reliable enough. Therefore it seems interesting to take a closer look at the calculation of congestion costs. So, the remainder of this report will handle about congestion costs more specifically. It will be studied whether it is true that congestion costs are systematically being underestimated, and whether they account for a larger share of the total costs incurred by road accidents than usually assumed. In order to do so, the congestion costs due to road accidents have to be calculated first. For this calculation the value of travel time has to be multiplied with the lost vehicle hours incurred by road accidents. According to De Brabander and Vereeck (2005) about 12% of the total number of traffic jams is caused by road accidents. This, however, does not mean that also 12% of the lost vehicle hours are caused by traffic jams as a result of accidents. Indeed, traffic jams caused by accidents will, on average, last longer than ordinary structural traffic jams. Hof and Vermeulen (2001) argue that 13.5% of all lost vehicle hours are the result of congestion due to road accidents.
• Total costs
The total cost is the sum of the various sub costs. In 2002, according to De Brabander (2006), the total costs as a result of road accidents in Belgium were €12.215.432.410. This represents 4.6% of Belgium’s Gross Domestic Product, which is higher than the average accident cost of developed countries. According to Connelly and Suspangan (2006) the average cost of road accidents in developed countries is about 2-3% of the GDP. The biggest part of the total costs consists of the intangible costs, costs by production losses and material costs. Congestion costs are the smallest part of the total cost (De Brabander, 2006).
However, as already mentioned above, congestion costs are being systematically underestimated. In the remainder of this report the calculation of congestion costs will therefore be examined in more detail. In the next chapter the value of time, a first important input variable for the computation of congestion costs, will be discussed.
3 .
V
A L U E O F T R A V E L T I M E
The value of travel time is a much needed input variable concerning the estimation of congestion costs, because the hours lost due to congestion have to be multiplied with this value of time in order to compute the congestion costs. It would be unrealistic to put a fixed value on the value of time, hence different values of time exist for various journey motifs. This chapter is about this variation in the value of time.
The value of travel time (VTT) refers to the cost spent for transportation, including the waiting and the actual transport itself. It consists of the personal, unpaid time lost to transportation, as well as the costs for businesses, being paid working hours that are lost while being on the road. The value of travel time savings (VTTS) consists of the benefits arising from reducing the travel time (Litman, 2009).
The costs associated with travel time can be divided into two major groups. First there are the on-the-job time losses; these include the costs to the employer who has to pay the lost hours of employees during work-related travel. Second, there are the off-the-job travel time losses. These are the trips for personal purposes and commuting, and represent the opportunity cost of time spent on journeys that could be spent on doing something else.
The total travel cost is the product of the time spent on travelling (expressed in hours) and the unity cost (expressed in euro per hour).
UnityCost
T
TravelCost
total=
travel×
With TravelCosttotal = the total cost of the trip (expressed in euro)
Ttravel = time spent on the trip (expressed in hours)
UnityCost = the cost of one hour travel = value of time (expressed in euro/hour)
This unity cost varies according to the purpose of the trip. For example, on-the-job trips will have a higher value of time than off-the-job trips. This is illustrated in table 1.
Table 1: Value of time per motif (euro/hour)
Freight transport
Persons transport
commuting
business
other
(1)
-
8,37
28,97
5,78
(2)
42,35
8,6
29,77
8,94
(3)
45,78
6,86
24,04
4,58
(4)
45,3
7,5
24,5
6
Sources: (1) De Nocker et al, 2006
(2) Rijkswaterstaat: Dienst Verkeer en Scheepvaart, 2006 (3) Vanhove, 2008
(4) De Brabander, 2006
A lot of other variation occurs in the valuation of travel time. This variation depends on various factors like the type of vehicle, the purpose of the trip, the occupancy of the
vehicle1, the traveler himself, the region, etc. The result of this variation is that, even if sufficient quality data is available, there is uncertainty about the estimates of the value of time and the congestion costs.
It should be noted that travel time is not always lost time. Indeed, some travel can be used useful, or people may enjoy a certain amount of time in the car, train or bus. Some types of travel time have very low costs, or even positive values. This can be the case when traveling is a desired activity and people are enjoying the experience of the trip. Mostly these are recreational trips or trips for leisure, which involve e.g. riding with a new car or social activities like joyriding with friends. Travelling can also be combined with another activity. People can for example work on the train, or read a book or the newspaper. The literature however, is still often based on the rather short-sighted idea that travel time is always lost time. There is no model available yet for calculating the value of travel time that takes into account the fact that travel time does not necessarily have to be lost time (Lyons & Urry, 2004). In our case, however, it can be assumed that most travel time has a negative perception, because this report is about the time lost due to congestion.
In the next chapter the second important variable to calculate the congestion costs, i.e. the lost vehicle hours, will be discussed. After a brief literature study, a new framework to compute the lost vehicle hours will be presented.
4 .
L
O S T V E H I C L E H O U R S
The indicator lost vehicle hours (VHL) shows the delays incurred by vehicles because of congestion and delayed traffic flows. In other words, lost vehicle hours draw a picture of the lost travel time of road users and thus are an important indicator for quantifying the economic effects of congestion (AVV, 2004). Congestion costs can be calculated by multiplying these lost vehicle hours with the value of time, which was discussed in the previous chapter.
However, the calculation of the VHL is quite complicated. Quality input data is needed, and to collect this data there is a need for a reliable, redundant network of measurement systems. In Flanders such a quality network is being installed on the main roads since 2005. Nevertheless, as already mentioned, the density of this network is not always high enough to perform reliable calculations. Therefore the focus in this chapter will lie on the methodology of the calculation of lost vehicle hours and the description of the data needed to perform the calculations. However, the quality and accuracy of the lost vehicle hours does not only depend on the travel time calculation, because the density of the measurement systems, the number of setting parameters, the interpolation method for unavailable data, the level of aggregation (per 10 seconds, minute, 15 minutes, …) etc. also need to be taken into account. Furthermore, the systems work well most of the time in free flow traffic, but situations with traffic delays or unexpected incidents should be handled differently when calculating travel time. It is in this specific types of situations that one algorithm may work better than another. So the methods described in this chapter should be tested and evaluated in different traffic situations to draw more significant conclusions on which method to use in which situation.
In this section a brief literature review on the existing methods for computing the lost vehicle hours is presented. First the method used in the Netherlands is explained. Second, a more graphical method based on a study of Tampère et al (2007) is presented. Finally, the better known and similar method of Morales (1986) will be discussed. The last part of this chapter will present a new framework for computing the lost vehicle hours, based on the discussed literature.
4.1
1
stmethod: The Netherlands (AVV, 2004)
4.1.1 Before 1999
In the Netherlands the former AVV (Advice on Traffic and Transport), now RWS-DVS (Rijkswaterstaat – Dienst Verkeer & Scheepvaart), is in charge of the calculation of the lost vehicle hours. Before 1999 the following framework was used. Data were not as accurate as they are now and there was a lot of under registration of congestion. Lost vehicle hours were calculated based on two formulas:
= × × × ℎ
With: VHL = Lost Vehicle Hours
GF = Getaway Flow (number of vehicles per lane that are able to leave the traffic jam during one hour)
Lanes = Number of available lanes
ℎ = × ℎ + +
With: Weight = Congestion weight (hours*km) Duration = Duration of the traffic jam (hours) Length = Length of the traffic jam (km)
Construction = Construction weight of the traffic jam (hours*km) Reduction = Reduction weight of the traffic jam (hours*km)
Duration and length were recorded during the registration of the traffic jam. For the construction and reduction of the traffic jam a fixed value of 2.5 minutes per kilometer was used, with the constraint that the total construction or reduction is no more than 30 minutes. The value for the delay was 4 minutes per kilometer and a getaway flow of 1500 pce/hour/lane was used2.
The number of lost vehicle hours due to unreported and non-observed traffic jams was estimated based on the total number of lost vehicle hours due to the reported traffic jams. The number of lost vehicle hours due to delayed traffic flows was also estimated. This was done by multiplying the lost vehicle hours with a fixed McKinsey-factor of 1.4.
4.1.2 After 1999
The basic ingredients for the present methodology in the Netherlands are data on speeds and intensities on the highway network. For the part of the network that is equipped with signaling infrastructure, this data is used to calculate the lost vehicle hours. For the part that is not equipped with the right infrastructure estimates of a model, called Flowsimulator, are used. This model simulates synthetic data that are similar to the data from the signaling infrastructure.
Lost vehicle hours are calculated for each quarter on each measurement site. First the actual speed and the standard speed (normally 100 km per hour) are expressed in hours per kilometer instead of kilometers per hour. By subtracting the standard speed of the actual speed the travel time losses in hours per kilometer are calculated. These travel time losses are then multiplied with the distance over which the measurement site has been declared applicable. This leads to the travel time losses expressed in hours. Finally, this number is multiplied by the number of vehicles, which is determined by multiplying the intensity (in vehicles per hour) with 0.25 hours (one quarter).
Or, expressed as an equation:
= × × ×
2
With: VHL = Vehicle Hours Lost
TTL = Travel Time Loss (hours/km)
d = Distance over which the data are applicable I = Intensity (vehicles/ hour)
t = Time over which the intensity is measured (0.25 hours)
And:
=
!"#$!%
−
'#!()!*)With: Vactual = The actually driven speed
Vstandard = The standard speed or comparison speed3
In Flanders a similar method is used to calculate the VHL. The comparison speed is taken as 90% of a normalized speed. The actual speed depends on the speed of the vehicles that enter the road segment and is adapted every minute. This way more accurate speed flows are calculated. The absence of enough measurements systems, however, results in road segments that are so long that calculated speed flows are not reliable anymore. Another problem is that in Flanders not al the roads are well enough equipped with the right measurement systems. The installation of double induction loops started in 2005, but there are still some roads in Flanders that are equipped with single induction loops. These are only capable of counting the passing traffic, not to measure speed, certainly not in a reliable way. To measure speed, a high density of systems of double loops is necessary. At this moment the density is high enough on the Ring of Antwerp and the E313 (the extension from the current network to a fully redundant network in the whole of Flanders is planned for 2012). A third problem with the annually reported VHL-figures in Flanders is that the Ring of Antwerp is not included in these figures, this while a large part of the lost vehicle hours find their origin in and around Antwerp. It is therefore advised that the reported figures are processed in a very critical way. All this strengthens the need for a well founded methodology for the calculation of the lost vehicle hours and a road network that is fully covered with double induction loops.
4.2
2
ndmethod: Method of Tampère et al (2007)
This model is based on a study of Tampère et al (2007) who has developed a methodology for identifying vulnerable sections in a road network. In a first stage of this model they make a long list of those vulnerable network links, based on the travel time losses and the occurrence of incidents on that particular link.
For the simplicity, we consider an accident that only caused congestion on the affected network link. So there is no repercussion of the traffic jam to the upstream links, as can be seen in figure 2.
3
The comparison speed is set at 100 kilometers per hour. If the actual speed exceeds this comparison speed, ‘profit hours’ are not taken into account.
Figure 2: Accident with no repercussion to the upstream network links
Source: Tampère et al (2007)
The model is based on the following figure:
Figure 3: Calculation of the lost vehicle hours due to an incident
Source: Tampère et al (2007)
The line under slope I from the origin in figure
network link. The line under the same slope, but shifted along the time axis, represents the outflow on that particular network link. An incident reduces the outflow to z
after a certain amount of time
resolve at a getaway flow C. This continues until after a period T all the accumulated traffic at the road network link is dissolved. From that moment, the outflow is back at its original level (slope I). The gray area A represents the total vehicle hours that are lost due to the accident. For A we find the following expression (Tampère et al, 2007):
The formula shows (and this is illustrated in figure
measured in lost vehicle hours is proportional to the square of the incident duration. Namely, if ∆t1 increases to ∆
A+A’.
no repercussion to the upstream network links
Source: Tampère et al (2007)
The model is based on the following figure:
: Calculation of the lost vehicle hours due to an incident
Source: Tampère et al (2007)
The line under slope I from the origin in figure 3 shows the inflow in a certain road network link. The line under the same slope, but shifted along the time axis, represents the outflow on that particular network link. An incident reduces the outflow to z
after a certain amount of time ∆t1 the capacity has fully recovered, the traffic jam will
resolve at a getaway flow C. This continues until after a period T all the accumulated traffic at the road network link is dissolved. From that moment, the outflow is back at its I). The gray area A represents the total vehicle hours that are lost due to the accident. For A we find the following expression (Tampère et al, 2007):
+ =
Δ
-2/1 −
1 2
The formula shows (and this is illustrated in figure 3 as well) that the effect of
measured in lost vehicle hours is proportional to the square of the incident duration. ∆t1’, the amount of vehicle hours lost will increase from A to
shows the inflow in a certain road network link. The line under the same slope, but shifted along the time axis, represents the outflow on that particular network link. An incident reduces the outflow to zero. If, the capacity has fully recovered, the traffic jam will resolve at a getaway flow C. This continues until after a period T all the accumulated traffic at the road network link is dissolved. From that moment, the outflow is back at its I). The gray area A represents the total vehicle hours that are lost due to the accident. For A we find the following expression (Tampère et al, 2007):
) that the effect of an incident measured in lost vehicle hours is proportional to the square of the incident duration. ’, the amount of vehicle hours lost will increase from A to
4.3
3
thmethod: Method of Morales (1986)
The premise of this theory is that an incident affects the road capacity. An incident reduces the capacity of the part of the road where it occurs. Congestion will arise when the incident reduces the capacity in that extent that the intensity exceeds the reduced road capacity. If the intensity already exceeds the road capacity before the accident, then congestion will increase even more due to the incident (De Ceuster, 2003).
For any road, delays due to incidents depend on the following data:
- Demand (λ: the number of arrivals per hour) at the time of the incident - The reduced capacity (µr) of the road after the incident
- The total incident duration
- The capacity after the incident (µ: drive off capacity or getaway flow)
Figure 4: Method of Morales
Source: De Ceuster, 2003
Figure 4 can be used to calculate the incident delay (the area AB1B2C). The horizontal
axis represents time, the vertical axis the cumulative traffic flow. The demand, in vehicles per minute, is shown by the line segment AC. If an incident takes place, the traffic flow gets stopped because capacity reduces (line segment AB1). At that moment
demand (λ) is greater than supply (reduced capacity µr). The reduction of the capacity
gets smaller when the vehicles that were involved in the accident are cleared (line segment B1B2). After the complete recovery of the incident, traffic can continue its path
(line segment B2C). At that moment full capacity is restored, but it will still take some
time for the congestion to be resolved. It is thus possible to determine the total incident duration on the basis of this theory.
In figure 5 the cumulative volume (expressed in number of vehicles) is again plotted against time. λ indicates the arrival intensity (vehicles per unit of time) and µ indicates the departure capacity. The reduced capacity (µR1 andµR2) can still vary throughout the
incident. Once µ falls below λ congestion is created. Total delay is then equal to the polygon AB1C1D1 (expressed in lost vehicle hours).
The length of the traffic jam (tQ) is a function of the incident duration (tR), λ, µ and µR:
3=
456 −6
6 − λ
47
The total delay (TD) caused by an incident is equal to:
=
435λ −6
2
47
These equations show, like in the previous method, that the total delay increases in proportional fashion with the square of the incident duration. If the duration of the incident can be decreased, then the total delay will be reduced (as can be seen in figure 5).
Figure 5: Incident duration and delay
4.4
New Framework
Each of the previous methods has some strengths and weaknesses. Therefore a new framework, which combines the strengths of the previous methods, is presented in figure 6. This model is applicable on any given road segment, for which accurate and reliable measurement systems (i.e. double loops) are available to measure the in- and outflow on that given segment. If an incident happens, the outflow (or capacity) reduces, but it does not reduce to zero. Namely, an incident does not always block the entire road, so that a reduced outflow is still possible. This reduced outflow is shown by the slope A in the figure. The inflow is given by slope I. After a while the capacity will regain its normal value (this can also happen in different steps if different driving lanes have to be cleared), and the congested traffic will get away at a getaway flow with slope C. Like in the two methods discussed above, the problem arises when, because of the accident, the capacity can no longer fulfill the demand. Because of this, the inflow and outflow curve are not parallel anymore, which results in lost vehicle hours. These lost vehicle hours are presented as the shaded area in figure 6.
Figure 6 – Own Framework
Source: Own setup
Because in this model inflow, outflow, reduced capacity and getaway flow are all linear functions, it is known that:
Outflow (Capacity): 57 = + 9 Reduced capacity: 6:57 = + + 9 -Getaway flow: 57 = + 9;
The lost vehicle hours can then be calculated using integrals:
= <= 57
>? >@− = 6
:57
>? >@A + <= 57
>B >?− = 57
>B >?A
This formula can be easily expanded if the recovery of the road capacity takes place in various stages. If the accident would reduce the outflow to zero, the formula proposed in the method of Tampère can be used (only if capacity recovers in just one step).
5 .
R
E L A T I O N B E T W E E N A C C I D E N T C O S T S A N D T H E
V A L U E O F T I M E
:
C O N G E S T I O N C O S T S
This part will cover costs incurred by the time lost due to congestion and traffic delays because of road accidents. By valuating these time losses, the cost of “being in a traffic jam” will be calculated. As mentioned before, multiplying the value of time and the lost vehicle hours, which have been discussed in the previous chapters, results in the costs incurred by congestion. It should be noted that not all congestion costs are being discussed here, but only those resulting from an accident. Structural, daily traffic jams caused by the overload of the road network or traffic jams caused by roadwork are not included.
First, incidental congestion in general is discussed. Afterwards this incidental congestion will be limited to congestion caused by road accidents. In a third paragraph, the various costs associated with these traffic jams resulting from road accidents are commented. Finally, the costs incurred by direct travel time losses are calculated, followed by a critical discussion of the limitations of this calculation and the used data.
5.1
Incidental traffic jams
According to Van Reisen (2006) incidental traffic jams, in the broadest form, can be defined as all traffic jams that are not situated at the everyday bottlenecks. In other words, incidental traffic jams are traffic jams that differ in cause, location, time, length and duration from the congestion at the fixed structural bottlenecks. These include both incidental congestion caused by problems in the capacity supply, such as congestion as a result of weather conditions, accidents and road works, as incidental congestion caused by problems in transport demand such as congestion due to seasonality and special events. Hereby, it has to be noted that most of the incidental traffic jams are caused by the first group of reasons, i.e. problems in capacity supply.
5.2
Congestion due to road accidents
This type of congestion falls under the category of incidental traffic jams. If it is known that congestion due to road accidents represents 60% of the incidental traffic jams, and the incidental traffic jams account for 20% of the total number of congestion, it can be stated that the number of traffic jams caused by an accident is about 12% of all congestion (De Brabander & Vereeck, 2005). This does not mean that also 12% of lost vehicle hours are caused by traffic jams as a result of accidents. Indeed, traffic jams caused by accidents will, on average, last longer than ordinary structural traffic jams. According to Wismans and Knibbe (2007) in The Netherlands approximately 20% of the number of lost vehicle hours is caused by incident congestion. Hof and Vermeulen (2001) argue that 13.5% of all lost vehicle hours are the result of congestion due to road accidents.
Congestion caused by accidents, along with congestion caused by weather conditions, are the least predictable types of traffic jams. These traffic jams are therefore often very unexpected and thence the cost of unreliability will play an important role in the calculation of the cost of this type of congestion.
5.3
Costs of congestion
As can be seen in Figure 7, tare divided into direct and external costs. These external costs include environmental nuisance (emissions, noise,…
separated into two parts. On the one hand there a
alternative driver behavior. Alternative behavior covers detours, leaving earlier or later to avoid traffic jams, using a different transport mode or completely renouncing from the journey. On the other hand there are the co
congestion costs. These are then further divided into the costs for the average extra travel time, costs for the unreliability of travel time and extra fuel costs. The costs for the average extra travel time, which are calculated later in this report,
average delay or cost for travel time losses and are expressed in
time. The costs of unreliability of travel time are equal to the dispersion around the mean delay and are expressed in
latter costs play a very important role in congestion due to road accidents, because these traffic jams are very unpredictable, and therefore the travel time losses are very difficult to estimate. Finally, there are the additional fuel costs, which will also play a role while standing in a traffic jam (Van Reisen, 2006).
Figure 7: Overview of the social costs due to congestion
Source: Van Reisen, 2006
5.3.1 Alternative behavior
Koopmans and Kroes (2003) argue that the measurement of congestion costs calculated solely based on the observed congestion, is probably not accurate since there exist alternative travel routes and m
transportation modes, but also travelling during off
destination or using another travel route, and even completely renouncing from the journey. It should be noted that alternative behavior will occur less frequently in the case of traffic jams resulting from accidents, because they are more difficult to anticipate due
Direct costs
On the road
Costs for average extra travel time
Costs for unreliablility of travel time
Extra fuel costs
Costs of congestion
, there are different types of congestion costs. First of all they are divided into direct and external costs. These external costs include environmental ,…) and road safety. The direct costs can in turn also be separated into two parts. On the one hand there are the welfare losses caused by alternative driver behavior. Alternative behavior covers detours, leaving earlier or later to avoid traffic jams, using a different transport mode or completely renouncing from the . On the other hand there are the congestion costs on the road itself, or observed congestion costs. These are then further divided into the costs for the average extra travel time, costs for the unreliability of travel time and extra fuel costs. The costs for the
which are calculated later in this report, average delay or cost for travel time losses and are expressed in Euros
time. The costs of unreliability of travel time are equal to the dispersion around the mean xpressed in Euros per minute standard deviation of travel time. These latter costs play a very important role in congestion due to road accidents, because these traffic jams are very unpredictable, and therefore the travel time losses are very difficult estimate. Finally, there are the additional fuel costs, which will also play a role while
an Reisen, 2006).
: Overview of the social costs due to congestion
Koopmans and Kroes (2003) argue that the measurement of congestion costs calculated solely based on the observed congestion, is probably not accurate since there exist alternative travel routes and modes. Such alternatives may include using other ation modes, but also travelling during off-peak hours, travelling to another destination or using another travel route, and even completely renouncing from the . It should be noted that alternative behavior will occur less frequently in the case traffic jams resulting from accidents, because they are more difficult to anticipate due
Social costs due to congestion
Direct costs
Costs for average extra travel time
Extra fuel costs
Alternative behavior
External costs
Environmental
nuisance Road safety
congestion costs. First of all they are divided into direct and external costs. These external costs include environmental and road safety. The direct costs can in turn also be re the welfare losses caused by alternative driver behavior. Alternative behavior covers detours, leaving earlier or later to avoid traffic jams, using a different transport mode or completely renouncing from the ngestion costs on the road itself, or observed congestion costs. These are then further divided into the costs for the average extra travel time, costs for the unreliability of travel time and extra fuel costs. The costs for the correspond to the uros per hour travel time. The costs of unreliability of travel time are equal to the dispersion around the mean per minute standard deviation of travel time. These latter costs play a very important role in congestion due to road accidents, because these traffic jams are very unpredictable, and therefore the travel time losses are very difficult estimate. Finally, there are the additional fuel costs, which will also play a role while
Koopmans and Kroes (2003) argue that the measurement of congestion costs calculated solely based on the observed congestion, is probably not accurate since there exist . Such alternatives may include using other peak hours, travelling to another destination or using another travel route, and even completely renouncing from the . It should be noted that alternative behavior will occur less frequently in the case traffic jams resulting from accidents, because they are more difficult to anticipate due
to their incidental nature. However, if good information coverage is provided, there will still be alternative behavior, but in lesser extent than there would be in the case of structural traffic jams. Dynamic speed signs can partly resolve this problem of information coverage.
The unobserved congestion costs, i.e. the costs for alternative travel behavior, are clarified by Koopmans and Kroes based on the following figure:
Figure 8: Supply and demand on the mobility market
Source: Koopmans and Kroes, 2003
In this figure, the amount of travel on a given road at a given time (horizontal axis) is plotted against the generalized costs (vertical axis). The marginal private cost curve (MPC) is horizontal at low traffic intensity, because traffic can drive without delay and is not faced with additional costs. The curve starts to rise at a critical amount of traffic, and then only gets steeper until point F, the maximal road capacity, is reached. At that point the marginal cost curve goes to infinity. Because there are several alternative options to avoid the congestion, the demand curve D1 is rather price elastic. Indeed, if costs rise, demand will fall. The observed congestion costs (lost time and fuel) are represented by the rectangle ABCD. The unobserved congestion costs are equal to the triangle CED. It is worth noting that, compared with the rectangle, the triangle is relatively small, what would mean that the observed congestion costs are greater than the unobserved. This would result in the fact that total congestion costs (in the case of moderate congestion) are not much higher than the observed congestion costs, and thus the costs for alternative behavior, in this case, only play a minor role.
However, if demand increases and the road capacity remains the same (the demand curve shifts from D1 to D2), the unobserved congestion costs become more important. The new demand curve intersects the marginal cost curve at a higher level, allowing both the rectangle and the triangle to grow. It can be seen that the costs by alternative behavior (the triangle) increase compared to the costs by the remaining travelers (the
rectangle). Koopmans and Kroes note that the rectangle’s surface increases in proportionate fashion with the capacity shortage, but the increase of the area of the triangle is proportional to the square of the capacity shortage. It can be concluded that the observed congestion costs can seriously underestimate the real congestion costs in a situation with a large capacity deficit, because the costs of alternative travel behavior are not observable and therefore they are not often included in the calculation. In the situation of congestion by road accidents this is, as previously mentioned, less of a problem, because in this case alternative behavior is more difficult as a result from the incidental nature of accidents (van Reisen, 2006).
5.3.2 Costs by the unreliability of travel times
Concerning the (un)reliability of travel time, both the ability to estimate travel time correctly and the variation in travel time are of great importance. The reliability will be high when the predictability of travel time is high or when the variation in travel time is small. Only if the predictability of travel time is small and the variation in travel time is high, there will be unreliability. Traffic jams due to accidents in particular, are a major cause for fluctuations in the expected travel time, because they are more difficult to anticipate. Thanks to the good estimation of the expected delay, people may be able to anticipate better on these traffic jams, which would reduce the congestion costs due to accidents (van Reisen, 2006).
If there are many, or high, fluctuations in the travel time, travel time will be unreliable. A person than can arrive too late, or he can anticipate on the unreliability and leave earlier (with the result that he will sometimes arrive too early at his destination). In both cases a situation arises where time is not used ideally. Next to the utility loss because of the unreliability of travel time, the individual can face additional utility losses by arriving too early or too late at his destination (Rietveld et al, 2005). In other words, the difference between the actual arriving time and the preferred arrival time can play an important role in the decisions of the traveler. This difference between the actual and the preferred arrival time is defined as ‘schedule delay’, so that
( )
(
h h)
D
PAT
t
T
t
S
=
−
+
With SD = schedule delay
PAT = preferred arrival time Th = time of departure
T(th) = amount travel time (dependent of th)
In general, people will appreciate too early and too late arrival times differently. Namely, if you arrive somewhere much too early, it can cost you some time you could have spent on doing something else. In contrary, if you are only 5 minutes early, this is not of great importance. However, if you are 5 minutes late, in many situations this can pose major problems. You can, for example, miss your train connection, arrive too late in a meeting, etc. And the later you arrive, the worse it gets. Hence the curve in the following picture is flatter while arriving too early, and it becomes very steep when arriving too late (Rietveld et al, 2005).
Figure 9: Valuation of 'schedule delay'
Source: Rietveld et al, 2005
Following figure 9, the previous formula can then be divided into SDE and SDL:
( )
(
)
(
h h)
DEMax
PAT
t
T
t
S
=
0
,
−
+
( )
(
)
(
t
T
t
PAT
)
Max
S
DL=
0
,
h+
h−
With SDE = Schedule delay early
SDL = Schedule delay late
5.3.3 The cost for average extra travel time
The costs for average extra travel time are all time losses incurred by the road users on the main and secondary roads summed over a certain time horizon, expressed in money. These costs only represent the waste of time while underway. So they do not cover the total economic impact of congestion and delays, nor the maximal benefits to be obtained by solving a traffic jam.
In these costs the relationship between the value of time and the economic costs of road accidents is the most apparent, because they are about the additional travel time caused by congestion due to accidents. To calculate these costs different data are needed. The number of lost vehicle hours due to traffic jams by accidents for both the main roads and the secondary roads are necessary. For further specification of these data it should be known which part of lost vehicle hours is undergone by trucks and which part by passenger cars, what the travel motif of the traveler is and what the occupancy (the number of occupants, being the driver and possible passengers) and value of time for the different motifs are. With all this data it will then be possible to calculate the overall costs of extra travel time by congestion due to road accidents. Below, the costs for extra travel time are calculated in six steps, based on Van Reisen (2006) and Maerivoet and Yperman (2008).
1. First of all, the lost time has to be calculated. These time losses (V) can be defined as the difference between the average travel time (T) and the travel time in an unloaded network with free flowing traffic (Tff). This free flow traffic is
usually taken at 90% of a normalized speed on that part of the road network. The time losses show how much time an average vehicle loses per kilometer on an average hour in a given period and can be calculated by using the following formula (Maerivoet & Yperman, 2008):
ff
T
T
V
=
−
If the average travel time is less than Tff, then the loss of time will be equal to
zero. This may occur in time periods characterized by very low travel times, e.g. during the night.
2. In the second step the total number of lost vehicle hours is specified. Lost vehicle hours are defined as the product of the traffic and the lost time. They show how much lost time is incurred by all vehicles on an average hour in a given period. The formula to calculate the lost vehicle hours is the following4 (Maerivoet & Yperman, 2008):
(
)
3600
V
q
VHL
=
×
With VHL = Vehicle hours lost V = Time losses
q = Traffic volume
Note that the first two steps are similar to the first method used to calculate the lost vehicle hours (i.e. the method used in the Netherlands). If another method is applied, the obtained VHL from this method can be used directly in the following step, and the time losses do not need to be calculated separately.
3. In a third step the proportion of the traffic jams due to accidents in the total number of lost vehicle hours will be determined. The part of traffic jams by an incident is, as earlier stated, about 13.5% of the total amount of lost vehicle hours (Hof & Vermeulen, 2001). Travel motifs are not yet taken into account in this step.
The annually reported figures for the lost vehicle hours in Flanders are shown in the following table. These figures, however, have to contend with some serious limitations. These restrictions are thoroughly discussed further in this report.
4
Table 2: Lost vehicle hours in Flanders
VHL incurred by
accidents (13.5%)
Year
VHL
2004
4.533.239
611.987
2005
4.282.549
578.144
2006
4.528.245
611.313
2007
5.409.571
730.292
2008
4.489.330
606.060
Source: Flemish Government, MOW, Traffic Centre & Hof en Vermeulen, 20015
4. In the fourth step the division per motif is applied to the lost vehicle hours. For each travel motif, the lost vehicle hours are multiplied with the share of the relevant motif.
Table 3: Travel Motif Distributions
Persons transport
Freight
transport
Commuting
Business
other
De Brabander (Vl)
23,31%
4,32%
57,85%
14,52%
OVG (Vl)
23,5%
3,8%
56,7%
16 %
Van Reisen (NL)
29%
22%
41,50%
7,50%
SWOV (NL)
39%
28%
25%
8%
Source: Own setup
As can be seen in the table above, variation in motif distribution exists. The Netherlands traditionally have a higher proportion of business transport, which is partly compensated with less freight transport. In the calculation presented here, each of the previous scenarios will be examined.
The lost vehicle hours due to road accidents per travel motif are given in the next table:
Table 4: VHL per travel motif
Persons transport
Freight
transport
commuting
business
other
D
e
B
ra
b
a
n
d
e
r
2004
142.654,23
26.437,85
354.034,63
88.860,55
2005
134.765,39
24.975,83
334.456,37
83.946,53
2006
142.497,08
26.408,72
353.644,61
88.762,66
2007
170.231,09
31.548,62
422.473,97 106.038,41
2008
141.272,48
26.181,77
350.605,45
87.999,85
O
V
G
2004
143.817,01
23.255,52
346.996,78
97.917,96
2005
135.863,87
21.969,48
327.807,71
92.503,06
2006
143.658,57
23.229,90
346.614,51
97.810,09
2007
171.618,64
27.751,10
414.075,61 116.846,73
2008
142.423,99
23.030,26
343.635,76
96.969,53
5 The factor 0.135 to calculate VHL incurred by accidents is based on a Dutch study (Hof &
v
a
n
R
e
is
e
n
2004
177.476,31
134.637,20
253.974,71
45.899,04
2005
167.661,79
127.191,71
239.929,81
43.360,81
2006
177.280,79
134.488,88
253.694,93
45.848,48
2007
211.784,70
160.664,26
303.071,22
54.771,91
2008
175.757,27
133.333,10
251.514,71
45.454,47
S
W
O
V
2004
238.675,03
171.356,43
152.996,82
48.958,98
2005
225.476,20
161.880,35
144.536,03
46.251,53
2006
238.412,10
171.167,66
152.828,27
48.905,05
2007
284.813,91
204.481,78
182.573,02
58.423,37
2008
236.363,22
169.696,67
151.514,89
48.484,76
Source: Own setupAn interesting remark is that travel times can be directly determined per vehicle category, which would mean that a global percentage classification is no longer necessary. This could improve the quality, because the distribution of vehicle categories and travel motifs are not constant on different highways and regions. This can be an interesting research perspective for the future.
5. Thereafter, the next formula (van Reisen, 2006) has to be applied for the different travel motifs to determine the costs for travel time losses per motif.
VoT
occupancy
VHL
Cost
ExtraTravelTime=
accidents×
×
With CostExtraTravelTime = Cost for the average extra travel time
VHLaccidents = Lost vehicle hours due to congestion by accidents
VoT = Value of Time
As can be seen in the table below, not only the value of time differs according to the motif (as mentioned in chapter 3), but also the average occupancy of the vehicles will be different for each motif. This is an important difference between the indicator ‘congestion costs’ and the lost vehicle hours. With the lost vehicle hours this distinction in travel motif is not made, so the economic impact of congestion is underestimated (Vanhove, 2008).
