Automatic ticketing at ferry crossings

Transcription

1 Automatic ticketing at ferry crossings Gisle Solvoll University of Nordland, Business school, NO-8049 Bodø, Norway Abstract This paper discusses the possibilities of implementing a new fare system based on automatic ticketing on ferry crossings in Norway and estimates the traffic and economic consequences of three different fare models. The main objectives with the new fare system is that ticketing should be carried out efficient, the fares should be equal across the country so the ferry users pay the same for the same distance travelled and that the fare system should be revenueneutral, i.e. the revenues should be about the same as today. Model 1 is based on the EU classification system with six vehicle categories. Model 2 consists of three vehicle categories based on the weight of the vehicle. Model 3 consists of 9 vehicle categories and is quite comparable with the present fare system. For all models, passenger payment is discontinued and the fare tariff is thereby related to characteristics of the vehicle and the length of the crossing. Model 1 and especially model 2 gives distributional effects in that some of the present vehicle categories will get lower fares while other will experience higher fares. Heavy but short vehicles will be worst off while light but long vehicles will be accordingly better off. Regardless of model chosen, automatic ticketing will encourage ferry users to drive several together in the same vehicle. Thus, a fare system where passenger fares is included in the vehicle fare will have a somewhat traffic reducing effect. Keywords: Ferry, automatic ticketing, fares, fare system. 1. Introduction The road network in the coastal areas of Norway is interconnected by a system of bridges, underwater tunnels and ferry routes. Even though many ferry services have been replaced with bridges and tunnels during the last two decades, the ferries still have a very important function in the transport infrastructure in the coastal areas of Norway. Jørgensen, Mathisen

2 and Larsen (2010) have estimated that the ferry services welfare for the users (consumer surplus) and the society (social surplus) amounted to about 5.8 billion NOK and 4.3 billion NOK, respectively in In 2014 there were 120 ferry services in Norway operated by mainly four shipping companies that have, in total, about 160 ferries at their disposal. 17 of the services are highway-services while the rest is county-services. The average length of a ferry crossing is about 8 kms, ranging from 0.3 kms up to 113 kms. In 2012 the ferries carried ca. 21 mill. vehicles and about 22 mill. passengers (driver excluded). In Ministry of Transport and Communications (2013) the goals for a new fare system on the Norwegian ferries are discussed. At page 115 it is written:... Introduction of automatic ticketing (AutoPASS) as payment-system in highway ferry services will give a more smooth traffic flow on the ferry services and make payment easier for both ferry crews and passengers.... The Directorate of Roads has therefore initiated a project to ensure the implementation and use of the payment-system in ferry services in an appropriate manner. Introduction of AutoPASS will require a new fare tariff and will affect the distribution of fares between groups of vehicles. University of Nordland was selected to clarify the traffic and economic issues related to the implementation of a new fare system on the Norwegian ferries. Based on the formulations above we can presume that one objective is that the new fare system must be both time and cost efficient; Time efficiency related to the ticket collection and cost efficient related to a reduction in ticketing costs. The new tariff system should thus simplify the everyday for both ferry users and ferry crew. It is also implied that passenger payment shall lapse. This is furthermore technically required. Moreover, the technical solutions chosen should be reliable and trustworthy so wrong ticketing to the greatest extent possible is avoided. Though not explicitly formulated, a national fare tariff as today is to be continued. Furthermore, according to the Directorate of Roads a fiscal requirement is that the new tariff system should be revenue-neutral. It should generate approximately as much revenue as the current tariff system does. We would also add that users should perceive the new tariff system as fair. This may be a problematic mission to fulfil, given that any change, 1 1 NOK is about 8.50 (April 2015).

3 imply that some will be better off and some worse off than today. Therefore, it would be likely to add the following main objectives as the basis for the new tariff system: 1. Efficient money collection. 2. Same fare for the same distance travelled. 3. Revenue neutrality. The aim of this paper is to discuss the possibilities of implementing automatic ticketing on ferry crossings in Norway and estimate the traffic and economic consequences of three different fare models. The paper is organised as follows. Chapter 2 gives a review of the present fare system on the Norwegian ferries. Chapter 3 is a discussion and description of how an automatic ticketing system on the ferries can be designed. The chapter also gives a brief description of the three different fare models. Chapter 4 focuses on the expected consequences a new fare system will have on the fare level for different categories of vehicles, the distribution of vehicles on the different fare categories, revenues on different ferry services and distributional effects of changing the fare system. Finally, in chapter 5 we draw some concluding remarks. 2. The fare system on the Norwegian ferries The current fare system on the Norwegian ferries was introduced in 1988, based on two important political guidelines; namely, that the fares should be equal the costs for driving a corresponding distance of road and that charges should be equal throughout Norway, see Solvoll (1997). It is accepted that the fare tariff starts with a fixed basic rate in addition to vehicle costs. The guidelines gives a direct expression of the Norwegian parliament s rural policy saying that the population and industry in coastal areas in Norway should not be charged with higher transport costs for the same distance than in the rest of the country. The present fare system is based on the above guidelines and a differentiation of fares between different vehicles categories according to the cost different vehicles have on the ferry services. The vehicle fares is split into a distance-dependent and a distance-independent component (basic fare). The distance-dependent part of the fare is independent of the cost of ferry operations and shall correspond to the costs for driving a corresponding distance of road. The task to the basic fare is to cover the difference in revenues in accordance to driving costs

4 and an acceptable subsidy level. The basic fare is distributed among the various vehicle categories using a size parameter. The parameter is for a passenger car (<6m) and for an articulated vehicle (19-22m), see Table 1. The political guidelines for the ferries present fare system are mathematically expressed by the following function: (1) T jj = a j g + c j x R (j=1.9) T jj is the ticket price for vehicle category j when the track length is x kms, c j is estimated driving costs per kms on road for vehicle category j, a j is a parameter that indicates the size of the vehicles in vehicle category j, g is a parameter that is annually adjusted according to the subsidy needs. R is a parameter that expresses the discount system and is defined such that R = 2 for ordinary fares and R < 2 for discounted fares. In 2015 R= 0,5. The division of vehicles into vehicle categories is done on the basis of the length of the vehicles. The smallest category consists of passenger cars while the largest category is made up of heavy goods vehicles. The driving costs by road (c j ) for the nine different vehicle categories are updated yearly. The size parameter (a j ) for a particular vehicle category, is determined on the basis of the areas and the weights of the vehicles included in that category. One passenger car is chosen as the nummeraire. The surface area is the factor that influences a j most, but for the largest vehicles, their weight also counts. The values of a j were adjusted most recently in From (1) it follows that the ferry fares for all 9 vehicle categories are divided into a basic distance-independent component (Ra j g) and a distance-dependent component (Rc j x). The distance-dependent component is annually adjusted in accordance with the costs of driving on road for the different vehicle categories (through c j ), and the size parameter (a j ) is technically determined and adjusted when technology necessitates this. The value of g, and thereby of the distance-independent component (Ra j g), is annually adjusted through g to ensure that the amount of subsidy given to the ferry service remains within a politically tolerable level. This adjustment is done on the basis of expected demand for ferry transport and anticipated growth in the cost of ferry operations, cf. Jørgensen, Pedersen and Solvoll (2004).

5 Table 1: The present vehicle categories and the corresponding size parameters. Vehicle category Vehicle length Size parameter 2 B2 < 6 meter 1,025 B3 6-7 meter 2,435 B4 7-8 meter 2,899 B meter 4,009 B meter 5,040 B meter 6,125 B meter 7,315 B meter 8,954 B meter 10, Fare system based on AutoPASS Norway was among the first countries that adopted electronic payment in toll plazas. The first systems for electronic payment of tolls in Norway was introduced in In 2001 came the AutoPASS tag, with associated standards and specifications. The AutoPASS tag contains limited information about the vehicle beyond whether the vehicle is above or below 3500 kg (the chip itself only contains an unique ID). The present payment system, where the chip can be used in any of Norway s around 40 toll stations, was introduced in Today, the AutoPASS tag can also be used to pay tolls in Sweden and Denmark and on five Danish ferry services. An extension of the chip application to include Norwegian ferries have long been demanded. Ministry of Transport and Communications (2013) recommends introducing AutoPASS as payment in all highway ferry services. However, technical and practical challenges means that AutoPASS payment on ferries must lead to simplification compared to the current tariff system. An absolute condition is that passenger payment must disappear so that ticketing only is linked to characteristics of the vehicle. The benefits of today's detailed ferry fare system with separate passenger payment, is that a larger part of the markets willingness to pay can be taken out and that the system is good 2 Equals the number of passenger car equivalents (PCE).

6 adapted to the individual affluence: i.e. the fare system has desired distributional effects. The disadvantage with a detailed tariff system is that it is more resource intensive; require more information; is more time consuming and hence less user friendly for passengers and that the system only to a limited extent can be adapted with modern ticketing technologies. It is among the reasons why the authorities want to introduce AutoPASS at all Norwegian highway ferry services. Use of AutoPASS on ferry services will also enable coordination with user fees on roads where users can link payment on ferries to their ordinary AutoPASS subscription. The transport industry in Norway has for a long time demanded a coordination of user fees on road and ferry services. Different fare systems claim different information about the vehicle. In Norway information can be collected from (Solvoll and Welde, 2013; Solvoll and Hanssen, 2014): Autosys: The Directorate of Roads database for driving licenses and vehicles. The database contains among other things information about the length of all Norwegian vehicles. EasyGo+: A common payment system for toll roads in Norway, Sweden, Denmark and Austria. The HGV-register connected to the system contains information about classification of vehicles in length categories according to the European Union vehicle categories. Declaration form: A scheme that has to be filled in when signing on an agreement for an AutoPASS tag. From 1st January 2015 the tag was mandatory for Norwegian and foreign vehicles over 3500 kg when driving on the Norwegian public road network. The EU classification system of vehicles consist of six vehicle categories. This is: M1: Vehicle for passenger transport with maximum eight seats in addition to driver s seat (passenger car). M2: Vehicle for passenger transport with over eight seats in addition to driver s seat and maximum total weight not exceeding 5000 kg. M3: Vehicle for passenger transport with over eight seats in addition to driver s seat and maximum allowed total weight over 5000 kg (Bus).

7 N1: Vehicle for freight of goods with allowed total weight not exceeding 3500 kg (van). N2: Vehicle for freight of goods with allowed total weight over 3500 kg but not over kg. (Lorry). N3: Vehicle for freight of goods with allowed total weight over kg (Lorry). If we use information about the weight of Norwegian registered vehicles from the Norwegian vehicle database, and distribute the vehicles in accordance to the length of the vehicles in the present fare system, a distribution as shown in Table 2 appear. Table 2. Relationship between length and weight of Norwegian registered vehicles in (Source: Autosys-database). Vehicle category Weight (length) < kg kg > kg Sum B2 (0-599 mm) B3 ( mm) B4 ( mm) B5 ( mm) B6 ( mm) B7 ( mm) B8 ( mm) B9 ( mm) B10 (1 900 mm >) Share 95,4 % 2,7 % 1,9 % 100,0% 3.1 Possible fare models In this chapter, we will briefly describe three fare models that have been evaluated as possible new fare systems when implementing automatic ticketing. The description is based on Solvoll and Hanssen (2014) Model 1

8 A possible new fare system (model 1) consists of six vehicle categories (M1: normal passenger car, M2; large passenger car, M3; bus, N1; van, N2; light truck, N3; heavy truck). Ticketing of motorcycles is performed manually. Vehicles with a trailer, small (H1) or large (H2) will be charged extra. Laser technology can be used to detect whether or not a vehicle is carrying a trailer. The fare categories then becomes as showed in Table 3. Table 3: Vehicle categories in a fare system based on automatic ticketing (AutoPASS). Model 1. Vehicle category Without trailer With trailer Passenger car (normal; max. 8 seats) M1 M1 + H1 Passenger car (large; <5 000 kg) M2 M2 + H1 Bus (>5 000 kg) M3 M3 + H1 Van (<3 500 kg) N1 N1 + H1 Lorry (light; kg) N2 N2 + H2 Lorry (heavy;> kg) N3 N3 + H2 Motorcycle MC Model 2 Model 2 consists of three vehicle categories (A1; vehicles under kg, A2; vehicles between 3500 kg and kg and A3; vehicles over kg). This model is approximately equal the system that is operated in the ferry crossing Plymouth-Torpoint in UK, that is also operated with tag payment. If the vehicles are carrying a trailer, an extra charge is included as in model 1. Ticketing of motorcycles is performed manually. The fare categories becomes as shown in Table 4. Table 4. Vehicle categories in a fare system based on automatic ticketing (AutoPASS). Model 2. Vehicle category Without trailer With trailer Vehicle < kg A1 A1 + H1 Vehicle kg kg A2 A2 + H2 Vehicle > kg A3 A3 + H2

9 Motorcycle MC Model 3 Model three is equal the present fare system except that existing vehicle category B3 and B4 are merged and a separate vehicle category for vehicles larger than 22 m is included. The length interval for the AutoPASS-groups AP6, AP7 and AP8 are somewhat adjusted compared to the corresponding present vehicle categories B8, B9 and B10. There is also a separate group for electric vehicles (not included in the table). The fare categories (AutoPASS-groups) then becomes as described in Table 5. Table 5. Vehicle categories in a fare system based on automatic ticketing (AutoPASS). Model 3. Vehicle category (length category) Classification (new AutoPASS-groups) Vehicle <6m (B2) AP1 Vehicle 6-8m (B3 og B4) AP2 Vehicle 8-10m (B5) AP3 Vehicle 10-12m (B6) AP4 Vehicle 12-14m (B7) AP5 Vehicle 14-17,5m (B8) AP6 Vehicle 17,5-19,5m (B9) AP7 Vehicle 19,5-22m (B10) AP8 Vehicle >22m AP9 Motorcycle MC 4. Consequences of a new fare system In this section we focus on the expected consequences a new fare system will have on the fare level for different categories of vehicles, the distribution of vehicles on the different fare categories and the revenues on each of the 17 highway-ferry services. Finally, we give some comments regarding distributional effects of changing the fare system.

10 4.1 Fares In table 6 it is showed how normal fares are set in the tree models are compared with the present fare system. The table show the fares on a crossing with length 8 kms that correspond to a crossing of about average length. Table 6. Ordinary fares on a ferry crossing with length 8 kms with present fare system and 3 models based on automatic ticketing (AutoPASS). Reference year % vat. included. NOK. Present fare system Model 1 Model 2 Model 3 Vehicle Vehicle Vehicle Vehicle Kjøretøy Vehicle Adult Child Vehicle Trailer Vehicle Trailer category category category category B M A AP1 128 B3 240 M A AP2 287 B4 281 M A AP3 399 B5 363 N MC 48 AP4 471 B6 428 N AP5 541 B7 492 N AP6 601 B8 589 MC 48 AP7 674 B9 661 AP8 773 B AP9 850 MC 60 MC 48 As seen from Table 6 the fare for a passenger car included driver (B2) was 98 NOK in An adult passenger had to pay 34 NOK. The fares in the new fare systems becomes 138 NOK for model 1 and 2, and 128 NOK for model 3. Compared with the present fare system a passenger car with one passenger will get a fare increase of about 5% in model 1 and 2 and a fare decrease of about 3% in model Traffic The calculation of the distribution of vehicles in the different vehicle categories is done based on information about the relationship between weight and length of the vehicles. Where the length categories are changed (as in model 3) a simple mathematical approach is used as we suppose that the length of the vehicles in a vehicle category is equally distributed within the

11 category in question. As seen from Table 7 the sum of vehicles transported is the same independent of model. This is a result from our assumption that the fares are set to secure revenue-neutrality. Thereby, as a simplification, we assume that demand effects from fare reductions in one vehicle category outweighs the effect on the demand for ferry services of a fare increase in another vehicle category. Table 7. Traffic on highway-crossings divided on vehicle categories with present fare system and 3 models based on automatic ticketing (AutoPASS). Reference year (Source: Ferry database, Autosys and own calculations). Present fare system Model 1 Model 2 Model 3 Vehicle category Number of vehicles Vehicle category Number of vehicles Vehicle category Number of vehicles AutoPASSgroup Number of vehicles B M A AP B M A AP B M A AP B N MC AP B N H AP B N H AP B MC AP B H AP B H AP MC MC Sum (excl. trailer) As seen from Table 7 the majority of the vehicles transported on Norwegian ferry crossings fall into vehicle category M1 (model 1), A1 (model 2) and AP1 (model 3). In model 2 some vehicles shorter than 6 m will fall in vehicle category N1. This is the reason why there is fewer vehicles in vehicle category A1 compared with vehicle category B2 and AP1. We can also notice the difference in the number of vehicles in vehicle category N3 and A3. The reason for this is that heavy vehicles in model 1 is distributed on more vehicle categories than only N3. We have also included the calculation of expected number of trailers (short and long) in model 1 and 2.

12 4.3 Revenue As fares in the new fare systems are set so that revenues generated shall be equal as in the reference year 2012, the sum of the revenues from all crossings are the same as can be seen from table 8. However, there is some differences between crossings. The differences from present revenues is in the range 0% to 18%, lowest on the crossing Mortavika-Arsvågen and highest on the crossing Bognes-Skarberget. Table 8. Present and estimated revenues on highway-crossings with tree fare models. Reference year Numbers in mill. NOK. 8% vat included. Difference from current revenues Crossings Present Estimated revenues Model 1 Model 2 Model 3 revenues Model 1 Model 2 Model 3 NOK Percent NOK Percent NOK Percent Lauvvik-Oanes 41,3 44,0 43,1 41,3 2,7 7% 1,8 4% 0,0 0% Hjelmeland- Nesvik 15,1 15,2 14,8 14,5 0,1 1% -0,2-1% -0,5-3% Mortavika- Arsvågen 193,2 193,0 194,4 194,9-0,2 0% 1,2 1% 1,7 1% Sandvikvåg- Halhjem 209,9 210,8 215,5 210,9 0,9 0% 5,7 3% 1,0 0% Anda-Lote 40,6 40,9 40,2 41,4 0,3 1% -0,4-1% 0,8 2% Mannheller- Fodnes 65,5 63,8 63,2 64,7-1,8-3% -2,3-3% -0,9-1% Hella-Dragsvik/ Vangsnes 24,5 24,4 24,0 20,0-0,1 0% -0,5-2% -4,4-18% Oppedal-Lavik 62,0 61,1 61,0 63,0-1,0-2% -1,0-2% 0,9 1% Halsa-Kanestraum 37,4 34,4 33,5 34,3-3,0-8% -3,9-10% -3,1-8% Molde-Vestnes 113,5 105,6 104,0 105,2-7,9-7% -9,6-8% -8,3-7% Solevåg-Festøya 52,6 54,6 53,0 54,2 2,0 4% 0,4 1% 1,6 3% Volda-Folkestad 36,3 34,8 34,5 34,6-1,6-4% -1,8-5% -1,7-5% Bodø-Moskenes- Værøy 45,4 47,9 48,7 48,4 2,6 6% 3,3 7% 3,0 7% Bognes-Lødingen 42,1 45,8 46,2 46,2 3,7 9% 4,0 10% 4,1 10% Bognes-Skarberget 18,5 21,6 21,1 21,6 3,1 17% 2,6 14% 3,2 17% Drag-Kjøpsvik 14,0 14,2 14,7 16,6 0,2 1% 0,6 5% 2,6 18% Sum 1011,9 1011,9 1011,9 1011,9-0,0 0% -0,0 0% 0,0 0% 4.4 Distributional effects When the number of fare categories are reduced, as in model 1 and 2, some of the present vehicle categories will get lower fares while other will experience higher fares. Thus, some

13 will perceive a new fare system as very unfair while other will look at it as a gift. A change from a mathematical length based fare system with nine vehicle categories to a fare system based on three weight classes, no passenger payment and an mark-up if the vehicle carrying a trailer, means that some vehicles may be subject to substantial changes in the fare they must pay. They who will be most affected are those vehicles that have either an abnormal weightlength relationship or those who normally travel with many people in the vehicle. Heavy but short vehicles will be worst off while light but long vehicles will be accordingly better off. Vehicles with one or more passengers will equal or better off than today in all three models. Therefore, the new fare system will encourage ferry users to drive several together in the same vehicle. Thus, a fare system where passenger fares is included in the vehicle fare will have a somewhat traffic reducing effect. 5. Concluding remarks This work explores how a new fare system on the Norwegian ferries based on the AutoPASSsystem can be designed. Three different fare systems are evaluated; a relatively detailed system with six vehicle categories a rougher system with only three fare categories and a system with the same number of vehicle categories as in the present fare system. For all three models there is a separate fare category for motorcycles (MC). In addition in model 1 and 2 an extra charge is included if the vehicle is carrying a trailer. Model three, which in length based, does not have a separate mark-up for the trailer because it is the total length of the vehicle (included any trailer) that is measured and provides a basis for the ticket price. It is assumed that the new fare system should be revenue-neutral. Because the ticketing is linked only to the vehicle the current revenues from passengers (excluded the driver) must be included in the vehicle fare. Approximately 20% of today s revenues comes from passengers. In the further, some comments are given to the calculations as well as some general comments regarding the fare system on the ferries. When the number of fare categories are reduced, some of the present vehicle categories will get lower fares while others will experience higher fares. When we have determined the fares in the new vehicle categories, we have tried to link the fare to the length category where the majority of the vehicles are. As the vehicles in some of the new vehicle categories appear in several length categories, some vehicles will necessarily experience a significant fare reduction while others will experience a corresponding fare increase. Thus, some will

14 consider a new fare system as very unfair while others will look at it as a gift. This applies primarily for model 1 and 2. It is also a challenge to implement a separate ticketing of trailers. Today vehicles carrying a trailer must pay after total length of the vehicle and trailer. Thus, the number of vehicles carrying a trailer is not visible in the ferry statistics. This makes it difficult to know for sure how many of the vehicles in the present length categories that is a short vehicle with a trailer or a long vehicle without a trailer. Maybe more difficult is the actual determination of which fare a trailer should have. Trailers have very different lengths, from the smallest garden trailer to the largest semi-trailer. When the length of the trailer is not measured by detection with a laser (so that the length of the trailer is not measured), the price for the trailer must either be fixed or differentiated by characteristics by the vehicle that pulls it. We have chosen a variant in which we distinguish between expected short and long trailers. With this simple dichotomy some ferry users probably feel that they are being very unfairly treated, especially those who usually have paid a relatively modest mark-up for a small trailer and in the new fare system ends up in almost the same vehicle category as those who pulls very long trailers. The new fare models, especially model 2, will cause that vehicles in some of the present length categories will get significant changes in the fare they have to pay. Although demand for ferry services is quite inelastic, cf. Solvoll etc. (2013) and Odeck and Bråthen (2008), a change in the fare system as indicated above will bring about demand effects. Those who get reduced fares will travel more and those receiving higher fares will travel less. Such effects will vary from crossing to crossing depending on the attractiveness to alternative transport options, the composition of the traffic and travel purposes. However, in the calculations we have not taken into account such effects. This is due to insufficient demand data on different crossings, the resources available to the analyse and the general uncertainty associated with analyses of changes in demand due to a change in a fare system that is designed on the basis of revenue neutrality. In theory the revenue effect of increased an decreased demand on different crossings and between different ferry users will outbalance each other and result in approximately unchanged revenues, at least for the crossings overall. However, our economic analysis of a change in the fare system show a certain redistribution of revenues between crossings, see Table 8. It should also be noted that the introduction of automatic ticketing would probably imply a potential for revenue losses for the transport companies operating the services. This will reduce the theoretical calculated revenues on the different crossings. Loss of revenues

15 due to shutdown of the automatic ticketing system and other causes has been estimated to be around 10% in a worst case. If the probability for loss of revenue is substantial, fares must be set higher than our calculations show to take account for this. Since fare increases have a negative impact on demand such a measure to secure sufficient revenues can prove to be social economically costly. Another problem is related to the effects of free passengers travel. This has two effects; incentives to travel with more people in the same vehicle and incentives to travel without having the car on the ferry (i.e. free transportation). The first effect can be economically favourable throughout a reduction in transport work (less driving), while the second effect can cause capacity problems at some ferry services, perhaps especially in the summer season and on crossings where the ferry competes with other forms of fjord crossings, such as fast craft services. If many ferry users choose free ferry transport (travel without being attached to a vehicle), some departures on certain ferry services will not be able to depart with maximum utilisation of car capacity of the ferry because the ferry then will exceed the number of passengers the vessel is certified to carry. This will lead to an increased number of remaining vehicles on the ferry landing and make it much harder to reach the transport authorities service target that throughout the year 98% of vehicles shall be able to travel with their desired departure. Finally is should be noted that changes in the fare system ideally should be rooted in knowledge of the cost structure in ferry transport and how different types of vehicles influence the cost of ferry operations. Economically optimal pricing of ferry services should be based on the marginal costs a certain vehicle imposes on the ferry operation. It is far from obvious that the current fare system and fare level is properly designed with respect to both the length of the ferry crossing and fare intervals between different types of vehicles. However, this problem lies far beyond the scope of the article.

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