DEGREE PROJECT IN TRANSPORT SCIENCE
SECOND CYCLE, 30 CREDITS
STOCKHOLM, SWEDEN 2020
KTH ROYAL INSTITUTE OF TECHNOLOGY
SCHOOL OF ARCHITECTURE AND BUILT ENVIRONMENT
Evolution of Public
Transport Network
Design due to the
Arrival of
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Author
Robby Yudo Purnomo,
robbyyp@kth.se
Transport and Geoinformation Technology
KTH Royal Institute of Technology
Examiner
Erik Jenelius
KTH Royal Institute of Technology
Supervisor
Hugo Badia Rodriguez
KTH Royal Institute of Technology
TRITA-ABE-MBT-20393
KTH Royal Institute of Technology
Abstract
There is rapid development in the transportation field. Soon, along with the rapid population growth, there will be a change in the mobility pattern. To prepare the different travel demand, there are several new advanced technologies that areon the development process such as the electrification of the vehicle, the micro-mobility service, and the automation of the vehicle. The latter subject is the main focus of this research. The main objective of this research is to observe and analyze the development of a new model to provide a tool for the analysis of the public transport system and the analysis of different scenarios related to the degree of development of automated vehicles and the characteristics of the area of service and demand. The network design in this research is a hybrid concept developed by Carlos Daganzo in 2010 that combines the grid network on the central area and radial network on the peripheral area. In the central area, there is two intersecting public transit (bus and metro). In contrast, on the peripheral area, a feeder bus will provide the service for the passengers and also there will be two feeder alternatives, namely fixed route and door to door. The objective function of the optimization is to minimize the total cost regarding the available decision variables. The total cost is consist of agency cost (infrastructure length, total vehicle distance travelled, total vehicle hours travelled) and user cost (waiting time, access time, in-vehicle time) and the minimization process need to follow the constraint of headway, spacing, and vehicles capacity. Based on the base optimization, the most optimum value for alpha, bus spacing, metro spacing, and inner area length regarding to the total cost is 0.23, 0.2 km, 4 km, and 0.3 km respectively. while the Fixed Route Feeder Service with Full Automation is the most beneficial type of service. It generates the lowest total cost per passenger regarding to any decision variables except feeder spacing due to the different formulation between fixed route and door to door service. On contrary, Door to Door Feeder Service with No Automation has the highest total cost per passenger. The total cost in figure, based on the optimum value for each decision variables. Therefore there is no optimum value for headway considering the trend of the total cost is linear
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Sammanfattning
Det är snabb utveckling inom transportämne. Snart, tillsammans med den snabba befolkningsökningen, kommer det att förändras rörlighetsmönstret. För att förbereda de olika resebehoven finns det flera nya avancerade teknologier som utvecklas, såsom fordonets elektrifiering, mikromobilitetstjänsten och fordonets automatisering. Det senare ämnet är fokus för denna forskning. Huvudsyftet med denna forskning är att observera och analysera utvecklingen av en ny modell för att tillhandahålla ett verktyg för analys av kollektivtrafiksystemet och analys av olika scenarier som relaterade till utvecklingsgraden för automatiserade fordon och områdets egenskaper av service och efterfrågan. Nätverksdesignen i denna forskning är ett hybridkoncept utvecklat av Carlos Daganzo 2010 som kombinerar nätnätet i det centrala området och det radiella nätverket i det perifera området. I det centrala området finns det två korsande kollektivtrafik (buss och tunnelbana). Däremot, i periferiområdet, kommer en matarbuss att tillhandahålla tjänsten för passagerarna och det kommer också att finnas två mataralternativ, nämligen fast rutt och dörr till dörr. Optimeringens målfunktion är att minimera den totala kostnaden för tillgängliga beslutsvariabler. Den totala kostnaden består av byråkostnad (infrastrukturens längd, totala fordonsavstånd, totala fordonsimmar) och användarkostnad (väntetid, åtkomsttid, tid i fordonet) och minimeringsprocessen måste följa begränsningen för framåt, avstånd och fordons kapacitet. Baserat på basoptimeringen är det mest optimala värdet för alfa, bussavstånd, tunnelbaneavstånd och inre arealängd avseende den totala kostnaden 0,23, 0,2 km, 4 km respektive 0,3 km. medan tjänsten med fast ruttmatare med full automatisering är den mest fördelaktiga typen av tjänster. Det genererar den lägsta totala kostnaden per passagerare för eventuella beslutsvariabler utom mataravstånd på grund av olika formuleringar mellan fast rutt och dörr till dörrservice. Tvärtom har Door to Door Feeder Service med ingen automatisering den högsta totala kostnaden per passagerare. Den totala kostnaden i siffra, baserad på det optimala värdet för varje beslutsvariabler. Därför finns det inget optimalt värde för framåt med tanke på att trenden för den totala kostnaden är linjär
Acknowledgement
First of all, I would like to thank the Almighty God for everything I achieve until now, and I am very grateful because of it.
Second, I would like to thank my supervisor, Hugo Badia Rodriguez, Ph.D, for all of his guidance and discussion so that I can finish my master thesis in time. Eventually, this research topic is one of his ideas. I want to thank my examiner Assoc Prof Erik Jenelius for his feedback on the improvement of this thesis, and also I would like to thank my opponents on the seminar Martina Komuhendo.
Third, I would like to thank my colleague from Transport and Geoinformation Technology batch 2018, particularly Francisco Malucelli who always help me to cope with my study and answer all of my questions. I appreciate your help. I also want to thank Assoc Prof Albania Nissan (KTH) and Prof Yusak Susilo (KTH & BOKU), the lecturer who always motivate and support me to be a better student and researcher during my study in Sweden.
I also like to thank the Swedish Institute for giving me the scholarship and opportunity to pursue my master’s degree at KTH Royal Institute of Technology. This scholarship is one of the most precious experiences of my life. Additionally, I would like to thank the Embassy of the Republic of Indonesia in Stockholm for all the help and guidance.
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Table of Contents
Abstract... iii Sammanfattning ... iv Acknowledgement ... v Table of Contents ... viList of Figures ... viii
List of Tables ... x
1 Introduction ... 1
1.1 Future of Transport System ... 1
1.2 The arrival of Autonomous Vehicle ... 2
1.3 Implementation of Automation on Public Transport System ... 3
1.4 Research Objective ... 5
2 Literature Review ... 6
2.1 Autonomous Vehicle ... 6
2.1.1 Definition ... 6
2.1.2 The benefit of Autonomous Vehicle ... 7
2.1.3 The obstacle of Autonomous Vehicles ... 8
2.2 Network Design Structure ... 9
2.2.1 Discrete Network Design ... 9
2.2.2 Constraint ... 10
2.2.3 Continuous Network Design... 11
3 Methodology ... 15
3.1 Proposed Network Design ... 15
3.2 Demand ... 16
3.3 Objective Function ... 16
3.3.1 Agency Cost ... 17
3.3.2 User Cost ... 19
3.3.3 Parameters ... 26
4 Result and Analysis ... 28
4.1 Base case study ... 28
4.1.1 Total Cost ... 28 4.1.2 Bus Headway ... 29 4.1.3 Metro Headway ... 30 4.1.4 Feeder Headway ... 31 4.1.5 Bus Spacing ... 31 4.1.6 Metro Spacing ... 32
4.1.7 Feeder Spacing (Fixed Route) / Inner Area (Door to Door) ... 33
4.2 Sensitivity Analysis ... 35
4.2.1 Sensitivity Analysis on Demand (Q) ... 36
4.2.2 Sensitivity Analysis on Length of the Side Square (D) ... 38
4.2.3 Sensitivity Analysis on Value of Time ... 40
5 Conclusion ... 43
5.1 Summary ... 43
5.2 Future Research ... 44
6 Bibliography ... 45
7 Appendix ... 48
7.1 MATLAB Code for Fixed Route ... 48
7.2 Sensitivity Analysis of Demand ... 50
7.3 Sensitivity Analysis of Total Area Length ... 51
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List of Figures
Figure 1. Population Growth Projection (a) Sweden (SCB.se, 2020) (b) the United Kingdom (Office of
National Statistics, 2019) ... 1
Figure 2. Micromobility Service Development ... 2
Figure 3. Autonomous Vehicle Features Timeline (Litman, 2020) ... 3
Figure 4. Autonomous Vehicle Sales, Fleet, and Travel Projections (Litman, 2020) ... 3
Figure 5. Autonomous Bus at Barkarby, Stockholm ... 5
Figure 6. Automation Levels from No Automation to Full Automation (NHTSA, 2013) ... 6
Figure 7. Heatmap of Traffic Conflict Locations for the Different Market Penetration Scenarios Aggregated for all Weekdays (Papadoulis, 2019) ... 7
Figure 8. Distribution of age-wise driving and increased driving by the elderly (Wadud, et al., 2016) ... 8
Figure 9. Example of Discrete Network Design (Buba & Lee, 2018) ... 9
Figure 10. (a) Radial (b) Ubiquitous (c) Grid (d) Time-transfer Systems (Thompson, 1977) ... 11
Figure 11. (i) Route having two transfers (a) and one transfer (b), (ii) Two routing schemes for a rectangle region (Newell, 1979) ... 12
Figure 12 Hybrid Transit Network Concept (Daganzo, 2010) ... 13
Figure 13. Bimodal Transit Network Design (Fan et al., 2018) ... 13
Figure 14. Alternative Feeder Service System (Badia and Jenelius, 2020b) ... 14
Figure 15. General Network Structure Design... 15
Figure 16. Accumulated Demand Ratio ... 16
Figure 18 Passengers Walking Distance ... 22
Figure 19. (a & b) Total Cost (c) Agency Cost (d) User Cost ... 28
Figure 20. Bus Headway vs (a) Total Cost (b) Agency Cost (c) User Cost ... 29
Figure 21. Metro Headway vs (a) Total Cost (b) Agency Cost (c) User Cost... 30
Figure 22. Feeder Headway vs (a) Total Cost (b) Agency Cost (c) User Cost ... 31
Figure 23 Bus Spacing vs (a) Total Cost (b) Agency Cost (c) User Cost ... 32
Figure 24 Metro Spacing vs (a) Total Cost (b) Agency Cost (c) User Cost ... 33
Figure 25. Feeder Spacing / Inner Area Length vs (a) Total Cost (b) Agency Cost (c) User Cost ... 34
Figure 26. Cost Structure ... 34
Figure 27. (a) Demand vs Alpha (b) Demand vs Total Cost ... 36
Figure 28. Demand vs Headway and Spacing/Inner Area ... 37
Figure 29. (a) Demand vs Bus (b) Demand vs Metro (c) Demand vs Feeder Occupancy... 37
Figure 30. (a) Length of Side Square vs Alpha (b) Area Length vs Total Cost ... 38
Figure 31. Area Length vs Headway and Spacing/Inner Area... 39
Figure 32. (a) Area Length vs Bus (b) Area Length vs Metro (c) Area length vs Feeder Occupancy ... 40
Figure 33. (a) Value of Time vs Alpha (b) Value of Time vs Total Cost ... 40
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List of Tables
Table 1. Important Aspects Regarding Autonomous Vehicles (Lopez-Lambas & Alonso, 2019) ... 4
Table 2. Five automation levels based on NHTSA (2013) ... 6
Table 3 Objective Function Component ... 16
Table 4 Total length of infrastructure (L) formula ... 17
Table 5 Vehicle distance travelled per hour (V) formula ... 17
Table 6 Vehicle hours travelled (M) formula ... 18
Table 7 Probability of mode usage (P) formula ... 19
Table 8 Expected number of transfer per trip formula... 20
Table 9 Waiting time for central-central trip ... 20
Table 10 Waiting time for central-peripheral trip ... 21
Table 11 Waiting time for peripheral-peripheral trip... 21
Table 12 Access time for central-central trip ... 22
Table 13 Access time for central-peripheral trip ... 22
Table 14 Access time for peripheral-peripheral trip ... 23
Table 15 In-vehicle time for central-central trip ... 23
Table 16 In-vehicle time for central-peripheral trip ... 24
Table 17 In-vehicle time for peripheral-peripheral area trip ... 24
Table 18 Vehicle critical occupancy ... 25
Table 19 List of Input Parameters ... 26
Table 20. List of Automation Level Abbreviation ... 28
Table 21. Cost Structure Value ... 35
1
Introduction
1.1 Future of Transport System
Transportation system is one of the most critical sectors in our daily activity; in other sentences, it is the backbone of our mobility behavior. The need for transportation stems from the interaction between social and economic activities dispersed in space. The diversity of these activities and the complexity of their patterns of interaction result in numerous determinants of transport needs (Kanafani, 1983). Nowadays, people start to change their travel and mobility behavior. There is a lot of new policy or trend among the society that encourage people to use more a sustainable and efficient transport system. For example, the increasing level of air pollution due to the number of traffic started to inspire people to use more sustainable modes such as public transport or active transport (walking and bicycling). The other example is that some company’s begin to implement "working from home" or "remote working" policy for their employee, which reduce the people number of the trip.
(a) (b)
Figure 1. Population Growth Projection (a) Sweden (SCB.se, 2020) (b) the United Kingdom (Office of National Statistics, 2019)
Shortly, people's mobility pattern will change. There are several key drivers of changes in mobility (1)
Population growth and ageing, based on Figure 1, the U.K.'s population is expected to grow by 11% out to
of people (Goletz, et al., 2016) Other external factors play a role such as changes like work, family life, education, and housing (Government Office of Science, 2019)
In parallel with the rapid development of technology, by 2040 we expect several transformations in the
transport system. For example (1) the
electrification of transportation, 55% of car
sales and 33% of the global fleet will be electric. It also stated that electrified buses and cars would displace a combined 7.3 million barrels of fuel per day in 2040 (Bloomberg, 2018). (2) increasing of
micro-mobility usage, the current influx of dockless
bike-share and electric scooters are showing remarkable adoption and support. Figure 2 also shows how e-scooter service started to grab some people’s attention and started to receive 3.6% adoption rate in the U.S. within their first year. And lastly (3) automation of
the transport system, it is predicted that by 2040
the autonomous technology will spread throughout the system, particularly the transit system (A Better City, 2018). On the next part and the rest of the paper, we will focus on the impact of the implementation of autonomous vehicle particularly on the optimum public transport network and how they could be the best solution for the public transport problem.
1.2 The arrival of Autonomous Vehicle
Automation technology has started to infiltrate to vehicle manufacture. On April 2014, Google tried to implement self-driving cars over 700,000 miles on California public roads and followed by some big vehicle manufacturer company around the world such as Audi, BMW, Cadillac, Ford, General Motors, Mercedes-Benz, Nissan, Toyota, Volkswagen, and Volvo.
Figure 4 shows the development and forecast of the Autonomous Vehicle in general. Today, AVs development supposed to be on the large-scale test and cost-benefit evaluation under actual operating conditions. There are several pieces of research about the development of the various stage of AVs implementation. Fagnant and Kockelman (2015) have analyzed the opportunities, barriers, and policies of Autonomous Vehicles. Abe (2019) also worked on the potential benefit of AVs as bus or taxis in Japan. Lopez-Lambas et al. (2019) and Kyriakidis et al. (2015) studied public perception and acceptability of AVs. Krueger et al. (2016) concluded the potential users of shared autonomous vehicles (SAVs) and Dynamic Ride-sharing (DRS). Lastly, evaluated the impact of semi and fully-automated buses on the design of a bus corridor and the implementation of operating measures such as platooning (Zhang, et al., 2019b) compare the applicability of fixed routes and door-to-door services as a feeder solution in different scenarios of maturity of AVs. The results identify under what circumstances of technological development door-to-door trips will increase significantly the range of scenarios where they are more competitive than the traditional fixed routes (Badia & Jenelius, 2020b). Bosch et al. (2018) and Peirce et al. (2019) analyzed the cost-effectiveness of autonomous vehicles implementation. Shortly, We are still expecting that the development of AVs is still on progress. By 2030s, the study of AVs starts to focus on specific applications. It can be on public transport services or even more narrow aspect such as the development of demand-responsive public transport. In the end, in the next 20 or 30 years, we can expect that AVs starts to operate in the real road network and become on the mobility service options and even it can encourage the restriction of human-driving.
Figure 4 shows the projection of the number of sales, travel distance, and the number of fleets of autonomous vehicles. Generally, it will keep increasing until approximately 2050 when the number of sales started to reach its saturated point. On the projection, 2040-2050 period will become the peak period of AVs. The number of sales, travel distance, and the fleet will increase significantly compared to the other
period. It is believed because, at that moment, AVs will be proven to be effective and beneficial on any aspect.
Figure 3. Autonomous Vehicle Features Timeline (Litman, 2020)
Figure 4. Autonomous Vehicle Sales, Fleet, and Travel Projections (Litman, 2020)
1.3 Implementation of Automation on Public Transport System
Automation on the transit system is believed as a breakthrough for better mobility and accessibility. In general, public perception will visualize automation as the future, a new advanced technology that can ease or even fulfil people's need better. A recent article from Lopez-Lambas and Alonso (2019) stated in detail about the autonomous buses
201 8 Develop performance and data collection requirements for autonomous vehicles 2020s Support large-scale AVs testing. Evaluate their benefirs and costs under actual operating conditions 203
0s Study AVs implementatio n for specific applications 204
Table 1. Important Aspects Regarding Autonomous Vehicles (Lopez-Lambas & Alonso, 2019) Autonomous Buses – General Aspects
Positive Aspects Negative Aspects • Saving on staff and driver costs
• Increased security and reduced risk of the most common accidents
• Reduced fuel consumption and less pollution generation due to the fact of more efficient driving • Optimization of time as there are no driving time
loses
• Improvement in equity, as elders and children would gain accessibility, and it would be less limiting for people without a driving license
• Major investment required
• New risk would arise as there would be less safety and security in special situations
• Automatization may reduce job opportunities • Territorial aspects, for example, reductions in the
transport cost might encourage people to reside further their workplace, increasing urban sprawl.
Autonomous Buses – Specific Aspects
Positive Aspects Negative Aspects • Potential to increase reliability and punctuality
(connected infrastructure, traffic signals prioritizing buses)
• Potential to reduce staff costs (if a public service is involved, society may benefit)
• Potential to increase investment (infrastructure and vehicle) and therefore, a possible multiplier effect
• Flexibility for changing routes, timetables, etc., as schedules do not depend on human drivers.
• Non-payment of tickets would be difficult to control
• Lack of an individual to address in case of any incidence, such as buying a ticket, specific information requirements, specific passenger requirements
• Possible reduction in passenger's safety/security perception as no individual would represent or assume the authority on board
• Driver's role as an information provider disappears
Amid the number of the positive effect of AVs, the negative impact also has a significant contribution to society. For example, the reduction of job opportunities is one of the biggest dilemmas of AVs implementation. It affects the social, economic, and political aspect. In one hand, it will also reduce the operational cost. Still, on the other hand, the reduction of driver means more people will be unemployed and probably will conduct a strike or demonstration about it. Another indirect effect of AVs is the potential to generate an urban sprawl caused by the reduction of travel cost.
While Autonomous Vehicle (AVs) would be a breakthrough on mobility trend due to the convenient on a private vehicle, it also affects the public transport system. Based on Figure 6, AVs have the various possibility as part of the diversified public transport system. (1) it can be a high capacity core network with fixed-line service, (2) AVs can be used as feeders to public transport stations particularly trunk line such as metro, (3) Swarm of AVs can act as Robo-taxis, and on-demand shuttles to strengthen the feeder service and last-mile solution, (4) the combination
with the ride-sharing system will produce Autonomous car-sharing vehicles and lastly (5) It can generate area-based on-demand autonomous mini-buses.
In Europe, there is CityMobil2 Project which currently demonstrating low-speed fully autonomous transit application in five cities (Fagnant & Kockelman, 2015). Since June 2016, Swiss operator Carpostal – Postauto operates two autonomous electric shuttles in the city centre of Sino on a 1.5km circuit. While from the other part of Europe, Stockholm also has implemented its autonomous buses. It ran at Barkarby region which is the northern part of Stockholm. It first introduced in October 2018 and operated from 7 AM to 7 PM (weekdays) and 12 PM to 7 PM (Weekend). The purpose of the operation is to connect
Barkarby residential area and main square. It has relatively low allowed maximum speed, 20km/h, and can only carry up to 11 passengers. Figure 5 shows an example of the autonomous bus at Barkarby during the operational hour.
1.4 Research Objective
The project attempts to evaluate how public transport network design will be changing or adapting in the future, taking into account the characteristics of the automated vehicles. The research will have two main contributions:
1. The development of a new model to provide a tool for the analysis of public transport systems. This model has to consider the expected impacts of AVs on the design of public transport services. 2. The analysis of different scenarios related to the degree of development of automated vehicles and
the characteristics of the area of service and demand to get general conclusions about how the new technology will change the future public transport systems. Stockholm will be the reference for the base case study
2
Literature Review
2.1 Autonomous Vehicle
2.1.1 Definition
Autonomous vehicles or self-driving vehicles are those in which at least some aspects of a safety-critical control function (e.g. steering, acceleration, or braking) occur without direct driver input. There is no need for driver to give any control for the vehicles, while several essential command may still crucial. The continuing evolution of automotive technology aims to deliver even more significant safety benefits and Automated Driving Systems (ADS). There is 5 level of automation based on National Highway Traffic Safety Administration (NHTSA). It starts from level 0, where no automation is applied on the vehicle to level 5 where full automation is implemented.
Figure 6. Automation Levels from No Automation to Full Automation (NHTSA, 2013) Table 2. Five automation levels based on NHTSA (2013)
Vehicle Controls Traffic and Environment (Roadway) Monitoring
Level 0
Drivers are solely responsible for all vehicle controls (braking, steering, throttle, and
motive power)
Drivers are solely responsible; the system may provide driver support/convenience features
through warnings.
Level 1
Drivers are still solely responsible, but vehicle systems can assist or augment the driver in operating one or more of the primary vehicle
controls. Only one of the primary vehicle controls systems may provide assistance for
any one time.
Drivers are solely responsible for monitoring the roadway and safe operation although warnings
may be provided as with Level 0.
Level 2
Drivers have shared authority with the system. Drivers can cede active primary control in certain situations and maybe physically disengaged from operating the vehicles. Drivers are expected to be available
to take control on short notice.
Drivers are responsible for monitoring the roadway and safe operations and are expected to
be available for control at all times. Warnings may still be provided
Level 3
Drivers are able to cede full control of all safety-critical functions under certain
conditions. Drivers are expected to be
available for occasional control, but with
sufficient transition time.
When ceding control, drivers can rely heavily on
the system to monitor traffic, and environmental
Vehicle Controls Traffic and Environment (Roadway) Monitoring
Level 4
Vehicles perform all safety-critical driving
functions and monitor roadway conditions for
an entire trip. Drivers will provide destination or navigation input but are not expected to be
available for control at any time during the
trip.
The System will perform all the monitoring.
Level 5
Vehicles perform all safety-critical driving functions and monitor roadway conditions for
an entire trip. Vehicles are not restricted in where and under which conditions they can travel. Drivers will provide destination or navigation input, but are not expected to be
available for control at any time during the trip.
The system will perform all the monitoring.
2.1.2 The benefit of Autonomous Vehicle
2.1.2.1 Safety
Autonomous vehicles have the potential to increase traffic safety by reducing the number of accidents. Over 40% of the fatal accident involve some combination of alcohol, distraction, drug involvement and/or fatigue of the driver (National Highway Traffic Safety Administration, 2019); therefore, self-driven vehicles would not fall prey to human failings. Driver error is believed to be the main reason behind over 90% of all accidents (Fagnant & Kockelman, 2015). Some analyst predicts that AVs will overcome many of the obstacles that inhibit them from accurately responding in complex environments. Papadoulis et. Al (2019) tried to evaluate the effect of Connected Automated Vehicle (CAV) based on simulation
results. Five different scenarios were tested based on their market penetration ratio: 0%, 25%, 50%, 75%, and 100%. The results indicated that the CAV control algorithm improves road safety significantly, as the reduction of conflicts was 12-47%, 50-80%, 82-92%, and 90-94% for all the scenarios excluding 0% market penetration (Papadoulis, et al., 2019).
2.1.2.2 Economic and societal benefit
Traffic congestion and accident can generate a considerable loss. Traffic congestion contributes to the decrease of quality of life and loss of productivity. In contrast, traffic accident provides to the value of life (it could be a fatal or major injury accident). An NHSTA study showed motor vehicle accident in 2010 cost $242 billion in economic activity, including $57.6 billion in lost workplace productivity, and $594 billion due to loss of life. It decreased quality of life due to injuries (NHSTA, 2013). Fagnant and Kockelman (2015) suggest the economic benefits are reaching $196 billion ($442 billion, comprehensive) with a 90% AV market penetration rate. This estimation is based on the assumption that congestion represents 66% of benefits, and crash savings represent 21% of benefits. Manyika (2013) also finds the estimated global AV impacts of $200 billion to $1.9 trillion by 2025 (Manyika, et al., 2013).
Figure 7. Heatmap of Traffic Conflict Locations for the Different Market Penetration Scenarios Aggregated for all Weekdays
2.1.2.3 Efficiency and convenience
Autonomous vehicles are believed to reduce traffic congestion. Americans spent an estimated 6.9 billion hours in traffic delay in 2014 (NHTSA, 2015). In the developing country like Indonesia, the annual economic loss caused by traffic congestion is IDR40 trillion (USD2 million) for vehicle operating cost and IDR60 trillion (USD4 million) for travel time. In other words, everyone loses approximately IDR3 million (USD200) a year (Tambun, 2019). With automated vehicles, the time and money spent commuting could be put a better use. A recent study stated that automated vehicles could free up as much as 50 minutes each day that had previously been dedicating to driving (National Highway Traffic Safety Administration, 2019). It is essential to note that when the traffic safety is increased, Federal of Highway Administration (FHWA) estimates that 25% of congestion is attributable to traffic incidents, therefore, AVs can significantly reduce congestion (Federal Highway Administration, 2005)
2.1.2.4 Mobility
Automated vehicle may provide new mobility options to millions more American. Today there are 49 million Americans over age 65, and 53 million people have some form of disability
(Wadud, et al., 2016). The
implementation of autonomous
vehicles can help those people by
creating a new mobility and
accessibility service. Figure 8 shows the distribution of age-wise driving. Highly automated driving can fill the gap for elderly, as shown at Figure 8, for people who are more than 60 years old experienced the decrease of daily driving distance rapidly, it can decrease from 30 miles per day to 15 miles per day. The autonomous vehicle can slow the decrease and keep the pace of daily driving for the elderly. Although it means that the number of private cars probably will keep increasing, on the other hand, it gives accessibility for particular group of people (elderly and disable). The most direct benefit is the potential for AVs to support, enhance, and replace the driver duties of older drivers, many AVs are already helping the older drivers, and the trend of increasing automation will do more (Chan, 2017)
2.1.3 The obstacle of Autonomous Vehicles
2.1.3.1 Vehicle Cost
Autonomous vehicle needs the most advanced technology. If AVs want to operate on the road, it requires several types of equipment such as the addition of new sensors, communication and guidance technology, and software for each automobile (Fagnant & Kockelman, 2015). AVs probably will implement Light Detection and Ranging (LIDAR) system that cost approximately $30,000 to $85,000 each and additional cost from other equipment (Shchetko, 2014). There is an estimation that AVs could cost between $25,000 and $50,000 per vehicles with mass production and likely will not fall to $10,000 for at least ten years. It is still excluding some additional cost such as insurance, fuel, and parking-cost
2.1.3.2 Litigation, Liability and Perception
If the autonomous vehicles performed in the real world, there will be a new dilemma regarding litigation and liability. Although AVs will reduce the traffic accident, there is a tiny probability that a traffic accident would still occur an unavoidable accident mainly. As stated before that most of the accident is related to human error. Therefore, if an accident occurred between two vehicles or probably an animal without any human interference, it would be hard for the insurance company to solve the case. The insurance company
should create a new policy that can suit the autonomous vehicles, so no one is losing (Fagnant & Kockelman, 2015).
The other problem is the public perception. Although the manufacturer believes and tries to convince everyone that AVs is safer, the initial perception of AVs will be different. It would be hard to feel safer on a vehicle without any human control. Nowadays technology on vehicles such as parking assistance and adaptive cruise control is beneficial and receive positive feedback. But when there is not just assistance but full automation, it will be a very different thing, and people will perceive it differently until it fully implemented on the real road network.
2.1.3.3 Security
The development of technology provides not only a positive impact but also a negative impact, notably if it used for the wrong purpose. Computer hackers, disgruntled employees, terrorist organizations, and/or hostile nations may target AVs and intelligent transportation system more generally, causing collisions and traffic disruptions (Fagnant & Kockelman, 2015). Until recently, all of the countermeasures for the potential danger of AVs is still on development.
2.2 Network Design Structure
Objectives in planning a transit network can be grouped into three major categories (Vuchic, 2005): • Perform maximum transportation work: the number of passenger-trips or passenger-km
expresses the maximization process. this implies the provision of high travel speed, passenger convenience, and other elements that attract passengers
• Achieve maximum operating efficiency: this objective can ultimately be expressed as the minimum total system cost for a required performance level
• Create positive impact: these include a variety of effects, from short-range ones, such as
reduction of highway congestion, to the long-range goals, such as achievement of high population mobility, desirable land use patterns, and high quality of life
2.2.1 Discrete Network Design
A node is used to represent a specific point for loading, unloading and/or transfer in a transportation network, it also represents traffic generation on the area. There are three kinds of nodes in a bus transit network system: (a) Nodes representing centroids of specific zones, in the other words, it become the representation of the zones; (b) Nodes representing road intersection, usually it occurred on the big road network. There are too many intersections on big road network system, therefore, sometime nodes only represent an intersection of major road; and (c) Nodes with which zone centroid nodes are connected to the network through centroid connectors (called “distribution nodes”). Note that nodes could be identifiable on the ground or fictitious (Rodrigue & Ducruet, 2020).
A link joins or connects a pair of nodes and represents a
particular mode of transportation between these nodes, which means that if different modes of transportation are involved with the same link, these are represented as two different links, for example, walk mode and bike mode. This is natural since the travel time associated with every mode specific link is different. A link usually provide the travel time data for each represented transit mode.
A route is a sequence of nodes. Every consecutive pair of the sequence must be connected by a link of the relevant mode. The bus line headway on any particular route is the inter-arrival time of buses running on that route. A graph (network) refers to an entity G = {N, A} consisting of a finite set of N nodes and a finite set of A links (arcs) which connect pairs of nodes. While a transfer path is a progressive path that uses more than one route (Fan & Machemehl, 2006)
In terms of modelling or optimization, the decision makers have to determine the decision variables for the specific problem. Typically, they will determine the optimum values with an optimization method. Most common decision variables for transit network design are routes and frequencies of the public transportation networks (Kepaptsoglou & Karlaftis, 2009)
The other terms on the modelling is objective function. It evaluates some quantitative criterion of immediate importance such as cost, profit, utility, or yield. On transit network design, the objective function would be to maximize the transit demand and direct trips (direct trips is more attractive for passengers) and to minimize the user cost such as travel times, trip length, and number of transfers, and also the agency cost such as operating and capital cost.
To achieve the objective function, there are some boundaries or limitations that keep the solution in the reasonable. Those limitation is called constraint. In this case, there are 5 different types of constraint that limit the solution, which is headway feasibility, load factor, fleet size, trip length, and maximum number of trips.
2.2.2 Constraint
2.2.2.1 Headway feasibility,
The most commonly used service frequencies in the transit industry can be grouped into three categories: supply frequency, policy frequency, and demand frequency
hmin ≤ hrm ≤ hmax rm∈ R
• Supply frequency is dependent on the operator’s resources including limited fleet size. It is the maximum frequency that the operator can provide under current resource and economic constraints
• Demand frequency is determined by transit demand. This frequency is the minimum frequency that provides just enough capacity to meet the demand on the maximum link flow so that on the other links of this route, the demand is always less than the capacity
• Policy frequency can serve as a lower bound and an upper bound for service frequency and is usually used by transit operators when the supply frequency is much greater than the demand frequency or vice versa. Policy headways are most effective in systems that provide service for low-demand areas. However, when low-demand is high, especially during peak hours in large cities, policy headway is much less efficient. In this case, the demand
2.2.2.2 Load factor
Lrm= Qrm
max * h
rm
𝑃 ≤ Lmax rm ∈ R
2.2.2.3 Fleet size ∑Nrm 𝑀 𝑚=1 = ∑Trm hrm 𝑀 𝑚=1 ≤ W rm ∈ R
This constraint represents the resource limits of the operating organization. The supply frequency is usually highly dependent on the operator’s resources. The limited fleet size is expected to have a significant impact on the level of service that can be provided by TRNDP solution network. This constraint guaranteed that the optimal network pattern never uses more vehicles than the currently available ones
2.2.2.4 Trip length
Dmin ≤ Drm ≤ Dmax rm∈ R
This constraint avoids routes that are too long because bus schedules on very long routes are too difficult to maintain. Meanwhile, to guarantee the efficiency of the network the length of routes should not be too small. Furthermore, the threshold of the maximum or minimum lengths of the bus routes are usually user-defined values
2.2.2.5 Maximum number of routes
M ≤ Rmax
There is a maximum number of routes, which is based on the fleet size and this has a great impact on the later driver scheduling work. This constraint is introduced to add realism to the optimal solution network. 2.2.3 Continuous Network Design
(a) (b) (c) (d)
Figure 10. (a) Radial (b) Ubiquitous (c) Grid (d) Time-transfer Systems (Thompson, 1977)
Thompson (1977) examined four different routing schemes. The purpose of the study is to reveal how different network structures result in different levels of mobility and different cost levels. The first scheme is a radial network; it connects the urban and sub-urban area directly. Each sub-urban area has a connection with the central transfer point. The flaw of the radial system is that it does not easily accommodate most travel destined to places other than the sub-urban. The next scheme is ubiquitous, a method to tackle the weakness of radial network without making people transfer between routes is to connect each pair of squares with its route. Unfortunately, the ubiquitous method does not appear to be a realistic solution because it requires very high service and even most densely populated area could not generate enough ridership to support it.
the grid system is that it relied on scheduled connection between routes and does not require the grid system's frequent service on most routes for most of the day. This method often consists of an off-street platform transfer for bus park. Every thirty minutes, passengers will appear and the bus from all direction will surround the platform and transferring passengers. Badia et al. (2016) and Badia (2019) extended the comparison between direct-trip based structures and transfer-based structures in connection with the urban form evolution to more decentralized travel patterns. Progressively, the increasing urban dispersion reinforces the applicability of transfer-based solutions.
(i) (ii)
Figure 11. (i) Route having two transfers (a) and one transfer (b), (ii) Two routing schemes for a rectangle region (Newell, 1979)
Figure 11 demonstrate two types of transfer on a grid network service. One transfer will occur when the origin is located on the N-S or E-W axis and the destination will be the other axis. For example, when the origin is on E-W axis, the destination supposed to be on N-S axis, otherwise it would be no transfer or two transfer trip. As stated before, two transfer only occurred when the origin and destination are located on the same axis but different line (not in the same line, it would be no transfer). On the right-side pictures, there are two alternative of routing schemes for a rectangular region. It could be a grid network or radial network. While grid network require transfer for most of the intersection, radial network encourage people to transfer on particular point. Usually, radial transfer has a transfer point on the same line. Newell (1979) proposed similar network scheme, he considered a system of linear bus routes forming a rectangular grid.
2.2.3.1 Hybrid Transit Network
Figure 12 Hybrid Transit Network Concept (Daganzo, 2010)
2.2.3.2 Bimodal Transit Design
An urban public transit system often consists of two overlapping and interweaving single-mode networks. A local bus network that features high line and stops densities but low speed and operating costs, and an express transit network that features high speed and capacity, but has to be sparsely spaced due to the high costs. The latter is often operated by Bus Rapid Transit (BRT) or rail. Among many others. The interweaving local and express networks furnish multiple route options, so that passengers with distinct OD can choose the routes that best suit their needs. For example, short-distance travellers whose origins and destinations are far from the express lines can choose to travel by local lines only, and long-distance travellers can take the local service as a feeder to access the express lines. (Fan, et al., 2018)
Figure 13. Bimodal Transit Network Design (Fan et al., 2018)
2.2.3.3 Feeder Service
Figure 14. Alternative Feeder Service System (Badia and Jenelius, 2020b)
Badia and Jenelius (2020b) distinguished the feeder service into two alternatives, namely fixed route and door to door service. Fixed route system is composed by a group of parallel lines that cross the area completely in the longitudinal direction. Then, these lines adjust their positions to get the road, and finally, they traverse that road to the station. To understand how this service operates, we explain the process followed by one bus that serves one of these lines. The bus starts in one extremes point of the line, for instance, the station, where users get on the bus to travel to the service area. Then, the bus crosses the road and a section of the side of the area to get the line that it serves. Once the bus is on the correspondent line, it stops in all the stops dropping off the passengers. When the bus arrives at the last stop starts the service in the opposite direction following the same path. In this case, the bus serves all the stops in the area but picking up users that want to reach the station. Finally, the bus gets the station, where the passengers get off the vehicle, and starts a new cycle
3
Methodology
In the methodology chapter, there are three main sub-chapter. The first part is the proposed network design where the base network for the optimization is constructed. The second part is the explanation on how the distribution of the demand across the network. The last part is the crucial one, it is about the derivation of the formula. It is the baseline of the model where it really affect the whole optimization process.
3.1 Proposed Network Design
Figure 15 is the proposed network structure design for the problem. A square area which consists of two sub-area. The first area is the center square. It represents the Central Business District (CBD) of the city where people mostly conduct their daily activity. It has a grid network structure and consist of two different kinds of transport mode, namely Bus and Metro. On the outer area, there is a peripheral area that represent suburban characteristic.
Figure 15. General Network Structure Design
As stated on the previous chapter, the network model is the combination of several previous published work. The combination of grid and radial network that become a hybrid model (Daganzo, 2010), the intersection between two modes, metro and bus (Fan, et al., 2018) and the optimum last mile solution on the peripheral area between fixed route and door to door service (Badia & Jenelius, 2020a). On the central area, there will be two public transport operation (i.e. bus and metro). The total side length is D while the side of central area length is α.D. The bus line marked as the red line with bus spacing of sb and the metro
line is the thick line with spacing of sm. On the peripheral area, the feeder service operate on an area of sm
3.2 Demand
Figure 16. Accumulated Demand Ratio
The demand is based on the Stockholm public transport operator (SL) data, therefore, the demand in this model is follow Stockholm city characteristics. The data shows that the daily demand for public transport is approximately 45,800 passengers/hour. Based on Figure 16, almost 70% of the demand are located on 20% of the area around the central point of the city. If the length of side square (D) is 20 km and the area would be 400 km2, then 70% (32,000 passengers/hour) of the population live on the 80 km2 area at the centre. while the other 30% population are scattered throughout the rest 320 km2 area. From the graph, we can obtain the equation of the distribution. We also assume the value of k = 0.192, Qc = demand portion on the central area, and Qp = demand portion on the peripheral area.
Portion Demand = 1 + k * ln (portion Area + exp (-1/k))
Qc = Q * portion demand
Qp = Q - Qc
3.3 Objective Function
The identification of the most competitive transit network should satisfy a proper trade-off between the user and agency perspective (Badia, et al., 2014). One way to find the optimum trade off between user and agency is to minimize both cost and find the optimum decision variables. The agency cost is consist of transport infrastructure length, vehicle distance travelled per hour and vehicle hours travelled during rush hour. While the user cost is the combination of waiting time, in-vehicle time, and access time.
min {Z = [€VV + €MM + €LL] + [A + W + T + (δ/vW) eT)]: s ≥ 0, H ≥ 0, 0 ≤ α ≤ 1, O ≤ C}
Agency Cost User Cost
Table 3 Objective Function Component
Agency Cost
L [km] Transport infrastructure length (double direction)
V [veh-km/h] Vehicle distance traveled per hour of operation
M [veh-h/h] Vehicle hours traveled during rush hour
O [pax/veh] Peak vehicle occupancy during the rush hour
€V [€/km-hr]
Unit Monetary Cost
€M [€/veh-km]
€L [€/veh-hr]
1/λμ - Equivalent hour of passengers factor
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Ac cu mu la te d D e ma nd Accumulated Area
User Cost
A [h] Average walking access time
W [h] Average walking time
T [h] Average in-vehicle-travel time
E [km] Average in-vehicle-travel distance
vc, vw [km/h] Vehicle’s commercial speed; walking speed
eT [-] Expected number of transfers per passenger
δ [km] Fixed distance penalty for transfers
To find the optimum objective cost, we need to derive and combine the agency cost and user cost. we can distinguish the user cost based on the modes (Metro, Bus, and Feeder) and distinguish the user cost based on the type of trip (central-central, central-peripheral, peripheral-peripheral)
3.3.1 Agency Cost
3.3.1.1 Total length L of the two-way infrastructure system (L)
Table 4 Total length of infrastructure (L) formula
Central Area Lmetro (𝛼.𝐷)2 𝑠m2
. 2 s
m= 2
(𝛼.𝐷)2 𝑠m Lbus (𝛼.𝐷)2 𝑠b2. 2 s
b-
(𝛼.𝐷)2 sm2. 2 s
m= 2 (𝛼. 𝐷)
2(
1 sb -1 sm)
Peripheral Area Lmetro 𝐷2− (𝛼.𝐷)2 sm2. s
m=
(1− 𝛼2) .𝐷2 Sm Total Length Lmetro2
(𝛼.𝐷)2 𝑠m+
(1− 𝛼2) .𝐷2 sm=
𝐷2(1 + 𝛼2) sm Lbus2 (𝛼. 𝐷)
2(
1 sb -1 sm)
Proof, in this formulation, we assume that in the central area, each line is a two direction way. We only focus the formulation on the central area because there is no specific infrastructure on the peripheral area except for the metro. The feeder bus is assumed to mixed with the traffic therefore does not need any new infrastructure. We obtained the total infrastructure by multiplying the line length with the number of stops on the area. We distinguish the metro stop and the bus stop. We can get the number of transfer stop for each mode, for metro is (𝜶.𝑫)𝟐
𝑺𝒎𝟐 while for bus will be the number of total stops subtracted by number of metro stop. Each metro stop has associated a length of 2s on the central area and s on the peripheral area. The spacing in the formulation is consist of sm, sb, and sf for metro, bus, and feeder bus respectively
3.3.1.2 Total vehicle distance traveled per hour (V)
Vfeeder [2 (sm sf) ( 3 sm 4 -sb 4)] . 1 Hf Fixed Route [(sm w) 2 ((sm 2 -w) + sm 2 +γ.r)] . 1 Hf Door to Door Total Vmetro 1 Hm. {[4 (α.D)2 sm ] + [ 6𝛼 (1− 𝛼) 𝐷2 𝑠 ]} Vbus
[2 . 2 (𝛼. 𝐷)
2(
1 sb -1 sm)] .
1 Hb Vfeeder [2 (sm sf) ( 3 sm 4 -sb 4)] . 1 Hf Fixed Route [(sm w) 2 ((sm 2 -w) + sm 2 +γ.r)] . 1 Hf Door to DoorProof, total vehicle distance traveled per hour for each mode can be obtained by multiply the total infrastructure by 2 (two direction) and divide it by the corresponding headway. For example, the total infrastructure for metro is [𝟒 (α.D)2
sm ] + [
𝟔𝜶 (𝟏− 𝜶) 𝑫𝟐
𝒔 ] and we multiply it by 1/Hm. For the bus, as stated
before, it only operates in the central area, therefore we only calculate the bus total infrastructure in the central area. The infrastructure on the peripheral area goes to feeder service. The total infrastructure for bus is [𝟐 (𝜶. 𝑫)𝟐
(
1sb
-1sm
)] and multiplied by 2 and divided by the bus headway. The last mode is the feeder
service. Although we do not consider the total infrastructure of the feeder service due to the mixed traffic operation. We still calculate the coverage of the feeder service to obtain the total vehicle distance. for the fixed route, first we need to determine the number of line 𝑺𝒎
𝑺𝒇 and multiply it by the length of each line (Sm
– Sb/2 + Sm/4). For the door to door service, we need to determine the number of areas 𝟏/𝟐 (𝑺𝒎
𝒘) 𝟐
and multiply it by the total length for each inner trip (𝑺𝒎
𝟐 − 𝒘) + 𝑺𝒎
𝟐 + 𝜸. 𝒓. Feeder service distance traveled also
needed to be multiplied by 2/Hb to be on total vehicle distance traveled per hour form. On the door to door service formulation, there is a parameter r which is the length of internal route. To estimate the length, we assume the non-backtracking route strategy in Daganzo (1984) and reformulated by Li & Quadrifoglio (2010) for routes with few stops. The model works with an approximation on the number of stops n = δ .Hf .w2.
3.3.1.3 Total vehicle hours traveled during rush hour (M)
Table 6 Vehicle hours travelled (M) formula
[(sm w) 2 ((sm 2 -w) + sm 2 +γ.r)] . 1 Hf.vf Door to Door
Proof, we can divide the total vehicles distance by the speed of each mode to obtain the total vehicle hours traveled. We need to aware that for feeder service, it will have two scenario which is fixed route and door to door
3.3.2 User Cost
3.3.2.1 Probability of Choosing Particular Mode
Table 7 Probability of mode usage (P) formula
Central-Central Pm 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑀𝑒𝑡𝑟𝑜 𝑆𝑡𝑜𝑝 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑇𝑜𝑡𝑎𝑙 𝑆𝑡𝑜𝑝 (αD)2 / Sm2 (αD)2 / Sb2
=
Sb2 Sm2 Pb 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐵𝑢𝑠 𝑆𝑡𝑜𝑝 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑇𝑜𝑡𝑎𝑙 𝑆𝑡𝑜𝑝 (αD)2 / Sb2 - (αD)2 / Sm2 (αD)2 / Sb2= 1 -
Sb2 Sm2 Pmm = Sb 4 Sm4 Pmb = Sb2 Sm2 . (1 - Sb2 Sm2) Pbm = Sb2 Sm2 . (1 - Sb2 Sm2) Pbb = (1 − Sb2 Sm2) 2 Central-Peripheral Pm 1 (Peripheral) Pm Sb Sm (Central) Pb 1 - Sb Sm (Central) Pmm Sb Sm . 1 = Sb Sm Pmb (1 − Sb Sm) . 1 = (1 − Sb Sm) Peripheral - Peripheral Pm 1 (Central) Pm 1 (Peripheral) Pmm 1 Pmmm 13.3.2.2 Expected number of transfers per trip (eT)
Table 8 Expected number of transfer per trip formula
Central-Central P (0-T) 0 P (1-T) 1 P (2-T) 0 eT 0 . P(0-T) + 1 . P(1-T) + 2 . P(2-T) = 1 Central-Peripheral P (0-T) 0 P (1-T) 1 P (2-T) 0 eT 0 . P(0-T) + 1 . P(1-T) + 2 . P(2-T) = 1 Peripheral-Peripheral P (0-T) 0 P (1-T) 0.5 P (2-T) 0.5 eT 0 . P(0-T) + 1 . P(1-T) + 2 . P(2-T) = 1.5
Proof, the base assumption of this formulation is that no one have a direct trip. For the simplification matter, everyone needs to make minimum one transfer. Therefore, the value of P(0-T) will be 0 (zero). The first type of trip is central-central trip. The other assumption is that people also will try to minimize the number of transfers. It is possible to have more than one transfer on the central area trip, but we assume that passengers will prefer to have longer in-vehicle time than to have more transfer (Cats, et al., 2011). Based on those assumptions, we can conclude that all of the trip on the central-central trip have a 100% probability of one transfer. The same principle also applied for the next trip type, central-peripheral trip. On the other hand, the last type of trip namely peripheral-peripheral trip will have different case. It will have the case of two transfer. Based on the calculation of the probability which consist of the multiplication of origin and destination probability. The probability of one transfer will be the same as two transfer because of their typical area of coverage. Both of them will have the value of 0.5
3.3.2.3 Waiting Time
Table 9 Waiting time for central-central trip
Central-Central Wmm =Hm Wmb =Hm+Hb 2 Wbm = Hm+Hb 2 Wbb =Hb W = Pmm . Wmm + Pmb . Wmb + Pbm . Wbm +Pbb . Wbb W = Sb4 Sm4 . Hm + Sb2 Sm2 . (1 - Sb2 Sm2) . (Hm+ Hb )+ (1 − Sb2 Sm2) 2 . Hb
Proof, on the central area, there are two types of transit modes, Metro and Bus. Each mode has its own headway namely Hm for metro and Hb for bus. There are four options to make a trip on the central area
and each option will have different waiting time except for the bus and bus-metro trip. For metro-metro trip, passengers will wait 𝑯𝒎
𝟐 at the origin and 𝑯𝒎
𝟐 at the transfer point, therefore they will wait for
Hm in total. For metro-bus trip or bus-metro trip, the combination of the waiting time will be between 𝑯𝒎
𝟐
and 𝑯𝒃
𝟐 which generate the waiting time of 𝑯𝒎+𝑯𝒃
𝟐 . The last options is the bus-bus trip, it has similar principle
bus-bus trip is Hb. The average waiting time for central-central trip is the total waiting time for each trip chain and multiply by the probability of choosing the particular type of trip.
Table 10 Waiting time for central-peripheral trip
Central-Peripheral Wmm Hm . (1 − α3) 3α . (1 − α2) + Hm 2 + Hf 2 Fixed Route Hm . (1 − α3) 3α . (1 − α2) + Hm 2 + 0.5 [Hf+ (γ. r v+(τs + τb).δ .Hf .w2)/n] Door to Door Wmb Hm . (1 − α3) 3α . (1 − α2) + Hb 2 + Hb 2 Fixed Route Hm . (1 − α3) 3α . (1 − α2) + Hb 2 + 0.5 [Hf+ (γ. r v+(τs + τb).δ .Hf .w2)/n] Door to Door W [Hm . (1−α3) 3α . (1−α2)+ Hm 2 + Hf 2] . Sb Sm + [ Hm . (1−α3) 3α . (1−α2)+ Hb 2 + Hb 2] . (1 − Sb Sm) Fixed Route {Hm . (1−α3) 3α . (1−α2) + Hm 2 +0.5 [Hf+ (γ. r v+(τs + τb)δ .Hf .w2)/n]} Sb Sm + {Hm. (1 − α 3) 3α .(1 − α2)+ Hb 2 + 0.5 [Hf + (γ. r v+(τs + τb)δ .Hf .w2)/n]} . (1 − Sb Sm) Door to Door
Proof, the trip that have either origin or destination on the peripheral area will have different approach because of the existence of the feeder service. We will divide the feeder service which is located on the peripheral area into two type, Fixed route and door to door service. On metro-metro trip, passengers is waiting for the feeder service for Hf2 (fixed route) while they need to wait for [Hf+(γ.r
v+(τs + τb)δ .Hf .w2)]
for door to door service (Badia & Jenelius, 2020a)After they arrived at the station, they need to wait approximately Hm . (𝟏−α𝟑)
𝟑α . (𝟏−α𝟐) due to the metro branching on peripheral area. At the central area they will wait for Hm/2 if they choose metro and Hb/2 if they choose bus.
Table 11 Waiting time for peripheral-peripheral trip
W Wmm . Pmm . P(1-T) + Wmmm . Pmmm . P(2-T) W [Hm . (1−α3) 3α .(1−α2) + Hm 2 + Hf ]. 0.5+ [ Hm . (1−α3) 3α . (1−α2)+ Hm + Hf]. 0.5 Fixed Route {Hm . (1−α3) 3α . (1−α2)+ Hm 2 + [Hf+(γ. r v+(τs + τb)δ .Hf .w2)/n]} 0.5 + {Hm . (1−α3) 3α . (1−α2)+ Hm + [Hf+(γ. r v+(τs + τb)δ .Hf .w2)/n]} 0.5 Door to Door
Proof, similar to the previous area, it involves two area where the origin and the destination of the trip will be located on the peripheral area. For metro-metro trip, on the peripheral area, the passengers will wait for the feeder service twice (at the origin and destination) therefore the waiting time for feeder service is Hf for fixed route and 2 [Hf+(γ.r
v+(τs + τb)δ .Hf .w2)] for door to door service. The average total
waiting time have different approach because on this trip, we have one transfer and two transfer trip therefore we need to weight the waiting time of each trip by the probability of number of transfer.
3.3.2.4 Access Time
Table 12 Access time for central-central trip
Central-Central Amm = sb vw Amb = sb vw Abm = sb vw Abb = sb vw A = Amm . Pmm + Amb . Pmb + Abm . Pbm +Abb . Pbb A =
s
bv
wProof, Although the network have two kinds of stop (metro and bus), it still form a complete network. Therefore, we can assume that people always have the same distance to the nearest stop either it is a metro stop or bus stop. We assume that people that use metro-metro trip is only the one that live close to the metro station or metro line. As people who live surrounded by bus stop are impossible to make metro-metro trip. They need to make either metro-bus trip or bus-bus trip. The average access distance to the metro line is the same as the average distance to the bus stop which is sb/2. Hence, the total access time for any kind of trip is sb (origin and destination). Next, all of the access distance must be divided by walking speed vw to obtain access time.
Table 13 Access time for central-peripheral trip
Central-Peripheral Amm sb+sl 4vw + sb 2vw Fixed Route sb 2vw Door to Door Amb sb+sl 4vw + sb 2vw Fixed Route sb 2vw Door to Door A = Amm . Pmm + Amb . Pmb
A = (sb+sl 4vw + sb 2vw) Fixed Route sb 2vw Door to Door
Proof based on Badia and Jenelius (2020b) the access time on the peripheral area is the walking distance to the nearest feeder service stop. It only occurred on the fixed route service which is sb+sl
4vw
where sb is bus
stop spacing and sl is the distance between consecutive line. On the other hand, there will be no access time for door to door service because we assume that the feeder will arrive as close as possible to the passengers’ house. For the access time on the city center it will follow the previous approach that the access time will be sb/2 vw for metro user and bus user
Table 14 Access time for peripheral-peripheral trip
Peripheral-Peripheral Amm sb+sl 2vw Fixed Route 0 Door to Door Ammm sb+sl 2vw Fixed Route 0 Door to Door A = Amm . Pmm . P(1-T) + Ammm . Pmmm . P(2-T) A = sb+sl 2vw Fixed Route 0 Door to Door
Proof, due to the origin and destination of the trip are located on the peripheral area. The access time of the passenger only occurred when they want to use the feeder service, therefore the total access time is twice of the one way trip to the nearest feeder service stop which is sb+sl
2vw for fixed route and 0 for door to
door service
3.3.2.5 In-vehicle Time
Table 15 In-vehicle time for central-central trip
Central-Central Tmm 2αD 3Vm Tmb 7αD 15Vm+ 3αD 15Vb T bm 7αD 15Vm+ 3αD 15Vb T bb 2αD 3Vb T Tmm.Pmm + Tmb.Pmb + Tbm.Pbm + Tbb.Pbb T 2αD 3Vm . Sb4 Sm4+ 2. ( 7αD 15Vm+ 3αD 15Vb). (1 - Sb2 Sm2)+ 2αD 3Vb . Sb2 Sm2
Proof, the expected distance between two point can be obtained by several method. In this case, we will apply two method that can represent the expected distance between two random points namely Manhattan method and Chebyshev method (Gaboune, et al., 1993). For metro-metro and bus-bus trip, we only implement Manhattan method to calculate the expected distance because there are no preferences between mode. In other words, passengers will only use one type of transport mode for the whole journey. First, we determine the expected distance on one direction (horizontal or vertical) which will be αD
3 and the other direction αD
3 to deliver the final expected distance of
2αD
3 . To obtain the in-vehicle time, we divide the
assumption. As stated before, passengers will prefer to use metro for the longer trip therefore we implement Chebyshev method for the metro trip which culminate the expected distance of 7αD
15 . While the
bus trip will follow the Manhattan assumption of the distance between two random points αD
3. the final
results of in-vehicle time for metro-bus trip and vice versa is 7αD
15Vm+
3αD 15Vb
Table 16 In-vehicle time for central-peripheral trip
Central-Peripheral Tmm D [(2 − 3α + α3)] 4Vm + 2αD 3Vm + Sm 2Vf Fixed Route D [(2 − 3α + α3)] 4Vm + 2αD 3Vm+ Sm - w + γr 2Vf Door to Door Tmb D [(2 − 3α + α3)] 4Vm + 7αD 15Vm+ 3αD 15Vb+ Sm 2Vf Fixed Route D [(2 − 3α + α3)] 4Vm + 7αD 15Vm+ 3αD 15Vb+ Sm - w + γr 2Vf Door to Door T Tmm.Pmm + Tmb.Pmb T [D [(2−3α + α3)] 4Vm + 2αD 3Vm+ Sm 2Vf]. Sb Sm + [ D [(2−3α + α3)] 4Vm + 7αD 15Vm+ 3αD 15Vb+ Sm 2Vf] .(1 − Sb Sm) Fixed Route [D [(2−3α + α3)] 4Vm + 7αD 15Vm+ 3αD 15Vb+ Sm 2Vf]. Sb Sm + [D [(2−3α + α3)] 4Vm + 7αD 15Vm+ 3αD 15Vb+ Sm - w + γr 2Vf ]. (1 − Sb Sm) Door to Door
Proof, on central-peripheral trip, there will be an additional expected distance on the formula. First, the expected distance when using feeder service. On the fixed route service, the distance is Sm
2Vf while for
door-to-door service is Sm - w + γr
2Vf . Second, the additional distance on the peripheral area,
D [(𝟐−𝟑α + α3)] 4Vm . the
movement on central area will follow the similar principle as previous derivation, 2αD
3Vm for metro-metro trip
and 7αD
15Vm+
3αD
15Vb for metro-bus trip
Table 17 In-vehicle time for peripheral-peripheral area trip
[D [(2−3α + α3)] 2Vm + αD 2Vm+ Sm - w + γr Vf ].0.5 + [ D [(2−3α + α3)] 2Vm + 5αD 12Vm+ Sm - w + γr Vf ].0.5 Door to Door
Proof, the trip between peripheral area is distinguish by the number of transfers. For one transfer trip, the destination will be the other side (different axis) of peripheral. For example, if the origin of the trip is on N peripheral, the destination is either on the W or E peripheral. Therefore, we can estimate the expected distance for the trip. The distance from the boundary (extreme point) between central and peripheral into any random point along the line is αD
2 and the expected distance between those random point to the boundary of the destination is also αD
2, while the probability of the destination is half of the total area. The result of the expected distance is αD2. Different approach is used for two-transfer trips, the destination of this trip is the opposite side of the origin or the same side but different area of the origin. First, we assume the trip for the same side destination, when the passengers arrived at the boundary, the expected distance is the distance between two random points αD3 and multiply by 14 for one side of the total peripheral. For the trip to the other side of peripheral, passengers need to cross the central area αD and when they reach the boundary, the expected distance would be the distance between two random points αD
3. Therefore, the total distance will be 5αD
12
3.3.2.6 Occupancy
Table 18 Vehicle critical occupancy
