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63-556: The Cheonggyecheon restoration project initially attracted significant public criticism, but since its opening in 2005 it has become popular among residents and tourists . Cheonggyecheon is an 10.84 km (6.74 mi) stream flowing west to east through downtown Seoul , and then meeting Jungnangcheon , which connects to the Han River and empties into the Yellow Sea . The stream was named as Gaecheon ("open stream") after

126-480: A e , b e ≥ 0 {\displaystyle a_{e},b_{e}\geq 0} , then at worst, traffic in the energy-minimizing equilibrium is twice as bad as socially optimal. Proof: Let Z {\displaystyle Z} be some traffic configuration, with associated energy E ( Z ) {\displaystyle E(Z)} and total travel time T ( Z ) {\displaystyle T(Z)} . For each edge,

189-487: A 20-minute increase. They are obliged to switch to the new route via A too, so it now takes 4000 100 + 4000 100 = 80 {\displaystyle {\tfrac {4000}{100}}+{\tfrac {4000}{100}}=80} minutes. Nobody has any incentive to travel A-End or Start-B because any driver trying them will take 85 minutes. Thus, the opening of the cross route triggers an irreversible change to it by everyone, costing everyone 80 minutes instead of

252-710: A day's round trip of any major city. International tourists come primarily from nearby countries or regions in Asia. Japan , mainland China , Hong Kong and Taiwan together account for roughly 75% of the total number of international tourists. In addition, the Korean Wave has brought increasing numbers of tourists from Southeast Asia and India. The Korea Tourism Organization (KTO) is targeting 100,000 arrivals from India in 2013. The number of Korean domestic tourists has increased since 2010. The number of people who participated in domestic travel (which includes one-day trips)

315-401: A doomed species from the network could in principle bring about the positive outcome of preventing a series of further extinctions. It has been suggested that in basketball, a team can be seen as a network of possibilities for a route to scoring a basket, with a different efficiency for each pathway, and a star player could reduce the overall efficiency of the team, analogous to a shortcut that

378-484: A general transportation network when a new route is added. (Note that their result applies to the addition of any new route, not just to the case of adding a single link.) As a corollary, they obtain that Braess's paradox is about as likely to occur as not occur when a random new route is added. Braess's paradox has a counterpart in case of a reduction of the road network, which may cause a reduction of individual commuting time. In Seoul , South Korea , traffic around

441-745: A group tour ban after the US military deployed the Terminal High Altitude Area Defense (THAAD) system in South Korea. From April 2017, Chinese tourists plummeted by more than 60% compared to the previous year. In 2020, the South Korean tourism industry made it a long-term goal to reduce its dependency on Chinese tourists. Since Lee Myung-bak 's visit to the Liancourt Rocks and his demand for an apology from

504-422: A mathematician at Ruhr University , Germany , noticed the flow in a road network could be impeded by adding a new road, when he was working on traffic modelling . His idea was that if each driver is making the optimal self-interested decision as to which route is quickest, a shortcut could be chosen too often for drivers to have the shortest travel times possible. More formally, the idea behind Braess's discovery

567-493: A new channel might cause higher fees, and similarly closing existing channels might decrease fees. The paper presented a theoretical analysis with conditions for the paradox, methods for mitigating the paradox as well as an empirical analysis, showing the appearance in practice of the paradox and its effects on Bitcoin's Lightning network. Consider a road network as shown in the adjacent diagram on which 4000 drivers wish to travel from point Start to End. The travel time in minutes on

630-459: A path for electrons in a nanoscopic network paradoxically reduced its conductance. That was shown both by simulations as well as experiments at low temperature using scanning gate microscopy . A model with springs and ropes can show that a hung weight can rise in height despite a taut rope in the hanging system being cut, and follows from the same mathematical structure as the original Braess's paradox. For two identical springs joined in series by

693-563: A result of the political status of the rocks. Many local districts hold annual festivals, such as the Boryeong Mud Festival and the Cheongdo Bullfighting Festival. In addition, people in South Korea come to Seoul to enjoy various cultural activities. Due to the metropolitan area centralization of the cultural infrastructure, there is a cultural gap between Seoul and other regions. According to

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756-411: A short rope, their total spring constant is half of each individual spring, resulting in a long stretch when a certain weight is hung. This remains the case as we add two longer ropes in slack to connect the lower end of the upper spring to the hung weight (lower end of the lower spring), and the upper end of the lower spring to the hanging point (upper end of the upper spring). However, when the short rope

819-488: A solution to the scalability problem of blockchain networks, allowing transactions of high rates without recording them on the blockchain. In such a network, users can establish a channel by locking funds on each side of the channel. Transactions are executed either through a channel connecting directly the payer and payee or through a path of channels with intermediate users that ask for some fees. While intuitively, opening new channels allows higher routing flexibility, adding

882-459: Is a traffic graph with x e {\displaystyle x_{e}} people driving along edge e {\displaystyle e} . Let the energy of e {\displaystyle e} , E ( e ) {\displaystyle E(e)} , be (If x e = 0 {\displaystyle x_{e}=0} let E ( e ) = 0 {\displaystyle E(e)=0} ). Let

945-587: Is an equilibrium. The above proof outlines a procedure known as best response dynamics, which finds an equilibrium for a linear traffic graph and terminates in a finite number of steps. The algorithm is termed "best response" because at each step of the algorithm, if the graph is not at equilibrium then some driver has a best response to the strategies of all other drivers and switches to that response. Pseudocode for Best Response Dynamics: At each step, if some particular driver could do better by taking an alternate path (a "best response"), doing so strictly decreases

1008-455: Is because the Nash equilibrium of such a system is not necessarily optimal. The network change induces a new game structure which leads to a (multiplayer) prisoner's dilemma . In a Nash equilibrium, drivers have no incentive to change their routes. While the system is not in a Nash equilibrium, individual drivers are able to improve their respective travel times by changing the routes they take. In

1071-407: Is cut, the longer ropes become taut, and the two springs become parallel (in the mechanical sense ) to each other. The total spring constant is twice that of each individual spring, and when the length of the long ropes is not too long, the hung weight will actually be higher compared to before the short rope was cut. The fact that the hung weight rises despite cutting a taut rope (the short rope) in

1134-553: Is held every August and Busan International Film Festival is held every October. Jagalchi Cultural Festival is developed into a representative cultural tourism festival in Korea. Because of these various festivals and places, many people travel to Busan. Also, the influence of Social Network Service made Busan a popular tourist attraction. The official Facebook of the Busan Culture and Tourism Ministry and official blog sites promote

1197-462: Is overused increasing the overall times for a journey through a road network. A proposed solution for maximum efficiency in scoring is for a star player to shoot about the same number of shots as teammates. However, this approach is not supported by hard statistical evidence, as noted in the original paper. Braess's paradox has been shown to appear in blockchain payment channel networks, also known as layer-2 networks. Payment channel networks implement

1260-413: Is that the Nash equilibrium may not equate with the best overall flow through a network. The paradox is stated as follows: "For each point of a road network, let there be given the number of cars starting from it and the destination of the cars. Under these conditions, one wishes to estimate the distribution of traffic flow. Whether one street is preferable to another depends not only on the quality of

1323-411: Is the energy-minimizing traffic flow, the inequality implies that T ( Z e ) ≤ 2 E ( Z e ) ≤ 2 E ( Z o ) ≤ 2 T ( Z o ) {\displaystyle T(Z_{e})\leq 2E(Z_{e})\leq 2E(Z_{o})\leq 2T(Z_{o})} . Thus, the total travel time for the energy-minimizing equilibrium

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1386-658: Is the observation that adding one or more roads to a road network can slow down overall traffic flow through it. The paradox was first discovered by Arthur Pigou in 1920, and later named after the German mathematician Dietrich Braess in 1968. The paradox may have analogies in electrical power grids and biological systems. It has been suggested that, in theory, the improvement of a malfunctioning network could be accomplished by removing certain parts of it. The paradox has been used to explain instances of improved traffic flow when existing major roads are closed. Dietrich Braess,

1449-476: Is the principal tourist destination for visitors; popular tourist destinations outside of Seoul include the major coastal city of Busan , the Seorak-san national park, the historic city of Gyeongju and subtropical Jeju Island . The majority of the South Korean tourist industry is supported by domestic tourism. Thanks to the country's extensive network of trains and buses, most of the country lies within

1512-549: The E {\displaystyle E} will be reduced by ∑ i = 0 n L e i ( x e i ) {\textstyle \sum _{i=0}^{n}L_{e_{i}}(x_{e_{i}})} . That is simply the total travel time needed to take the original route. If the new route is then added, e 0 ′ , e 1 ′ , … , e m ′ {\displaystyle e'_{0},e'_{1},\ldots ,e'_{m}} ,

1575-576: The Emperor of Japan over Japanese colonialism in Korea in 2012, the Japanese public's image of South Korea deteriorated significantly. Japanese tourists to South Korea halved from 3.5 million in 2012 to 1.8 million in 2015, while South Korean tourists to Japan doubled from 2 million in 2012 to 4 million in 2015. South Korea's historical tourist attractions include the ancient capitals of Seoul , Gyeongju and Buyeo . Some natural landmarks include

1638-632: The Veronica Rudge Green Prize in Urban Design from Harvard University 's Graduate School of Design . 37°34′12″N 127°0′23″E  /  37.57000°N 127.00639°E  / 37.57000; 127.00639 Tourism in South Korea Tourism in South Korea and its industry caters to both foreign and domestic tourists. In 2023, 11.0 million foreign tourists visited South Korea , making it

1701-640: The urban heat island effect: along the stream, temperatures are 3.3° to 5.9 °C cooler than on a parallel road 4-7 blocks away. The number of vehicles entering downtown Seoul has decreased by 2.3%, with an increasing number of users of buses (by 1.4%) and subways (by 4.3%: a daily average of 430,000 people) as a result of the demolition of the two heavily used roads. Between 2003 and the end of 2008, use of buses increased by 15.1% and use of subway by 3.3% in Seoul. With air pollution reduced by 35% from 74 to 48 micrograms per cubic meter, respiratory diseases among

1764-514: The 20th most visited country in the world. Most non-Korean tourists come from East Asia and North America , such as Taiwan and the United States. The popularity of Korean popular culture , often known as the " Korean Wave ", in countries around the world has significantly increased tourist arrivals. South Korea has 16  World Heritage Sites , including  Changdeokgung Palace ,  Namhansanseong and Hwaseong Fortress . Seoul

1827-776: The Ministry of Culture, Sports and Tourism, 36.4 percent of the total cultural infrastructure such as public library, museum, and art galleries are concentrated in Seoul. Therefore, many people in South Korea travel to Seoul. The Seoul Trail is a walking trail that goes around the city. Busan is the second largest city in South Korea. It is located in the southeastern coast in Korea, so Busan has abundant tourist attractions such as beach and hot spring. People in South Korea visit beaches in Busan in hot summer. Also, there are various festivals in Busan. 11 festivals are held annually, including local festivals and art events. Busan sea festival

1890-511: The Start–A road is the number of travellers (T) divided by 100, and on Start–B is a constant 45 minutes (likewise with the roads across from them). If the dashed road does not exist (so the traffic network has 4 roads in total), the time needed to drive Start–A–End route with a {\displaystyle a} drivers would be a 100 + 45 {\displaystyle {\tfrac {a}{100}}+45} . The time needed to drive

1953-473: The Start–B–End route with b {\displaystyle b} drivers would be b 100 + 45 {\displaystyle {\tfrac {b}{100}}+45} . As there are 4000 drivers, the fact that a + b = 4000 {\displaystyle a+b=4000} can be used to derive the fact that a = b = 2000 {\displaystyle a=b=2000} when

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2016-472: The area. In 2008 Youn, Gastner and Jeong demonstrated specific routes in Boston, New York City and London where that might actually occur and pointed out roads that could be closed to reduce predicted travel times. In 2009, New York experimented with closures of Broadway at Times Square and Herald Square , which resulted in improved traffic flow and permanent pedestrian plazas. In 2012, Paul Lecroart, of

2079-428: The case of Braess's paradox, drivers will continue to switch until they reach Nash equilibrium despite the reduction in overall performance. If the latency functions are linear, adding an edge can never make total travel time at equilibrium worse by a factor of more than 4/3. In 1983, Steinberg and Zangwill provided, under reasonable assumptions, the necessary and sufficient conditions for Braess's paradox to occur in

2142-530: The city sped up when a motorway was removed as part of the Cheonggyecheon restoration project. In Stuttgart , Germany , after investments into the road network in 1969, the traffic situation did not improve until a section of newly built road was closed for traffic again. In 1990 the temporary closing of 42nd Street in Manhattan , New York City , for Earth Day reduced the amount of congestion in

2205-555: The city's eco-environment. Instead of using the restoration as an instrument of urban development the environmental organizations have called for a gradual long-term ecological and historical recovery of the entire Cheonggyecheon stream basin and its ecological system. The cost of managing Cheonggyecheon has been rising every year. From October 2005 to the end of 2016, maintenance and management cost of Cheonggyecheon totalled ₩85.7 billion, which averaged out to ₩7.1 billion per year. The Cheonggyecheon Restoration Project has received in 2010

2268-406: The city. The stream was covered up with concrete over 20 years starting in 1958, and a 5.6 km-long (3.5 mi), 16 m-wide (52 ft) elevated highway was completed in 1976. The area became an example of successful industrialization and modernization of South Korea. In July 2003, Mayor of Seoul Lee Myung-bak , initiated a project to remove the elevated highway and restore the stream. It

2331-452: The energy is the sum of an arithmetic progression , and using the formula for the sum of an arithmetic progression, one can show that E ( Z ) ≤ T ( Z ) ≤ 2 E ( Z ) {\displaystyle E(Z)\leq T(Z)\leq 2E(Z)} . If Z o {\displaystyle Z_{o}} is the socially-optimal traffic flow and Z e {\displaystyle Z_{e}}

2394-416: The energy of the graph. If no driver has a best response, the graph is at equilibrium. Since the energy of the graph strictly decreases with each step, the best response dynamics algorithm must eventually halt. If the travel time functions are linear, that is L e ( x ) = a e x + b e {\displaystyle L_{e}(x)=a_{e}x+b_{e}} for some

2457-495: The first refurbishment project to construct a drainage system during the Joseon period. The work, which included dredging and bolstering the banks of the stream and building bridges, was carried out every 2–3 years during this period from the reign of Taejong , the third king of Joseon. King Yeongjo especially undertook the refurbishment work as a national project. Gaecheon was renamed to Cheonggyecheon, its current name, when Korea

2520-482: The hanging system is counter-intuitive, but it does follow from Hooke's law and the way springs work in series and in parallel. Adilson E. Motter and collaborators demonstrated that Braess's paradox outcomes may often occur in biological and ecological systems. Motter suggests removing part of a perturbed network could rescue it. For resource management of endangered species food webs , in which extinction of many species might follow sequentially, selective removal of

2583-446: The institute of planning and development of the Île-de-France , wrote that "Despite initial fears, the removal of main roads does not cause deterioration of traffic conditions beyond the starting adjustments. The traffic transfer are limited and below expectations". He also notes that some private vehicle trips (and related economic activity) are not transferred to public transport and simply disappear ("evaporate"). The same phenomenon

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2646-503: The number of drivers trying the new route reaches 2500, with 1500 still in the Start–B–End route, their time will be 2500 100 + 4000 100 = 65 {\displaystyle {\tfrac {2500}{100}}+{\tfrac {4000}{100}}=65} minutes, which is no improvement over the original route. Meanwhile, those 1500 drivers have been slowed to 45 + 4000 100 = 85 {\displaystyle 45+{\tfrac {4000}{100}}=85} minutes,

2709-622: The original 65. If every driver were to agree not to use the A–B path, or if that route were closed, every driver would benefit by a 15-minute reduction in travel time. If one assumes the travel time for each person driving on an edge to be equal, an equilibrium will always exist. Let L e ( x ) {\displaystyle L_{e}(x)} be the formula for the travel time of each person traveling along edge e {\displaystyle e} when x {\displaystyle x} people take that edge. Suppose there

2772-447: The original route is e 0 , e 1 , … , e n {\displaystyle e_{0},e_{1},\ldots ,e_{n}} while the new route is e 0 ′ , e 1 ′ , … , e m ′ {\displaystyle e'_{0},e'_{1},\ldots ,e'_{m}} . Let E {\displaystyle E} be total energy of

2835-502: The peaks of the Baekdudaegan , particularly Seorak-san and Jiri-san , the caves of Danyang and Hwanseongul , and beaches such as Haeundae and Mallipo . Apart from Jeju island, there are many smaller islands. Excursion ferries are quite common along the south and west coasts and also to Ulleung-do Island, off the east coast. Limited tourism mainly by South Koreans to the Liancourt Rocks (Dokdo) has grown in recent years as

2898-490: The potential for the phenomenon to occur in power transmission networks where power generation is decentralized. In 2012, an international team of researchers from Institut Néel (CNRS, France), INP (France), IEMN (CNRS, France) and UCL (Belgium) published in Physical Review Letters a paper showing that Braess's paradox may occur in mesoscopic electron systems. In particular, they showed that adding

2961-414: The previous mayoral administration of Goh Kun , which feared gentrification of the adjacent areas that housed many shops and small businesses in the machine trades. Indeed, the price of land within 50 meters of the stream has increased by 30-50%, double the rate of property increases in other areas of Seoul. From 2002 to 2003, Cheonggyecheon area also saw a 3.5% increase in the number of businesses, which

3024-526: The purpose of preserving the unique identity of the natural environment and the historic resources in the CBD of Seoul , and to reinforce the surrounding business area with information technology, international affairs and digital industries. The stream was opened to the public in September 2005 and was lauded as a major success in urban renewal and beautification. However, there was considerable opposition from

3087-623: The residents of the area have been considerably reduced; before the restoration, they were more than twice as likely to suffer from respiratory disease as those in other parts of the city. The project sped up traffic around the city when the motorway was removed. It has been cited as a real-life example of Braess's paradox . Budgeted at ₩349 billion, the final cost of the project was over ₩386 billion (approximately US$ 281 million). Some Korean environmental organizations have criticized its high costs and lack of ecological and historical authenticity, calling it purely symbolic and not truly beneficial to

3150-538: The restoration work and coordinated changes in the downtown traffic system based on the research of the Cheonggyecheon Restoration Research Corps. The restoration of two historic bridges, Gwangtonggyo and Supyogyo, was also a contentious issue, as several interest groups voiced opinions on how to restore historical and cultural sites and remains and whether to replace the bridges or not. The Cheonggyecheon restoration project had

3213-411: The road is opened and one driver tries Start–A–B–End. To his surprise he finds that his time is 2000 100 + 2001 100 = 40.01 {\displaystyle {\tfrac {2000}{100}}+{\tfrac {2001}{100}}=40.01} minutes, a saving of almost 25 minutes. Soon, more of the 4000 drivers are trying this new route. The time taken rises from 40.01 and keeps climbing. When

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3276-480: The road, but also on the density of the flow . If every driver takes the path that looks most favourable to them, the resultant running times need not be minimal. Furthermore, it is indicated by an example that an extension of the road network may cause a redistribution of the traffic that results in longer individual running times." Adding extra capacity to a network when the moving entities selfishly choose their route can in some cases reduce overall performance. That

3339-445: The system is at equilibrium. Therefore, each route takes 2000 100 + 45 = 65 {\displaystyle {\tfrac {2000}{100}}+45=65} minutes. If either route took less time, it would not be a Nash equilibrium: a rational driver would switch from the longer route to the shorter route. Now suppose the dashed line A–B is a road with an extremely short travel time of approximately 0 minutes. Suppose that

3402-440: The total energy E {\displaystyle E} will be increased by the total travel time needed to take the new route. Because the new route is shorter than the original route, E {\displaystyle E} must decrease relative to the original configuration, contradicting the assumption that the original set of routes minimized the total energy. Therefore, the choice of routes minimizing total energy

3465-404: The total energy of the traffic graph be the sum of the energies of every edge in the graph. Take a choice of routes that minimizes the total energy. Such a choice must exist because there are finitely many choices of routes. That will be an equilibrium. Assume, for contradiction, this is not the case. Then, there is at least one driver who can switch the route and improve the travel time. Suppose

3528-668: The tourist attractions in Busan. Byeolmaro Observatory, Donggang Photo Museum, Bongraesan Mountain. Hanbando terrain in Soyanggang River South Korea has hosted many international events, including the 1988 Summer Olympics , the 1993 Taejon Expo , the 2002 FIFA World Cup (jointly hosted with Japan), the 2005 APEC conference, the 2010 G-20 Seoul summit , the 2014 Asian Games , and the 2018 Winter Olympics . 0. For entering South Korea, individuals must apply ETA “ K-ETA ” for visiting visa free program for tourists. Braess%27s paradox Braess's paradox

3591-455: The traffic graph, and consider what happens when the route e 0 , e 1 , . . . e n {\displaystyle e_{0},e_{1},...e_{n}} is removed. The energy of each edge e i {\displaystyle e_{i}} will be reduced by L e i ( x e i ) {\displaystyle L_{e_{i}}(x_{e_{i}})} and so

3654-606: Was $ 19,469.9 million. In 2019, the contribution of travel and tourism to the Korean GDP was up 4.2% of the total economy (₩ 81.4 billion). Which accounted for 4.8% of total employment (1.3%). The impact of international visitors accounted for ₩ 26.5 billion (World Travel and Tourism Council). Spending habits include: Visitors arriving to South Korea for tourism by nationality: China has been South Korea's largest tourism source for years. In 2016, visitors from China made up 46.8% of tourists in South Korea. However China imposed

3717-586: Was a major undertaking since the highway had to be removed and years of neglect and development had left the stream nearly dry. 120,000 tons of water were to be pumped in daily from the Han River, its tributaries, and groundwater from subway stations. To address the consequent traffic problem , the Cheonggyecheon Restoration Project Headquarters established traffic flow measures in the downtown section affected by

3780-439: Was about 238.3 million (in 2015), increased by 4.9% compared to 2014 (227.1 million). In 2014, Korean's domestic tourism expenditure was ₩14.4 trillion. Also, Korean overseas tourist numbers have been increasing since 2010. From 2012 to 2014, the number of South Koreans travelling overseas has risen by about 8.2% on average. In 2014, number of Korean overseas tourists was about 16.1 million. And Korean overseas tourism expenditure

3843-529: Was also observed when road closing was not part of an urban project but the consequence of an accident. In 2012 in Rouen , a bridge was destroyed by fire. Over the next two years, other bridges were used more, but the total number of cars crossing bridges was reduced. In 2012, scientists at the Max Planck Institute for Dynamics and Self-Organization demonstrated, through computational modelling ,

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3906-627: Was double the rate of business growth in downtown Seoul. And its number of working people also increased by 0.8%, while that of downtown Seoul decreased by 2.6%. Creating an environment with clean water and natural habitats was the most significant achievement of the project. From 2003 (pre-restoration works) to the end of 2008, biodiversity increased by 639%; the number of plant species increased from 62 to 308, fish species from 4 to 25, bird species from 6 to 36, aquatic invertebrate species from 5 to 53, insect species from 15 to 192, mammals from 2 to 4, and amphibians from 4 to 8. The stream helps to reduce

3969-466: Was under Japanese rule . During this time, financial difficulties disrupted and prevented Japanese forces from covering up the stream despite several attempts to do so. After the Korean War , more people migrated into Seoul to make their living and settled down along the stream in shabby makeshift houses. The accompanying trash, sand, and waste, and deteriorating conditions resulted in an eyesore for

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