scholarly journals Families of graphs with twin pendent paths and the Braess edge

2021 ◽  
pp. 9-31
Author(s):  
Sooyeong Kim
Keyword(s):  
Random Walk ◽  
Asymptotic Behaviour ◽  
Travel Time ◽  
Undirected Graph ◽  
Cut Vertex ◽  
The Family ◽  
Average Travel Time ◽  
Asymptotic Behaviours

In the context of a random walk on an undirected graph, Kemeny's constant can measure the average travel time for a random walk between two randomly chosen vertices. We are interested in graphs that behave counter-intuitively in regard to Kemeny's constant: in particular, we examine graphs with a cut-vertex at which at least two branches are paths, regarding whether the insertion of a particular edge into a graph results in an increase of Kemeny's constant. We provide several tools for identifying such an edge in a family of graphs and for analysing asymptotic behaviour of the family regarding the tendency to have that edge; and classes of particular graphs are given as examples. Furthermore, asymptotic behaviours of families of trees are described.

On the local behaviour of ladder height distributions

1994 ◽  
Vol 31 (03) ◽  
pp. 816-821 ◽  
Author(s):  
J. Bertoin ◽  
R. A. Doney
Keyword(s):  
Random Walk ◽  
Asymptotic Behaviour ◽  
Mass Function ◽  
Height Distribution ◽  
Local Behaviour ◽  
Ladder Height ◽  
Asymptotic Behaviours

There is a well-known connection between the asymptotic behaviour of the tail of the distribution of the increasing ladder height and the integrated tail of the step distribution of a random walk which either drifts to –∞, or oscillates and whose decreasing ladder height has finite mean. We establish a similar connection in a local sense; this means that in the lattice case we link the asymptotic behaviours of the mass function of the ladder height distribution and of the tail of the step distribution. We deduce the asymptotic behaviour of the mass function of the maximum of the walk, when this is finite, and also treat the non-lattice case.

On the local behaviour of ladder height distributions

1994 ◽  
Vol 31 (3) ◽  
pp. 816-821 ◽  
Author(s):  
J. Bertoin ◽  
R. A. Doney
Keyword(s):  
Random Walk ◽  
Asymptotic Behaviour ◽  
Mass Function ◽  
Height Distribution ◽  
Local Behaviour ◽  
Ladder Height ◽  
Asymptotic Behaviours

There is a well-known connection between the asymptotic behaviour of the tail of the distribution of the increasing ladder height and the integrated tail of the step distribution of a random walk which either drifts to –∞, or oscillates and whose decreasing ladder height has finite mean. We establish a similar connection in a local sense; this means that in the lattice case we link the asymptotic behaviours of the mass function of the ladder height distribution and of the tail of the step distribution. We deduce the asymptotic behaviour of the mass function of the maximum of the walk, when this is finite, and also treat the non-lattice case.

scholarly journals The Effect of Route-choice Strategy on Transit Travel Time Estimates

2019 ◽  
Author(s):  
Nate Wessel ◽  
Steven Farber
Keyword(s):  
Travel Time ◽  
Shortest Path ◽  
Imperfect Information ◽  
Optimal Path ◽  
Shortest Paths ◽  
Route Choice ◽  
Travel Times ◽  
Selection Strategies ◽  
Time Estimates ◽  
Average Travel Time

Estimates of travel time by public transit often rely on the calculation of a shortest-path between two points for a given departure time. Such shortest-paths are time-dependent and not always stable from one moment to the next. Given that actual transit passengers necessarily have imperfect information about the system, their route selection strategies are heuristic and cannot be expected to achieve optimal travel times for all possible departures. Thus an algorithm that returns optimal travel times at all moments will tend to underestimate real travel times all else being equal. While several researchers have noted this issue none have yet measured the extent of the problem. This study observes and measures this effect by contrasting two alternative heuristic routing strategies to a standard shortest-path calculation. The Toronto Transit Commission is used as a case study and we model actual transit operations for the agency over the course of a normal week with archived AVL data transformed into a retrospective GTFS dataset. Travel times are estimated using two alternative route-choice assumptions: 1) habitual selection of the itinerary with the best average travel time and 2) dynamic choice of the next-departing route in a predefined choice set. It is shown that most trips present passengers with a complex choice among competing itineraries and that the choice of itinerary at any given moment of departure may entail substantial travel time risk relative to the optimal outcome. In the context of accessibility modelling, where travel times are typically considered as a distribution, the optimal path method is observed in aggregate to underestimate travel time by about 3-4 minutes at the median and 6-7 minutes at the \nth{90} percentile for a typical trip.

scholarly journals Capturing the Drunk Robber on a Graph

10.37236/3398 ◽  
2014 ◽  
Vol 21 (3) ◽  
Author(s):  
Natasha Komarov ◽  
Peter Winkler
Keyword(s):  
Random Walk ◽  
Undirected Graph ◽  
Simple Random Walk ◽  
Adjacent Vertex ◽  
Expected Time ◽  
Capture Time ◽  
Vertex Graph

We show that the expected time for a smart "cop"' to catch a drunk "robber" on an $n$-vertex graph is at most $n + {\rm o}(n)$. More precisely, let $G$ be a simple, connected, undirected graph with distinguished points $u$ and $v$ among its $n$ vertices. A cop begins at $u$ and a robber at $v$; they move alternately from vertex to adjacent vertex. The robber moves randomly, according to a simple random walk on $G$; the cop sees all and moves as she wishes, with the object of "capturing" the robber—that is, occupying the same vertex—in least expected time. We show that the cop succeeds in expected time no more than $n {+} {\rm o}(n)$. Since there are graphs in which capture time is at least $n {-} o(n)$, this is roughly best possible. We note also that no function of the diameter can be a bound on capture time.

scholarly journals Delay Measurement of Manually Controlled Intersection Using GPS

2014 ◽  
Vol 8 (1) ◽  
pp. 130-135
Author(s):  
S. Nithya ◽  
D. Senthurkumar ◽  
K. .Gunasekaran
Keyword(s):  
Travel Time ◽  
Traffic Control ◽  
Weather Conditions ◽  
Heterogeneous Traffic ◽  
Gps Data ◽  
Peak Period ◽  
Control Delay ◽  
Average Travel Time ◽  
Vehicle Acceleration ◽  
Acceleration And Deceleration

The travel time studies are one of the most important measures used for evaluating the performance of road networks. The Global Positioning System (GPS) is a space-based system that provides position and time information in all weather conditions. GPS data could be used to obtain the values of traffic control delay, vehicle queue, average travel time and vehicle acceleration and deceleration at intersections.The task of estimation of delay becomes complex if it is performed for intersections carrying heterogeneous traffic and that to for over saturated conditions. Most of the urban signalized intersections are manually controlled during peak hours. GPS device fitted in a vehicle was run repeatedly during morning peak period and the period during which vehicles were allowed to cross the intersection was recorded with video graphic camera. The attempt to identify the control delay with the GPS data from the test vehicle while crossing manually operated major intersection is presented in this paper.

scholarly journals THE ACCESSIBILITY OF EUROPEAN REGIONS AND AIRPORT NETWORK

2015 ◽  
Vol 6 (2) ◽  
pp. 87-109 ◽  
Author(s):  
Renato Redondi ◽  
Paolo Malighetti ◽  
Stefano Paleari
Keyword(s):  
Travel Time ◽  
High Speed ◽  
Waiting Times ◽  
Weighted Average ◽  
Air Transport ◽  
High Speed Train ◽  
Territorial Unit ◽  
Average Travel Time ◽  
Direct Flight ◽  
Total Travel Time

The objective of this work is to evaluate the accessibility of European municipalities by air transport. We focus on travels that typically require the use of air transport by computing the quickest paths between any pair of municipalities separated by more than 500 km. The total travel time includes three components: i) travel by car or High Speed Train to reach the origin airport, ii) travel by air from the origin airport to the destination airport, including waiting times when no direct flight is available and iii) travel by car or High Speed Train from the destination airport to the municipality of destination. For each territorial unit, we calculate the population-weighted average travel time to reach any other municipality in Europe.

Freight Vehicle Travel Time Analysis: A Case Study of Birgunj Nagdhunga Corridor

2021 ◽  
Vol 08 (02) ◽  
pp. 1-13
Author(s):  
Abhishek Jha ◽  
Keyword(s):  
Travel Time ◽  
Traffic Congestion ◽  
License Plate ◽  
Monitoring Method ◽  
Factors Affecting ◽  
Average Travel Time ◽  
Major Factors ◽  
Vehicle Travel Time ◽  
Freight Vehicles

This study covers the freight vehicle, which clears the custom clearance process for Kathmandu and transports the same goods to Kathmandu from Birgunj. In this study average travel time for freight vehicles from Birgunj to Nagdhunga has been studied, along with the factors affecting the travel time from Birgunj to Nagdhunga. License plate monitoring method of the freight vehicles was done to find the average travel time and a questionnaire survey was done to identify the factors affecting travel time of the freight vehicle. The travel time from Birgunj to Nagdhunga is different for different types of, vehicle and good. The fastest average travel time is of fixed container of 40 feet size with 23.2 hours and longest average time is for fixed container of 20 feet size with 28.95 hours. The average travel time for non-degradable goods is 26.5 hours and for degradable goods is 22.38 hours. Major factors affecting the travel time are traffic congestion along the route, bad road condition along the route and hilly road with sharp bends, turns and grade.

scholarly journals Disparities in travel times between car and transit: Spatiotemporal patterns in cities

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Yuan Liao ◽  
Jorge Gil ◽  
Rafael H. M. Pereira ◽  
Sonia Yeh ◽  
Vilhelm Verendel
Keyword(s):  
Travel Time ◽  
Travel Demand ◽  
Time Of Day ◽  
Sao Paulo ◽  
São Paulo ◽  
Real World Data ◽  
Car Use ◽  
Real Time Traffic ◽  
Average Travel Time ◽  
Car Travel

AbstractCities worldwide are pursuing policies to reduce car use and prioritise public transit (PT) as a means to tackle congestion, air pollution, and greenhouse gas emissions. The increase of PT ridership is constrained by many aspects; among them, travel time and the built environment are considered the most critical factors in the choice of travel mode. We propose a data fusion framework including real-time traffic data, transit data, and travel demand estimated using Twitter data to compare the travel time by car and PT in four cities (São Paulo, Brazil; Stockholm, Sweden; Sydney, Australia; and Amsterdam, the Netherlands) at high spatial and temporal resolutions. We use real-world data to make realistic estimates of travel time by car and by PT and compare their performance by time of day and by travel distance across cities. Our results suggest that using PT takes on average 1.4–2.6 times longer than driving a car. The share of area where travel time favours PT over car use is very small: 0.62% (0.65%), 0.44% (0.48%), 1.10% (1.22%) and 1.16% (1.19%) for the daily average (and during peak hours) for São Paulo, Sydney, Stockholm, and Amsterdam, respectively. The travel time disparity, as quantified by the travel time ratio $$R$$R (PT travel time divided by the car travel time), varies widely during an average weekday, by location and time of day. A systematic comparison between these two modes shows that the average travel time disparity is surprisingly similar across cities: $$R < 1$$R<1 for travel distances less than 3 km, then increases rapidly but quickly stabilises at around 2. This study contributes to providing a more realistic performance evaluation that helps future studies further explore what city characteristics as well as urban and transport policies make public transport more attractive, and to create a more sustainable future for cities.

scholarly journals Impacts of the Qinghai–Tibet Railway on Accessibility and Economic Linkage of the Third Pole

2018 ◽  
Vol 10 (11) ◽  
pp. 3982 ◽  
Author(s):  
Shicheng Li ◽  
Jian Gong ◽  
Qinghai Deng ◽  
Tianyu Zhou
Keyword(s):  
Sustainable Development ◽  
Travel Time ◽  
Eastern China ◽  
Weighted Average ◽  
Spatial Disparity ◽  
The Sustainable Development ◽  
Capital Cities ◽  
The Third ◽  
Average Travel Time ◽  
Economic Linkages

Constructing the Qinghai–Tibet Railway (QTR) was a landmark project and was beneficial to the sustainable development of the Third Pole. To understand the sustainable development of remote regions by the provision of railway, we studied the QTR’s impact on accessibilities and economic linkages for four cities in the Third Pole, Xining, Golmud, Nagqu, and Lhasa, and between these four cities and 29 capital cities in mid-eastern China. First, employing average shortest travel time (ASTT) and weighted average travel time (WATT) as indicators, we calculated the railway-based accessibilities for June 2006 and January 2013. Then, using a gravity model, railway-based economic linkages were determined. The results demonstrate that: (i) ASTT for Xining–Golmud decreased by 4.14 h from June 2006 to January 2013. Both ASTT and WATT indicated that the accessibilities of the four cities and between these four cities and 29 capital cities in mid-eastern China improved significantly, and the spatial disparity in accessibility for the four cities decreased, which increased the balance and sustainability of the transportation system; (ii) the average contribution rate of the QTR to improving economic linkages for six routes among the four cities was 25.29%, with the Xining–Nagqu and Nagqu–Lhasa linkages improving most significantly; (iii) the QTR strengthened economic linkages between the four cities and mid-eastern cities. Because of the QTR, the economic linkages between the four cities and 29 capital cities increased 27.58% on average. The spatial disparity in interurban economic linkages also decreased. Transporting products from Tibet should be promoted to strengthen the sustainability of economic growth.

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