Periodic Timetabling with Integrated Routing: Toward Applicable Approaches

2020 ◽  
Vol 54 (6) ◽  
pp. 1714-1731
Author(s):  
Philine Schiewe ◽  
Anita Schöbel
Keyword(s):  
Real World ◽  
Public Transportation ◽  
Computation Time ◽  
Upper And Lower Bounds ◽  
Problem Size ◽  
Classic Problem ◽  
Passenger Travel ◽  
Periodic Timetabling ◽  
Public Transportation Planning ◽  
Passenger Routing

Periodic timetabling is an important, yet computationally challenging, problem in public transportation planning. The usual objective when designing a timetable is to minimize passenger travel time. However, in most approaches, it is ignored that the routes of the passengers depend on the timetable, so handling their routing separately leads to timetables that are suboptimal for the passengers. This has recently been recognized, but integrating the passenger routing in the optimization is computationally even harder than solving the classic periodic timetabling problem. In our paper, we develop an exact preprocessing method for reducing the problem size and a heuristic reduction approach in which only a subset of the passengers is considered. It provides upper and lower bounds on the objective value, such that it can be adjusted with respect to quality and computation time. Together, we receive an approach that is applicable for real-world problems. We experimentally evaluate the performance of the approach on a benchmark example and on three close-to-real-world instances. Furthermore, we prove that the ratio between the classic problem without routing and the problem with integrated routing is bounded under weak and realistic assumptions.

Circles on lattices and Hadamard matrices

2019 ◽  
pp. 2-9 ◽  
Author(s):  
N. A. Balonin ◽  
M. B. Sergeev ◽  
J. Seberry ◽  
O. I. Sinitsyna
Keyword(s):  
Hadamard Matrices ◽  
Lattice Points ◽  
Practical Significance ◽  
Upper And Lower Bounds ◽  
Problem Size ◽  
Orthogonal Matrices ◽  
Video Information ◽  
Scientific Schools ◽  
Gauss Theorem ◽  
Triangular Numbers

Introduction: The Hadamard conjecture about the existence of Hadamard matrices in all orders multiple of 4, and the Gauss problem about the number of points in a circle are among the most important turning points in the development of mathematics. They both stimulated the development of scientific schools around the world with an immense amount of works. There are substantiations that these scientific problems are deeply connected. The number of Gaussian points (Z3 lattice points) on a spheroid, cone, paraboloid or parabola, along with their location, determines the number and types of Hadamard matrices.Purpose: Specification of the upper and lower bounds for the number of Gaussian points (with odd coordinates) on a spheroid depending on the problem size, in order to specify the Gauss theorem (about the solvability of quadratic problems in triangular numbers by projections onto the Liouville plane) with estimates for the case of Hadamard matrices. Methods: The authors, in addition to their previous ideas about proving the Hadamard conjecture on the base of a one-to-one correspondence between orthogonal matrices and Gaussian points, propose one more way, using the properties of generalized circles on Z3 .Results: It is proved that for a spheroid, the lower bound of all Gaussian points with odd coordinates is equal to the equator radius R, the upper limit of the points located above the equator is equal to the length of this equator L=2πR, and the total number of points is limited to 2L. Due to the spheroid symmetry in the sector with positive coordinates (octant), this gives the values of R/8 and L/4. Thus, the number of Gaussian points with odd coordinates does not exceed the border perimeter and is no less than the relative share of the sector in the total volume of the figure.Practical significance: Hadamard matrices associated with lattice points have a direct practical significance for noise-resistant coding, compression and masking of video information.

scholarly journals A Lower Bound for the Query Phase of Contraction Hierarchies and Hub Labels and a Provably Optimal Instance-Based Schema

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 164
Author(s):  
Tobias Rupp ◽  
Stefan Funke
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Real World ◽  
Road Network ◽  
Upper And Lower Bounds ◽  
Bounded Degree ◽  
Shortest Path Routing ◽  
Graph Classes ◽  
Speed Up ◽  
To Come

We prove a Ω(n) lower bound on the query time for contraction hierarchies (CH) as well as hub labels, two popular speed-up techniques for shortest path routing. Our construction is based on a graph family not too far from subgraphs that occur in real-world road networks, in particular, it is planar and has a bounded degree. Additionally, we borrow ideas from our lower bound proof to come up with instance-based lower bounds for concrete road network instances of moderate size, reaching up to 96% of an upper bound given by a constructed CH. For a variant of our instance-based schema applied to some special graph classes, we can even show matching upper and lower bounds.

scholarly journals Exploring Equity in Public Transportation Planning Using Smart Card Data

Sensors ◽  
2021 ◽  
Vol 21 (9) ◽  
pp. 3039
Author(s):  
Kiarash Ghasemlou ◽  
Murat Ergun ◽  
Nima Dadashzadeh
Keyword(s):  
Smart Card ◽  
Public Transportation ◽  
Transportation Planning ◽  
Demand Characteristic ◽  
Monthly Data ◽  
Smart Card Data ◽  
Planning Methods ◽  
Public Transportation Planning ◽  
Daily Travel ◽  
A Share

Existing public transport (PT) planning methods use a trip-based approach, rather than a user-based approach, leading to neglecting equity. In other words, the impacts of regular users—i.e., users with higher trip rates—are overrepresented during analysis and modelling because of higher trip rates. In contrast to the existing studies, this study aims to show the actual demand characteristic and users’ share are different in daily and monthly data. For this, 1-month of smart card data from the Kocaeli, Turkey, was evaluated by means of specific variables, such as boarding frequency, cardholder types, and the number of users, as well as a breakdown of the number of days traveled by each user set. Results show that the proportion of regular PT users to total users in 1 workday, is higher than the monthly proportion of regular PT users to total users. Accordingly, users who have 16–21 days boarding frequency are 16% of the total users, and yet they have been overrepresented by 39% in the 1-day analysis. Moreover, users who have 1–6 days boarding frequency, have a share of 66% in the 1-month dataset and are underrepresented with a share of 22% in the 1-day analysis. Results indicated that the daily travel data without information related to the day-to-day frequency of trips and PT use caused incorrect estimation of real PT demand. Moreover, user-based analyzing approach over a month prepares the more realistic basis for transportation planning, design, and prioritization of transport investments.

A UNIFIED ALGORITHM FOR THE ESTIMATION AND SCHEDULING OF DATA FLOW GRAPHS

1996 ◽  
Vol 06 (03) ◽  
pp. 287-318 ◽  
Author(s):  
YUAN HU ◽  
BRADLEY S. CARLSON
Keyword(s):  
Lower Bound ◽  
Data Flow ◽  
Optimal Algorithm ◽  
Solution Space ◽  
Computation Time ◽  
Upper And Lower Bounds ◽  
Unified Algorithm ◽  
Data Flow Graphs ◽  
Flow Graphs ◽  
Sharp Lower Bound

A unified algorithm is presented to solve the problem of estimation and scheduling for performance constrained data flow graphs. The algorithm achieves superior results by first computing a lower bound on the number of functional units required to satisfy the performance constraint T, and then scheduling the operations into the best control steps using the lower bound algorithm. The lower bound not only greatly reduces the size of the solution space, but also provides a means to measure the proximity of the final solution to an optimal one. Our algorithm is the first one to use a sharp lower bound estimation technique to direct scheduling. In addition, our unified algorithm can easily be incorporated into a branch-and-bound algorithm to solve the scheduling problem optimally. Since our algorithm computes a sharp lower bound, the computation time of an optimal algorithm can be greatly reduced. Experiments indicate that our scheduling algorithm can produce results very close to the lower bound. For all of the test cases the difference between our upper and lower bounds is not greater than one.

The generalized sousveillance society

2010 ◽  
Vol 49 (3) ◽  
pp. 489-507 ◽  
Author(s):  
Jean-Gabriel Ganascia
Keyword(s):  
Present State ◽  
Real World ◽  
Public Transportation ◽  
Virtual World ◽  
Information Technologies ◽  
The Internet ◽  
Public And Private ◽  
The World ◽  
Modern Information ◽  
Flow Of Information

This article is based on the notion of ‘sousveillance’, which was invented by Steve Mann to describe the present state of modern technological societies where anybody may take photos or videos of any person or event, and then diffuse the information freely all over the world. The article shows how sousveillance can be generalized both to the real world and to the virtual world of the Infosphere using modern information technologies. As a consequence, the separation between public and private spheres tends to disappear. We believe that generalized sousveillance may transform the overall society, e.g. modern public transportation like the Paris subway might have to change the way it disseminates information due to the impossibility of managing the flow of information coming from its infrastructures. To attempt to elucidate a society based on generalized sousveillance, the article introduces the notion of the ‘Catopticon’, derived from Bentham’s Panopticon: while the architecture of the Panopticon was designed to facilitate surveillance by prohibiting communication and by installing surveyors in a watchtower, the architecture of the ‘Catopticon’ allows everybody to communicate with everybody and removes surveyors from the watchtower. The article goes on to explore the opportunities the Catopticon might offer if extended to the whole planet. It also shows the limitations of the extended Catopticon; some are extrinsic: they consist of various resistances which restrict access to the Internet; others are intrinsic: for instance, we can exchange simultaneously only with a few people, while we may have millions of contacts. As a consequence, the various new ‘regimes of distinction’ mentioned above play a key role in modern societies.

Public Transportation Dynamic Guidance Model and Algorithm

2011 ◽  
Vol 368-373 ◽  
pp. 3113-3116
Author(s):  
Liang Zou ◽  
Ling Xiang Zhu
Keyword(s):  
Travel Time ◽  
Public Transportation ◽  
Computation Time ◽  
A Algorithm ◽  
Travel Costs ◽  
Computational Performance ◽  
Key Factor ◽  
Straight Line Distance ◽  
Average Computation Time ◽  
Guidance Model

The current public transportation guidance models are static and based on travel times, travel distance and travel costs. However latest survey shows that travel time has become the key factor for passenger travel route selection in big cities. Dynamic public transportation guidance model based on travel time and waiting time was proposed and the effectiveness of this model is proved in this paper. To solve this model efficiently, this paper proposed the application of A* algorithm in dealing with this models using straight line distance between two bus stops in electronic maps as Priori knowledge. Finally, the developed model and algorithm were implemented with 50 random OD pairs based on Guangzhou’s public transportation networks (containing 471 public transportation routes and 1040 stops) and Guangzhou’s electronic map. Their computational performance was analyzed experimentally. The result indicates that the models and algorithm proposed in this paper are very efficient. The average computation time of the algorithm proposed in this paper is 0.154s and the average number of nodes selected of this algorithm is 194.2.

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