Time-expanded Model Research Articles

Innovative GTFS Data Application for Transit Network Analysis Using a Graph-Oriented Method

Public transit networks are constantly evolving in the face of frequent economic and social challenges. There exists a large knowledge base on travel demand; however, there is a shortage of information on travel supply and networks. To our knowledge, no analysis tool can, at this point, systematically characterize a network and observe changes over time in a structured and automated manner. This paper addresses this issue and proposes a graph-oriented method for developing an analysis tool that will characterize a single network and then provide the necessary means to compare two distinct networks. A time-expanded model was applied to import General Transit Feed Specification (GTFS) data into a graph database. With built-in algorithms, shortest paths were computed and indicators were derived from these paths. A small case study demonstrates the applicability of the method. This approach still needs to be optimized to process networks that are more complex.

Traffic Signal Optimization: Combining Static and Dynamic Models

In this paper, we present a cyclically time-expanded network model for simultaneous optimization of traffic assignment and traffic signal parameters, in particular, offsets, split times, and phase orders. Since travel times are of great importance for developing realistic solutions for traffic assignment and traffic signal coordination in urban road networks, we perform an extensive analysis of the model. We give an example showing that a linear time-expanded model can reproduce realistic nonconvex travel times especially for use with traffic signals and we verify this by simulation. Furthermore, we show how exact mathematical programming techniques—namely, mixed-integer linear programming—can be used for optimizing the control of traffic signals. We provide computational results for real-world instances and demonstrate the capabilities of the cyclically time-expanded model by simulation results obtained with state-of-the-art traffic simulation tools.

Engineering graph-based models for dynamic timetable information systems

In the last years we have witnessed remarkable progress in providing efficient algorithmic solutions to the problem of computing best journeys (or routes) in schedule-based public transportation systems. We have now models to represent timetables that allow us to answer queries for optimal journeys in a few milliseconds, also at a very large scale. Such models can be classified into two types: those representing the timetable as an array, and those representing it as a graph. Array-based models have been shown to be very effective in terms of query time, while graph-based ones usually answer queries by computing shortest paths, and hence they are suitable to be combined with the speed-up techniques developed for road networks.In this paper, we study the behavior of graph-based models in the prominent case of dynamic scenarios, i.e., when delays might occur to the original timetable. In particular, we make the following contributions. First, we consider the graph-based reduced time-expanded model and give a simplified and optimized routine for handling delays, and a re-engineered and fine-tuned query algorithm. Second, we propose a new graph-based model, namely the dynamic timetable model, natively tailored to efficiently incorporate dynamic updates, along with a query algorithm and a routine for handling delays. Third, we show how to adapt the ALT algorithm to such graph-based models. We have chosen this speed-up technique since it supports dynamic changes, and a careful implementation of it can significantly boost its performance. Finally, we provide an experimental study to assess the effectiveness of all proposed models and algorithms, and to compare them with the array-based state of the art solution for the dynamic case. We evaluate both new and existing approaches by implementing and testing them on real-world timetables subject to synthetic delays.Our experimental results show that: (i) the dynamic timetable model is the best model for handling delays; (ii) graph-based models are competitive to array-based models with respect to query time in the dynamic case; (iii) the dynamic timetable model compares favorably with both the original and the reduced time-expanded model regarding space; (iv) combining the graph-based models with speed-up techniques designed for road networks, such as ALT, is a very promising approach.

Cockroach Swarm Optimization Algorithm for Travel Planning

In transport planning, one should allow passengers to travel through the complicated transportation scheme with efficient use of different modes of transport. In this paper, we propose the use of a cockroach swarm optimization algorithm for determining paths with the shortest travel time. In our approach, this algorithm has been modified to work with the time-expanded model. Therefore, we present how the algorithm has to be adapted to this model, including correctly creating solutions and defining steps and movement in the search space. By introducing the proposed modifications, we are able to solve journey planning. The results have shown that the performance of our approach, in terms of converging to the best solutions, is satisfactory. Moreover, we have compared our results with Dijkstra’s algorithm and a particle swarm optimization algorithm.

Solving the K-shortest paths problem in timetable-based public transportation systems

Finding the K-shortest paths in timetable-based public transportation systems is an important problem in practice. It has three typical variants: the K-earliest arrival problem (K-EAP), the K-shortest travel time problem (K-STTP), and the K-minimum number of transfers problem (K-MNTP). In this article we show that these problems can be solved efficiently by first modeling the timetable information with the time-expanded approach, then applying the Martins and Santos (MS) algorithm. Then we model the timetable information with the time-dependent approach and propose a modified version of the MS algorithm for solving the K-EAP. Experimental results on real-world data show that for K smaller than 100, which is enough for most applications, the execution times of the MS algorithm for the problems in the time-expanded model are less than 100 ms on a server with a 1.86-GHz central processing unit (CPU) and 4 GB of memory. For solving the K-EAP the modified MS algorithm in the time-dependent model is even more efficient (about three times faster for K ≤ 100) than the original algorithm in the time-expanded model. Our results imply the great potential of the MS algorithms in practical transportation service systems.