A theoretical foundation for the relationship between generalized origin–destination matrix and flow matrix based on ordinal graph trajectories

Abstract

This paper shows the relationship between flow, generalized origin-destination (OD), and alternative route flow from a set of ordinal graph trajectories. In contrast to traffic assignment methods that employ OD matrix to produce flow matrix, we use ordinal trajectory on a network graph as input and produce both the generalized OD matrix and the flow matrix, with the alternative and substitute route flow matrices as additional outputs. By using linear algebra-like operations on matrix sets, the relationship between network utilization (in terms of flow, generalized OD, alternative route flow, and desire line) and network structure (in terms of distance matrix and adjacency matrix) are derived. is to catch the same agent identification at two locations. The two locations should be considered as source and sink along the cordon area set by the study. Because of such difficulties and hassle in the OD survey, many researchers have proposed to estimate the OD matrix on the basis of traffic count in predetermined links. The whole technology to do the OD survey has been based on traffic counting the agents who pass certain predetermined locations of the observers.Recent technology on tracking is catching up, and the product of tracking an agent's position is a set of trajectories. With improvements in technology, it is now possible to collect actual individual trajectories on a network using existing tracking devices such as video [4], GPS [5], and mobile or wireless devices [6]. Advanced methods that combine multiple sensor information have even been developed for more precise automatic location systems [7,8], and this type of information has enabled better analysis of various aspects of transit systems [5,9].In contrast to counting, tracking technologies do not require the observers to be in stationary locations. The agent itself is still associated with an identification number, but the agent can now generate location data at certain predetermined periodic time interval. The tracking devices can be video cameras, RFID devices, GPS systems, and possibly many other new devices. In fact, by using (microscopic) simulation, it is also possible to produce estimated trajectories based on the OD matrix and the network graph.With trajectories coming up as a new product, the obvious question is how to link these trajectories together with the other two existing products-OD matrix and traffic flow. The set of trajectories has not come up in the earlier literature of transportation planning because gathering trajectories itself requires the maturity of the tracking technology (e.g., cell phone with GPS) that, until recently, has not been widely utilized by the public.Even with the recent availability of tracking technology, the standardization has not reached the point where there is agreement to share data among the tracking data holders. The lack of full trajectory data on real traffic, however, does not mean that we cannot produce, at least theoretically, a link between the trajectory as input data and the OD matrix and traffi...

Vehicle trajectory reconstruction using automatic vehicle identification and traffic count data

“…Herrera et al [15] employed mobile data to reconstruct the path flow. To obtain the OD matrix and the traffic volume metrics, Teknomo et al [16] converted trajectory data into a group of linear algebraic equations to represent the relationship between the OD matrix and the path flow. Parry et al [17] integrated discrete trajectory and traffic volume data to perform an analysis of OD estimation based on the maximum likelihood estimation method.…”

“…Based on gravity, we can assume that a vehicle always arrives from an adjacent zone or a traffic analysis zone with a higher volume. Subsequently, the gravity flow model is established as indicated in Equation (16). Let P y t:tþΔtx i ð Þ 4 Þ obey the probability density function given by Equation (16).…”

Vehicle path reconstruction using automatic vehicle identification data: An integrated particle filter and path flow estimator

“…An AVI system can collect information such as vehicle IDs, vehicle passing times and vehicle positions. In previous studies, the collected data from AVI system can be used for origin-destination (OD) matrix estimation (Van Der Zijpp, 1997;Dixon and Rilett, 2002;Zhou and Mahmassani, 2006;Parry and Hazelton, 2012), path flow estimation (Bell et al, 1997;Castillo et al, 2008a;Castillo et al, 2010;Teknomo and Fernandez, 2012), travel time estimation (Dion and Rakha, 2006;Tam and Lam, 2011), traffic flow operation risk assessment (Abdel-Aty et al, 2012;Ahmed and Abdel-Aty, 2013) and vehicle path reconstruction (Feng et al, 2015). These are fundamental issues for urban traffic management.…”

“…To gain more information about vehicle path data, the path flow method can be integrated into the vehicle path reconstruction model, such as Bell et al (1997), Castillo et al (2008a), Chen et al (2009) and Teknomo and Fernandez (2012). The PFE model was developed by Bell and Shield (1995), redefined by Bell et al (1997) and enhanced by Chootinan et al (2005), Chen et al (2009) and Chootinan and Chen (2011).…”