Time-dependent Origin-destination Research Articles

Day-to-Day Evolution of Network Flows Under Departure Time Dynamics in Commuter Decisions

Day-to-day dynamics in an urban traffic network induced by departure time dynamics in commuter decisions are investigated. This investigation relaxes some key restrictions about fixed departure time and equilibrium assumptions to analyze the stability and performance of urban traffic networks over a multiple day planning horizon. A simulation-based framework is developed to analyze day-to-day dynamics by integrating an empirically calibrated model of dynamic departure time decisions with a dynamic network assignment model. Computational experiments are used to investigate the effect of the following experimental factors: recurrent network congestion level, time-dependent loading profile, and users’ sensitivity to commute experience and trip-time volatility on network performance and reliability. The findings provide evidence of considerable day-to-day variations and stochasticity in network flows and performance, even under the assumption of fixed routes and in the absence of information. The results indicate that ( a) the network performance under departure time dynamics can deviate significantly from equilibrium; ( b) the departure time adjustment process is remarkably stable and reaches stationarity, although the departure time choices do not appear to be at equilibrium; ( c) departure time dynamics introduce significant volatility in trip times from day to day; and ( d) increasing the sensitivity of users to commute and network performance attributes (schedule delay, trip-time variability) can lead to more stable system behavior and reliability. These results have important implications for estimation of time-dependent origin–destination matrices, dynamic network analysis, and effective congestion management strategies.

The Access-Control Problem on Capacitated FIFO Networks With Unique O-D Paths is Hard

This paper is concerned with the performance of multicommodity capacitated networks in a deterministic but time-dependent environment. For a given time-dependent origin-destination table, this paper asks if it is easy to find a way of regulating the input flows into the network to avoid queues from growing internally, i.e., to avoid capacity violations. Problems of this type are conventionally approached in the traffic/transportation field with variational methods such as control theory (if time is continuous) and with mathematical programming (if time is discrete). However, these approaches can only be expected to work well ifthe set off easible solutions is convex. Unfortunately, it is found in this paper that this is not the case. It is shown that continuous-time versions of the problem satisfying the smoothness conditions of control theory can have a finite but very large number off easible solutions. The same happens for the discrete time case. These difficulties arise even with the simplest versions of the problem (with unique origin-destination paths, perfect information, and deterministic travel times). The paper also shows that the continuous-time feasibility problem is NP-hard, and that if we restrict our attention to (practical) problems whose data can be described with a finite number ofbits (e.g., in discrete time), then the problem is NP-complete. These results are established by showing that the problem instances of interest can be related to the Directed Hamiltonian Path problem by a polynomial transformation.

The Access-Control Problem on Capacitated FIFO Networks With Unique O-D Paths is Hard

This paper is concerned with the performance of multicommodity capacitated networks in a deterministic but time-dependent environment. For a given time-dependent origin-destination table, this pape...

Estimation and Prediction of Time-Dependent Origin-Destination Flows with a Stochastic Mapping to Path Flows and Link Flows

This paper presents a new suite of models for the estimation and prediction of time-dependent Origin-Destination (O-D) matrices. The key contribution of the proposed approach is the explicit modeling and estimation of the dynamic mapping (the assignment matrix) between time-dependent O-D flows and link volumes. The assignment matrix depends upon underlying travel times and route choice fractions in the network. Since the travel times and route choice fractions are not known with certainty, the assignment matrix is prone to error. The proposed approach provides a systematic way of modeling this uncertainty to address both the offline and real-time versions of the O-D estimation/prediction problem. Preliminary empirical results indicate that generalized models with a stochastic assignment matrix could provide better results compared to conventional models with a fixed matrix.

Access control on networks with unique origin–destination paths

This paper presents improved time-dependent control strategies for small freeway networks with bottlenecks and unique origin–destination paths. It is assumed that there are no spill-overs from any of the freeway exits so that freeway queues and delays can be completely avoided by regulating access to the system so as to maintain bottleneck flows strictly below capacity. It is also assumed that the time-dependent origin–destination table and the time-dependent bottleneck capacities are known, although not always a priori. The proposed control strategies attempt to minimize the total delay (including both system delay and access delay) while avoiding queues inside the system. The problem is formulated as a constrained calculus of variations exercise that can be cast in the conventional form of optimal control theory and can also be discretized as a mathematical program. Although the first-in-first-out (FIFO) requirement for the access queues introduces undesirable non-linearities, exact solutions for four important special cases can be obtained easily. More specifically, for networks with (1) a single origin or (2) a single bottleneck, a myopic strategy which requires the solution of a sequence of simple linear programs is optimal. For networks with (3) a single destination the non-linearities disappear and the problem becomes a large-scale linear program. This is also true for general networks if (4) the fractional distribution of flow across destinations for every origin is independent of time. A greedy heuristic algorithm is proposed for the general case. It has been programmed for a personal computer running Windows. The algorithm is non-anticipative in that it regulates access at the current time without using future information. As a result, it is computationally efficient and can be bolstered with dynamically-updated information. Globally optimal for cases (1) and (2), the heuristic has been developed with slow-varying O–D tables in mind. Significant improvements will likely require anticipatory information. An illustrative example is given.

Alternative Approaches for Real-Time Estimation and Prediction of Time-Dependent Origin–Destination Flows

This paper examines two different approaches for real-time estimation/prediction of time-dependent Origin–Destination (O–D) flows. Both approaches lend themselves to formulation as state-space models. The first approach is an extension of previous work by the authors. The key idea in this approach is to define the state-vector in terms of deviations in O–D flows instead of the O–D flows themselves. We demonstrate that approximations to this model make the real-time estimation process computationally more tractable with little deterioration in quality of estimates. In the second approach, the state vector is defined in terms of deviations of departure rates from each origin and the shares headed to each destination. This approach attempts to capture the differential variation of departure rates and shares over time. Performance of the proposed models is evaluated using actual traffic data from different sources. Preliminary results indicate that the filtering procedure is robust and that, compared to the original model, a formulation based on departure rates and shares yields better predictions with some loss of accuracy in filtered estimates.

Estimation of time-dependent origin–destination matrices for transit networks

In this paper, the estimation of time-dependent origin–destination (O–D) matrices for transit network based on observed passenger counts is given. The dynamic assignment framework is based on a schedule-based transit network model, which can help determine the time-dependent least cost paths between all O–D pairs, and for each of them the clock arrival times at the end nodes of all observed links (if any) in the transit network. An entropy-based approach is then employed to estimate the time-dependent O–D matrices based on the observed passenger counts at those observed links in the network. An efficient sparse algorithm is also proposed to solve the resulting mathematical programming problem. The estimation methodology is tested in a transit network from the Mass Transit Railway (MTR) system in Hong Kong which is one of the busiest railway systems in the world. Both cases with and without prior information of the O–D matrices are considered for this network. The predicted matrices are then compared with the true matrices obtained from a sophisticated electronic fare collection system of MTR. Good agreement between predicted and observed matrices are found.

Estimation of a Time Dependent OD Matrix from Traffic Counts Using Dynamic Traffic Simulation

This study proposes and develops an OD (Origin-Destination) estimating method from traffic counts using dynamic traffic simulation. The proposed method intends to get an OD matrix which is required by dynamic traffic simulation so as to reproduce observed counts. After development, we evaluate how accurately it can estimatean OD matrixusing actual road network. In result, we confirm that the method cannot estimate exact OD matrix because it intends to get an OD matrix by which simulation can reproduce observed counts. However, we understand what a extent (a) accuracy of simulation performance, (b) number of observed counts and (c) other information effect the accuracy of estimated OD.

A Priori Stochastic Dynamic Traffic Assignment for On-Line Operations Under Information Systems

Existing dynamic traffic assignment (DTA) formulations predominantly assume the time-dependent origin-destination (O-D) trip matrix to be known a priori for the planning horizon or require robust a priori O-D predictions. Such assumptions are unduly optimistic for general networks in an on-line operational framework. Also, the associated solution approaches are computationally intensive in a centralized architecture. To address these key on-line issues, a stochastic DTA approach is proposed in which O-D desires are explicitly recognized as random variables. To ensure that the associated solution methodology is feasible for on-line implementation, a combination of on-line and off-line strategies is proposed. In this paper, an a priori optimization strategy is used to address the off-line problem. Experimental results indicate that the off-line solution serves as an effective and robust initial on-line solution.

Solving an Instantaneous Dynamic User-Optimal Route Choice Model

Dynamic models of the behavior of automobile drivers in choosing routes through urban transportation networks are required for the design and operation of intelligent transportation systems generally, and traveler information systems in particular. In this paper, drivers' route choice behavior based on current, or instantaneous, information on network conditions is described using an optimal control theory formulation. The time-dependent origin-destination vehicle trip pattern is assumed to be known. The instantaneous dynamic user-optimal route choice problem is to allocate vehicle flows to the current minimal-cost routes, defined as the routes that minimize the route travel cost between each decision node (any node on the route including the origin) and the destination node based on the currently prevailing travel times. The continuous time formulation of the problem is transformed into a discrete time nonlinear programming (NLP) formulation. Each of a sequence of NLPs is then solved by an algorithm based on the Frank-Wolfe technique. In this sequence, approximate link travel times are updated iteratively in order to represent flow propagation over routes. Computational results from applying the algorithm to two test networks conclude the paper.

A game theoretic/network equilibrium solution approach for the railroad freight car management problem

The paper presents the development and solution procedures of a mathematical model of the management of a fleet of cars shared by autonomous profit maximizing managers faced with time-varying demands requiring shared service responsibility. Motivation for the model development arises from the freight car management problem, in which many railroads independently manage an interchangeable fleet of cars that serve customers with time-dependent origin-destination patterns; this often requires the cooperative service of more than one railroad. The problem is formulated as an N-person, noncooperative game played on a temporal-spatial network. An iterative sequential procedure is developed for which car management decisions for each railroad over a specified time horizon are based on the previously calculated optimized decisions of car management decisions for all other railroads. Several realistic test case problems are reported that exhibit rapid convergence to an equilibrium solution. It is proposed that this modeling procedure be used as a basis for evaluating (and possibly generating optimal) interrailroad agreements for the exchange of empty freight cars.