Wenyi Zhang

Microscopic driving theory with oscillatory congested states: Model and empirical verification

The essential distinction between the Fundamental Diagram Approach (FDA) and Kerner’s three-phase theory (KTPT) is the existence of a unique gap–speed (or flow–density) relationship in the former class. In order to verify this relationship, empirical data are analyzed with the following findings: (1) linear relationship between the actual space gap and speed can be identified when the speed difference between vehicles approximates zero; (2) vehicles accelerate or decelerate around the desired space gap most of the time. To explain these phenomena, we propose that, in congested traffic flow, the space gap between two vehicles will oscillate around the desired space gap in the deterministic limit. This assumption is formulated in terms of a cellular automaton. In contrast to FDA and KTPT, the new model does not have any congested steady-state solution. Simulations under periodic and open boundary conditions reproduce the empirical findings of KTPT. Calibrating and validating the model to detector data produces results that are better than that of previous studies.

A Nonlinear Pairwise Swapping Dynamics to Model the Selfish Rerouting Evolutionary Game

In this paper, a nonlinear revision protocol is proposed and embedded into the traffic evolution equation of the classical proportional-switch adjustment process (PAP), developing the present nonlinear pairwise swapping dynamics (NPSD) to describe the selfish rerouting evolutionary game. It is demonstrated that i) NPSD and PAP require the same amount of network information acquisition in the route-swaps, ii) NPSD is able to prevent the over-swapping deficiency under a plausible behavior description; iii) NPSD can maintain the solution invariance, which makes the trial and error process to identify a feasible step-length in a NPSD-based swapping algorithm is unnecessary, and iv) NPSD is a rational behavior swapping process and the continuous-time NPSD is globally convergent. Using the day-to-day NPSD, a numerical example is conducted to explore the effects of the reaction sensitivity on traffic evolution and characterize the convergence of discrete-time NPSD.

Alpha-reliable combined mean traffic equilibrium model with stochastic travel times

Based on the reliability budget and percentile travel time (PTT) concept, a new travel time index named combined mean travel time (CMTT) under stochastic traffic network was proposed. CMTT here was defined as the convex combination of the conditional expectations of PTT-below and PTT-excess travel times. The former was designed as a risk-optimistic travel time index, and the latter was a risk-pessimistic one. Hence, CMTT was able to describe various routing risk-attitudes. The central idea of CMTT was comprehensively illustrated and the difference among the existing travel time indices was analyzed. The Wardropian combined mean traffic equilibrium (CMTE) model was formulated as a variational inequality and solved via an alternating direction algorithm nesting extra-gradient projection process. Some mathematical properties of CMTT and CMTE model were rigorously proved. Finally, a numerical example was performed to characterize the CMTE network. It is founded that that risk-pessimism is of more benefit to a modest (or low) congestion and risk network, however, it changes to be risk-optimism for a high congestion and risk network.

A Feeder-Bus Dispatch Planning Model for Emergency Evacuation in Urban Rail Transit Corridors.

The mobility of modern metropolises strongly relies on urban rail transit (URT) systems, and such a heavy dependence causes that even minor service interruptions would make the URT systems unsustainable. This study aims at optimally dispatching the ground feeder-bus to coordinate with the urban rails’ operation for eliminating the effect of unexpected service interruptions in URT corridors. A feeder-bus dispatch planning model was proposed for the collaborative optimization of URT and feeder-bus cooperation under emergency situations and minimizing the total evacuation cost of the feeder-buses. To solve the model, a concept of dummy feeder-bus system is proposed to transform the non-linear model into traditional linear programming (ILP) model, i.e., traditional transportation problem. The case study of Line #2 of Nanjing URT in China was adopted to illustrate the model application and sensitivity analyses of the key variables. The modeling results show that as the evacuation time window increases, the total evacuation cost as well as the number of dispatched feeder-buses decrease, and the dispatched feeder-buses need operate for more times along the feeder-bus line. The number of dispatched feeder-buses does not show an obvious change with the increase of parking spot capacity and time window, indicating that simply increasing the parking spot capacity would cause huge waste for the emergent bus utilization. When the unbalanced evacuation demand exists between stations, the more feeder-buses are needed. The method of this study will contribute to improving transportation emergency management and resource allocation for URT systems.

Nonlinear Min-Cost-Pursued Route-Swapping Dynamic System

This study proposes a nonlinear min-cost-pursued swapping dynamic (NMSD) system to model the evolution of selfish routing games on traffic network where travelers only swap from previous costly routes to the least costly ones. NMSD is a rational behavior adjustment process with stationary link flow pattern being the Wardrop user equilibrium. NMSD is able to prevent two behavioral deficiencies suffered by the existing min-cost-oriented models and keep solution invariance. NMSD relaxes the homogeneous user assumption, and the continuous-time NMSD (CNMSD) and discrete-time NMSD (DNMSD) share the same revision protocol. Moreover, CNMSD is Lyapunov-stable. Two numerical examples are conducted. The first one is designed to characterize the NMSD-conducted network traffic evolution and test the stability of day-to-day NMSD. The second one aims to explore the impacts of network scale on the stability of route-swaps conducted by pairwise and min-cost-pursed swapping behaviors.

Modeling Traveler's Day-to-Day Rerouting Behavior considering Multiday Experiences

This paper proposes a multiday nonlinear pairwise swapping dynamic (MNPSD) model to describe travelers day-to-day selfish rerouting behaviors. By introducing a perceived route cost measure, formulated as the descending weighted average of the actual route costs experienced in the past several days, MNPSD can capture various experiential perception levels. It is proved that both stationary path flow pattern and stationary link flow pattern of MNPSD are equivalent to Wardrop user equilibrium. Given that the perceived weight decreases exponentially, numerical sensitivity analyses are executed to explore the effects of experiential perceptions on rerouting behaviors. Numerical results suggest that (1) the ultimate states of route swaps depend much more on the reaction sensitivity than on the capacity interference, (2) too much dependence on the historical experience can increase the risk of instability rather than stability, and (3) for high reaction sensitivity network, the instability can be remedied by incorporating proper perception experience.

Individual departure time decision considering departure scheduling utility

The scheduling utility plays a fundamental role in addressing the commuting travel behaviours. A new scheduling utility, termed as DMRD-SU, was suggested based on some recent research findings in behavioural economics. DMRD-SU admitted the existence of positive arrival-caused utility. In addition, besides the travel-time-caused utility and arrival-caused utility, DMRD-SU firstly took the departure utility into account. The necessity of the departure utility in trip scheduling was analyzed comprehensively, and the corresponding individual trip scheduling model was presented. Based on a simple network, an analytical example was executed to characterize DMRD-SU. It can be found from the analytical example that: 1) DMRD-SU can predict the accumulation departure behaviors at NDT, which explains the formation of daily serious short-peak-hours in reality, while MRD-SU cannot; 2) Compared with MRD-SU, DMRD-SU predicts that people tend to depart later and its gross utility also decreases faster. Therefore, the departure utility should be considered to describe the traveler’s scheduling behaviors better.

Alternative Solution for Addressing Failed Home Deliveries

Freight planners are becoming increasingly more concerned about the impact of failed home deliveries on additional carrier journeys (repeat deliveries) and customer trips (to retrieve goods from carrier depots). A local collection-and-delivery point (CDP) concept, which allows customers to collect their failed deliveries, has emerged as a solution for home delivery failures. Data from a 2007 customer survey across two areas along with historical delivery data provided by a major carrier company in the United Kingdom were used in a study of the problem. Nine carrier companies were interviewed to gain an understanding of current operating characteristics of carriers and the key problems encountered during delivery operations. The study quantified the transport costs for the carrier and customer trips of the conventional home delivery method, in which the carrier makes repeat deliveries in the case of first-time failure and appraises the benefits of using CDP networks for handling those failures. The results suggest that a network of CDPs would function most effectively when (a) the proportion of first-time home delivery failures is significant, (b) a significant number of people walk to their local CDP, (c) the carriers depot is located far from the collection area and is not in a convenient location that allows the trip to be combined with another trip; and (d) there is a dense network of CDPs around the residential area.

Day-to-day rerouting modeling and analysis with absolute and relative bounded rationalities

ABSTRACT In contrast to a large number of studies in the route choice behavior with absolute bounded rationality, little concern is laid on that with relative bounded rationality which is hypothetically suggested in this paper and can also be an indispensable component of the bounded rationality. This study is conducted to investigate travelers’ day-to-day rerouting behaviors with the above two bounded rationalities. Along this line, an absolute and a relative boundedly rational swapping process (abbreviated as ABRSP and RBRSP, respectively) model are proposed in the frame of nonlinear pairwise swapping rule. It is found that both ABRSP and RBRSP show satisfactory properties. The numerical results suggest that ABRSP and RBRSP share some general similarity in macroscopic convergence, while still showing obvious distinctions in swapping process, and RBRSP cannot be approximated or substituted by ABRSP or its extensions. Therefore, the suggested relative bounded rationality, even if it is hypothetical, still deserves to be taken seriously.

A bi-objective integer programming model for partly-restricted flight departure scheduling

The normal studies on air traffic departure scheduling problem (DSP) mainly deal with an independent airport in which the departure traffic is not affected by surrounded airports, which, however, is not a consistent case. In reality, there still exist cases where several commercial airports are closely located and one of them possesses a higher priority. During the peak hours, the departure activities of the lower-priority airports are usually required to give way to those of higher-priority airport. These giving-way requirements can inflict a set of changes on the modeling of departure scheduling problem with respect to the lower-priority airports. To the best of our knowledge, studies on DSP under this condition are scarce. Accordingly, this paper develops a bi-objective integer programming model to address the flight departure scheduling of the partly-restricted (e.g., lower-priority) one among several adjacent airports. An adapted tabu search algorithm is designed to solve the current problem. It is demonstrated from the case study of Tianjin Binhai International Airport in China that the proposed method can obviously improve the operation efficiency, while still realizing superior equity and regularity among restricted flows.