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With the growing environmental awareness, people are concerned about the air pollution issues because these issues not only cause adverse environmental effects but also damage human’s health condit...

This research aimed to develop theoretically and empirically a hierarchical linear model that captures interrelationships between bus drivers’ aberrant driving behavior, on the one hand, and three influential factors, on the other hand. The influential factors studied are safety climate, stress, and inattention. This theoretical framework then was used to explore how it could help to prevent fatal accidents through reduction of aberrant driving behavior by occupational bus drivers. Measures adopted from a driver behavior questionnaire, driver behavior inventory, attention-related driving error scale, and safety climate questionnaire were used after screening. Data were collected from 1140 respondents in 30 bus companies in Taiwan. A ten-step procedure is developed for testing nine hypotheses. Results supported all the hypotheses within the proposed cross-sectional modeling framework showing that the direct effect of safety climate, stress and inattention on aberrant driving behavior in a bus company is critical. Further, mediation by safety-focused cognitive and emotional engagement by drivers to improve safety performance cannot be overlooked. A 2018 revision to Taiwan’s Labor Standards Act concerns the reduction of bus drivers’ aberrant driving behavior; the expected benefit thus produced in terms of traffic safety is discussed. To realize the potential benefit and also eliminate negative effects of the amendment upon the national economy and mitigate inconvenience thus incurred to people’s daily life, a follow-up study is required.

Soon enough, autonomous driving systems may not need drivers at all. Ideally, a passenger can ride an autonomous vehicle (AUV) from one location to another without (either partial or complete) huma...

Motorcycle express cargo delivery service (MECDS), part of the ‘sharing economy’, allows utilisation of motorcycle surplus capability without requiring additional investment. Investigating interrel...

The doubly constrained entropy distribution/assignment (DEDA) problem that combines a gravity-based trip distribution (TD) problem and a traffic assignment (TA) problem has long been formulated as an optimization model and solved by two solution algorithms, i.e., partial- and full-linearization solution algorithms. As an alternative, this research first treats the DEDA problem by the augmented Lagrangian dual (ALD) method as the singly constrained entropy distribution/assignment (SEDA) problem, which in turn is addressed, via a tactical supernetwork representation, as an “extended” 1-origin-to-1-destination TA problem. A quick-precision TA solution algorithm, − called TAPAS (Traffic Assignment by Paired Alternative Segments), − is then adopted for solutions. The proposed approach is demonstrated with a numerical example for the correctness of the result, using Lingo 11 solver and the partial linearization solution (PLS) algorithm. Moreover, through the use of TAPAS in the innermost loop, the proposed approach also has the merit of generating unique path flow solution, which is very useful in route guidance under the intelligent transportation systems environment, among other academic applications. In addition, the proposed approach can be easily applied, or with minor modification at most, to various combined models in travel demand forecasting.

Sequential auto carrier loading is a postprocess of the auto carrier loading problem (ACLP) and can be formulated as an integer programming problem for each auto dealer along the auto carrier route except the dealer that is the last stop. The associated objective function for each individual subproblem is to minimize the number of reloads and, for those vehicles that are reloaded, to minimize the total arcs in the path from the reassigned slots to the exit slot. The sequential ACLP (SACLP) process also relaxes the assumption made in the literature that if at any auto dealer a vehicle is unloaded and reloaded again, it is reloaded back to its original slot. To solve the SACLP, an iterative heuristic algorithm that takes into consideration the effect of empty slots is proposed. At each auto dealer, after its demand has been unloaded, any unloaded vehicles destined for the upcoming dealers are reloaded back to better unassigned slots on the auto carrier and are subject to various loading constraints. Computational experiments on five instances indicated that use of the SACLP improved the solutions obtained from the ACLP by itself.

This paper addresses a variation of pickup and delivery problems, named the paired many-to-many pickup and delivery problem (PMPDP), which has never been formally classified in the literature. Given “paired” demands between customer nodes, the PMPDP is to find a set of feasible vehicle routes starting from and ending at the depot such that the constructed objective function can be optimized subject to a set of desired constraints. When the PMPDP is applied to public library delivery operations, interchangeably used with the library vehicle routing problem (LVRP) hereafter, the customer nodes are replaced by library branches and the items to be delivered and picked up become books, videos and materials. To explore the LVRP, a mathematical model is rigorously formulated and a two-stage solution algorithm involving a modified bee colony optimization method is elaborately developed. Using real data from the San Francisco library system, the computational results show that our approach performs fairly well as compared with those approaches that have appeared in the literature. Provided each customer node is visited once, the sensitivity analysis indicates that when the number of dispatched library vehicles is more than what are needed, then the obtained result may get worse.

The traffic equilibrium problem (TEP) is an essential module in transportation planning. This paper studies an extended TEP version, i.e. the path-specific traffic equilibrium problem (PS-TEP), which has many applications in the real world. Due to inherent path interactions, the PS-TEP cannot be formulated as an optimization model but can be formulated as a variational inequality model. The corresponding user equilibrium conditions are characterized by the equal and minimum generalized path cost, which in turn can be expressed as a function of actual path costs and path-specific disutility. To interpret the PS-TEP as an extension of the TEP, an augmented network representation that includes a basic network (incurred actual path costs) and an additional virtual network (incurred path-specific disutility) is proposed. A path-based solution algorithm, called the gradient projection method, is modified for demonstration. Four path-specific cost schemes of the path-specific disutility are used for elaboration ...

Travel time information is generally nonlinear and nonstationary in a dynamic environment, and therefore no consistent tendency can be easily observed. This research developed a novel approach that combined the empirical decomposition method for speed data analysis and gray theory for travel time prediction to predict the arrival time at each stop along a bus route. In addition, sensitivity analysis was performed for different numbers of stops. With an average prediction error of less than 3.5%, the experiments showed that the proposed prediction approach, which employed both historical and real-time speed data collected from the geographic positioning system, outperformed Chou's approach, which used only historical speed data. The proposed prediction method could be readily incorporated into a cell phone–based information retrieval system that indicated bus position en route as well as its arrival times at all stops.

A supernetwork is usually defined as an augmented network that consists of a “basic network” for route choice and a “virtual network” for other travel choices. Supernetwork representations are useful pedagogical devices to interpret various combined travel choice models as an extension of the fixed demand traffic assignment problem. Based on three proposed criteria, this paper reviews current supernetworks and modifies them as needed for better representation. A nested combined model consisting of four choices subject to variable demand is described with an example. Using supernetwork representations, combined travel choice models have great potential to become more popular than sequential four-step travel demand forecasting, even with feedback. In addition, recently developed quick-precision traffic assignment algorithms could be more efficient than traditional multistage solution algorithms for solving combined travel choice models. The proposed new supernetwork representations can be extended to other network problems in the supply chain network or other economics networks with minor modifications.

The problem addressed in this paper-the linehaul-feeder vehicle routing problem with virtual depots (LFVRP-VD)-can be regarded as an extension of the vehicle routing problem. During delivery operation, one large vehicle departs from the physical depot (PD) and services all virtual depots (VDs). A set of small vehicles delivers to customers and, if necessary, reloads either from the PD or from the large vehicle at a VD before continuing work. The objective of the operation is to minimize the total travel and waiting costs for all vehicles. Two heuristics that embed the cost-sharing method and the threshold method are proposed for initial solution construction. Seventeen test problems are extensively examined. The results show that the cost-sharing method outperforms the threshold method in terms of several selected performance measures. In addition, the more candidates available a VD can choose, the better the obtained objective value.

We address the task of repairing damaged infrastructures as a series of multidepot vehicle-routing problems with time windows in a time-rolling frame. The network size of the tackled problems changes from time to time, as new disaster nodes will be added to and serviced disaster nodes will be deleted from the current network. In addition, an inaccessible disaster node would become accessible when one of its adjacent disaster nodes has been repaired. By the “take-and-conquer” strategy, the repair sequence of the disaster nodes in the affected area can be suitably scheduled. Thirteen instances were tested with our proposed heuristic, that is, Chen et al.'s approach. For comparison, Hsueh et al.'s approach (2008) with necessary modification was also tested. The results show that Chen et al.'s approach performs slightly better for larger size networks in terms of objective value.

This paper addresses the linehaul-feeder vehicle routing problem with virtual depots and time windows (LFVRPTW). Small and large vehicles deliver services to customers within time constraints; small vehiclesen routemay reload commodities from either the physical depot or from the larger vehicle at a virtual depot before continuing onward. A two-stage solution heuristic involving Tabu search is proposed to solve this problem. The test results show that the LFVRPTW performs better than the vehicle routing problem with time windows in terms of both objective value and the number of small vehicles dispatched.

We propose a nonlinear mathematical model to consider production scheduling and vehicle routing with time windows for perishable food products in the same framework. The demands at retailers are assumed stochastic and perishable goods will deteriorate once they were produced. Thus the revenue of the supplier is uncertain and depends on the value and the transaction quantity of perishable products when they are carried to retailers. The objective of this model is to maximize the expected total profit of the supplier. The optimal production quantities, the time to start producing and the vehicle routes can be determined in the model simultaneously. Furthermore, we elaborate a solution algorithm composed of the constrained Nelder-Mead method and a heuristic for the vehicle routing with time windows to solve the complex problem. Computational results indicate our algorithm is effective and efficient.

This paper presents a study that characterizes, formulates, and solves the reverse logistic recycling flow equilibrium (RLRFE) problem. The RLRFE problem is concerned with the recycling channel in which recyclable collectors, processors, landfills, and demand markets form a multi-tiered network to process the recycled material flows from sources destined either for landfills or demand markets. Motivated by a government policy making or enterprise conglomerate recycling system design and operation needs, the RLRFE problem is elaborated from a system-optimal perspective using the variational inequality (VI) approach. For each origin–destination (OD) pair, the corresponding equilibrium conditions are established as a variation of the Wardrop second principle. In light of demand and cost function interactions, a nested diagonalization solution (ND) algorithm is proposed that gradually transforms the RLRFE problem into a traffic assignment model. To address multiple landfills in the recycling network and to understand how a variable-demand problem can be analyzed as a fixed-demand problem, we propose a supernetwork representation of the RLRFE problem. A numerical analysis on a test case illustrates the model formulation and the proposed algorithm.

In this article, the real-time time-dependent vehicle routing problem with time windows is formulated as a series of mixed integer programming models that account for real-time and time-dependent travel times, as well as for real-time demands in a unified framework. In addition to vehicles routes, departure times are treated as decision variables, with delayed departure permitted at each node serviced. A heuristic comprising route construction and route improvement is proposed within which critical nodes are defined to delineate the scope of the remaining problem along the time rolling horizon and an efficient technique for choosing optimal departure times is developed. Fifty-six numerical problems and a real application are provided for demonstration.

The reverse supply chain network design problem is formulated as a bilevel model. In the upper level, the total cost incurred in the reverse supply chain network is minimized subject to the budget constraint, among others, whereas in the lower level the corresponding flow pattern in the network is characterized by the variable demand equilibrium conditions; this is essentially a variation of the Wardrop second principle. A sensitivity analysis–based algorithm, with special treatment of the material conversion factor at each recycler processor agent, or both, is proposed for solutions. A numerical example is then provided for demonstration.

This paper applies stochastic frontier/metafrontier analysis to study output and disaggregate input efficiencies of international container ports during 2004–2011 to identify avenues for strengthening port operations. One output variable, four input variables and six environmental variables reflecting different conditions confronted by ports were used to evaluate technical efficiency, disaggregate input efficiency and meta technical efficiency for 35 international container ports using stochastic frontier/metafrontier analysis. Moreover, input efficiency is discussed separately for each selected input variable. The results show that the Asia-Pacific group is significantly superior to the Europe/America group in output efficiency for throughput and in input efficiency for ship-to-shore cranes and trucks; the Europe/America group is significantly superior in input efficiency of container storage. To improve performance, port operators should pay more attention to inefficient variables in each individual group and allocate more resources to improving those. A few remarks at the end concern applications of suitable frontier/metafrontier models.

Travel demand forecasting including four travel choices, i.e., trip generation, trip distribution, modal split and traffic assignment constructs the core of transportation planning. In its current application, travel demand forecasting has associated with three important issues, i.e., interface inconsistencies among four travel choices, inefficiency of commonly used solution algorithms, and undesirable multiple path solutions. In this paper, each of the three issues is extensively elaborated. An ideal unified framework for the combined model consisting of the four travel choices and variable demand functions is also suggested. Then, a few remarks are provided in the end of the paper, {"references":["D.E. Boyce, M. Lupa, and Y. Zhang, \"Introducing 'feedback' into four-step travel forecasting procedure vs. equilibrium solution of combined model,\" Transportation Research Record, vol. 1443, 1994, pp. 65–74.","H. Bar-Gera, and D.E. Boyce, \"Solving the sequential procedure with feedback,\" paper presented at the Sixth International Conference of Chinese Transportation Professionals, Dalian, China, 2006.","S.P. Evans \"Derivation and analysis of some models for combining trip distribution and assignment,\" Transportation Research, vol. 10, 1976, pp. 37–57.","M. Florian, S. Nguyen, and J. Ferland, \"On the combined distribution-assignment of traffic,\" Transportation Science, vol. 9, 1975, pp. 43–53.","M. Abdulaal, and L. J. LeBlanc, \"Methods for combining modal split and equilibrium assignment models,\" Transportation Science, vol. 13, 1979, pp. 292–314.","M. Florian, and S. Nguyen, \"A combined trip distribution modal split and assignment model,\" Transportation Research, vol. 12, 1978, pp. 241–246.","H.K. Chen, 2013.07.27-28, \"A combined model with the four travel choices and variable demand,\" International Academic Conference on Social Sciences (IACSS 2013), Istanbul, Turkey.","H.K. Chen, and K.C. Yen, \"A algorithm for the combined model with the four travel choices and variable demand,\" 2014. (In Chinese)","M. Beckmann, C. B. McGuire, and C. B. Winsten, Studies in the Economics of Transportation, Yale University Press: New Haven, 1956.\n[10]\tM. Frank, and P. Wolfe, \"An algorithm for quadratic programming\", Naval Research Logistics Quarterly, vol. 3, 1956, pp. 95–110.\n[11]\tR. Jayakrishnan, W.T. Tsai, J.N. Prashker, and S. Rajadhyaksha, \"A Faster Path-Based Algorithm for Traffic Assignment,\" University of California Transportation Center, Working Papers qt2hf4541x, University of California Transportation Center, 1994.\n[12]\tT. Larsson, M. Patriksson, Simplicial Decomposition with Disaggregated Representation for the Traffic Assignment Problem, Transportation Science, vol. 26, no. 1, 1992, pp. 4-17.\n[13]\tM. Patriksson, The Traffic Assignment Problem: Models and Methods, VSP: Utrecht, 1994.\n[14]\tH. Bar-Gera, \"Traffic assignment by paired alternative segments (TAPAS),\" Transportation Research part B, vol. 44, 2010, pp. 1022–1046\n[15]\tR.B. Dial, \"A path-based user-equilibrium traffic assignment algorithm that obviates path storage and enumeration,\" Transportation Research part B, vol. 40, 2006, pp. 917–936.\n[16]\tG. Gentile, \"Linear user cost equilibrium: a new algorithm for traffic assignment,\" Submitted to Transportation Research Part B, 2009.\n[17]\tH. Bar-Gera, \"Origin-based algorithm for the traffic assignment problem,\" Transportation Science, vol. 36, no. 4, 2002, pp. 398–417.\n[18]\tM. Florian, I. Constantin, and D. Florian, \"A new look at the projected gradient method,\" In CD-ROM of TRB 2009 Annual Meeting, 2009.\n[19]\tR.L. Tobin, and T. Friesz, \"Sensitivity analysis for equilibrium network flow,\" Transportation Science, vol. 22, no. 4, 1988, pp. 242–250.\n[20]\tH. Bar-Gera, and D. Boyce, \"Route flow entropy maximization in origin-based traffic assignment,\" In: Ceder, A. (Ed.), Proceedings of the 14th International Symposium on Transportation and Traffic Theory, Jerusalem, Israel, Elsevier Science, Oxford, UK, 1999, pp. 397-415.\n[21]\tJ.G. Wardrop, \"Some theoretical aspects of road traffic research,\" In Proceedings of Institution of Civil Engineers, Part II, no. 1, 1952, pp. 325–378.\n[22]\tH. Bar-Gera, \"Primal method for determining the most likely route flows in large road networks,\" Transportation Science, Vol. 40, No. 3, pp. 269-286, 2006.\n[23]\tY. Nie, \"A class of bush-based algorithms for the traffic assignment problem,\" Transportation Research part B, vol. 44, no. 1, 2010, pp. 73–89.\n[24]\tY. Sheffi, Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods, Prentice-Hall Inc: New Jersey, USA, 1985.\n[25]\tH.K. Chen, \"Supernetwork representations for combined travel choice models,\" Open Transportation Journal, Vol. 5, 2011, pp. 92-104."]}

A discrete-time predictive dynamic user-optimal departure time/route choice problem has been formulated and solved with the nested diagonalization method by Chen, H.K., Hsueh, C.F. (1998a. A discrete-time dynamic user-optimal departure time/route choice model. Transportation Engineering, ASCE 124 (3), 246–254). That model did not impose constraints on either departure times at origin or arrival times at destination, which are typically required for regular work trips. However, for better representing practical situations, the time-window constraints associated with both the departure times and arrival times, along with link capacity side constraints, need to be incorporated into the aforementioned model. The resulting dynamic capacitated user-optimal departure time/route choice model with time-window can appropriately model the queuing delay associated with each capacitated time–space link and also can properly differentiate off-peak and peak phenomena within the analysis period. A numerical example is provided for demonstration.

This paper is a follow-up study to the dynamic user-optimal departure time/route choice problem, by imposing hard time-windows on origin departure times and on destination arrival times. However, by an appropriate network representation, the dynamic user-optimal departure time/route choice problem with hard time-windows is mathematically equivalent to the dynamic user-optimal route choice problem and can be solved accordingly by the nested diagonalization method. The enhancements of the proposed model are that off-peak and peak phenomena within the analysis period can be properly differentiated and that the influence of earlier departures on latter ones can be naturally presented. A numerical example is provided for demonstration.

A discrete‐time predictive dynamic user‐optimal departure time/ route choice problem has been formulated and solved with the nested diagonalization method by Chen and Hsueh (1998a). That model did not impose constraints on either origin departure times or destination arrival times, which are typically required for regular work trips. For the purpose of better representing practical situations, the time‐window constraints associated with both departure times and arrival times are incorporated into the previous dynamic user‐optimal departure time/ route choice model, resulting in a dynamic user‐optimal departure time/ route choice model with time‐window, where the off‐peak and peak phenomena can be properly differentiated within the analysis period, and the influence of earlier departures on later arrivals with respect to perceived route disutilities can be appropriately modeled.

The dynamic system-optimal route choice problem is formulated as a discrete-time link-based model using the variational inequality approach. This model complies with the dynamic system-optimal equilibrium condition in which for each origin-destination pair, the marginal route travel times experienced by travellers are equal and minimal. A nested diagonalisation procedure is then proposed for obtaining the solution. Numerical examples are provided for showing equilibrated route travel times, demonstrating Braess's paradox and an approximating static counterpart solution. In addition, a two-stage procedure is used for computing a toll imposition such that a dynamic system-optimal is also a dynamic user-optimal solution.

The primary purpose of this paper is to develop a robust adaptive vehicle separation control in the increasingly important roles of intelligent transportation system (ITS). A hybrid neuro-fuzzy system (HNFS) is proposed for developing the adaptive vehicle separation control to minimize the distance (headway) between successive cars. This hybrid system consists of two modules: a headway identification (prediction) module and a control decision module. Each of these modules is realized with a distinct neuro-fuzzy network that upgrades hierarchical granularity and reduces the complexity in the control system. Given the current headway and relative velocity between the two consecutive cars, the headway identification module predicts the headway of the next time instant. This identified headway, together with the desired velocity are input to the control decision module whose output is the actual acceleration/deceleration control output. The HNFS encapsulates the adaptive learning capabilities of a neural network into a fuzzy logic control framework to fine-tune the fuzzy control rules. On the other hand, rules derived initially from well-defined fuzzy phase plane accelerate the training of the neural network. Simulation results are very encouraging. It is observed that the headway decreases significantly without sacrificing speed. Furthermore, both stability and robustness of HNFS are demonstrated.

One link-based algorithm (Frank-Wolfe) and three route-route based algorithms are compared for use in the dynamic user-optimal route choice problem. Computational experience with five test networks indicates that the route-based algorithms are in general superior to the link-based algorithm in terms of execution time but slightly inferior in terms of memory requirement.

Link capacity side constraints are explicitly incorporated into the variational inequality-based dynamic user-optimal route choice problem. The corresponding dynamic capacitated user-optimal conditions for each origin-destination pair and time interval state that the generalized route travel times (composed of route travel times and queuing delays) experienced by travelers are equal and minimal. An augmented Lagrangian dual method that embeds the gradient projection algorithm is then proposed and validated with a numerical example. The computational performance of the gradient projection algorithm is also compared with the disaggregate simplicial decomposition algorithm in a preliminary attempt.

This paper formulates a discrete-time, link-based dynamic user-optimal route choice problem using the variational inequality approach. The proposed model complies with the dynamic user-optimal equilibrium condition in which for each origin-destination pair, the actual travel time experienced by travelers departing during the same interval is equal and minimal. A nested diagonalization procedure is then proposed and demonstrated with a numerical example.

This paper describes the solution of the traffic assignment model under fuzzy information. The assumption about perfect network information is relaxed. The fuzzy algorithm, successive representative method, is proposed in this study. This algorithm assigns a set of O-D trip rates to a transportation network in which the link travel times are fuzzy. The assignment assumes that route choice is based on fuzzy link travel times. The fuzzy travel times are modeled not only as fuzzy numbers, but also as flow dependence. This dependence is accounted for by assuming that the fuzzy travel time for each link is a fuzzy mapping of the flow on that link. Four fuzzy operations are used in the successive representative method, including fuzzy addition, fuzzy multiplication, fuzzy comparison and defuzzification. Our algorithm is exemplified by the road network around Osaka. Sensitivity analysis of the algorithm are also presented.

The asymmetric traffic assignment model can improve the traditional traffic assignment model by adopting detailed network representation and more realistic asymmetric cost functions. The diagonalization, streamlined diagonalization, and projection methods are three widely mentioned solution algorithms for solving asymmetric traffic assignment models. The diagonalization and streamlined diagonalization methods have the advantage of requiring less computer memory but typically require greater computational time. The projection method has the advantage of converging more rapidly but requires a large computer memory. In order to balance computer memory and computational time, we propose two new algorithms; i.e., hybrid and streamlined hybrid methods. According to our case study, the proposed algorithms show their superiority over the diagonalization and streamlined diagonalization methods in terms of computational time, and over the projection method in terms of computer memory. Both new algorithms c...

We propose a new algorithm for solving a fuzzy goal programming (FGP) problem with symmetrically triangular membership functions of fuzzy goals and priority structure. The efficiency of the algorithm is justified by showing its computational superiority over that by Tiwari et al.

A traffic assignment‐simulation model for planning, rather than operational, purposes is proposed to evaluate what possible benefit might be obtained by adapting a traffic center‐based vehicle route guidance system (VRGS). The model consists of three modules: a multiple driver class traffic assignment module, a traffic signal control module, and a vehicle route guidance system module. Multiple driver class traffic assignment generates the time‐dependent K shortest paths based on “static”, “semi‐dynamic”, and “dynamic” link travel times for each of three classes of driver, namely, non‐equipped drivers, those who are equipped but have partially compliant drivers, and those who are equipped and have totally compliant drivers. Traffic signal settings adopt a table look‐up traffic‐responsive signal scheme to “optimize” signal performance locally. Different VRGS scenarios, which are presented for comparison, are delineated by the proportion of equipped vehicles, the proportion of equipped vehicles in compliance...

This chapter deals with a time-dependent supply chain network equilibrium (TD-SCNE) problem, which allows product flows to be distributed over a network, not only between two successive sectors in the same time period (a transaction), but also between two successive periods for the same agency (an inventory). Since product price and flow interactions are inherently embedded within it, the TD-SCNE problem is formulated as a variational inequality (VI) model. A three-loop-nested diagonalization method, along with a specially designed supernetwork representation, then is proposed and demonstrated with a numerical example. In equilibrium, for each time-dependent retailer agency or demand market, the product prices of transactions are the same and minimum, no matter when or where the product comes from, which is a realization of the Wardropian first principle. The proposed framework can be extended with minor modifications to other TD-SCNE-related equilibrium problems.

This paper formulates the dynamic signal timing optimization (DSTO) problem as a bilevel model. In the upper level, total network travel time is minimized subject to some necessary signalisation constraints. In the lower level, the dynamic user-optimal route choice is formulated as a variational inequality model, which complies with the dynamic extension of Wardrop's first principle. The sensitivity analysis using a generalized inverse approach performed in the link variable is adopted to solve the DSTO problem. It is not required to generate further a nondegenerate extreme path solution from the link flow solution obtained by the FW method in the sensitivity analysis. This is the case as any path flow solution can be readily accommodated for use. Four heuristics with the same framework of the nested diagonalization (ND) method, but differing in updating decision variable or determining step size, are proposed and compared in terms of both computational performance and precision level. Numerical examples show that all four heuristics algorithms can obtain equilibrium solutions in compliance with the dynamic extension of War drop's first principle. However, considering a balance between precision level and computational performance, the Armijo-based method is recommended.

As a commentary note, this paper attempts to elaborate and make constructive critiques on Chen et als paper in which four issues may be identified: (1) travelers rerouting behavior is not respected when degeneracy of link capacities occurs, (2) variations of link flows and capacities in time is not considered, (3) sensitivity information of network capacity with respect to link flow cannot be directly derived, and (4) the trial-and-error method used in solving the bi-level network reliability problem is computationally inefficient. A new reliability model formulation is thus proposed to resolve the first two shortcomings. The methodological framework of Chen et al is still adopted but with necessary modifications based in the last two comments. A numerical example is then provided to validate the proposed framework.

The paper incorporates both the link capacity and first-in-first-out constraints into the dynamic user equilibrium problem. The corresponding dynamic equilibrium conditions for each origin-destination pair and time interval state that the generalized route travel times experienced by travelers are equal and minimal. A nested Lagrangian method embedding the gradient projection algorithm is then proposed and demonstrated with a numerical example.

The stochastic dynamic user-optimal route choice model assumes that the perceived travel times are incomplete and/or imprecise. To illustrate the perceived travel times, an error term is often hypothesized to accompany the actual travel times, and many probability distributions have been applied to represent the real situation. For a specified error term of the perceived travel times, we assume all drivers make their route choice decisions based on their perceptions of O-D travel times. A notable example is the Gumbel distribution which yields the logit model. The resulting traffic flows are expected to be more dispersed over parallel routes for the stochastic dynamic route choice model than for its deterministic counterpart.

The network flow constraints construct the feasible region for dynamic travel choice models. Although the feasible region associated with each dynamic travel choice model may be different, the basic components of the network flow constraints are essentially the same. The complete requirements of dynamic travel choice models include the constraints of flow conservation, flow propagation, nonnegativity, definition, first-in-first-out (FIFO) and oversaturation.

The dynamic system-optimal (DSO) route choice problem requires that travelers comply with a certain driving behavior so that the system-optimal flow pattern, in terms of some predetermined performance measures, can be obtained. This problem is normative in the sense that the transportation system operator has control over the travelers, who must follow the system’s instruction. This assumption is rather restrictive because it is extremely difficult to impose such constraints on travelers, especially in an open transportation system network. As a consequence, travelers who are instructed to take longer routes may unilaterally change routes so as to decrease their travel times, which implies the dynamic system-optimal flow pattern is not stable, and therefore unlikely to sustain itself Nevertheless, the dynamic system-optimal problem is important because the system-optimal travel time may serve as a yardstick by which different flow patterns can be measured. Indeed, the system-optimal flow pattern is desired by many types of traffic control policies such as tolls and signal controls in order to enhance the efficiency of road network utilization.