Dynamic and stochastic routing for multimodal transportation systems

The authors present a case study of a multimodal routing system that takes into account both dynamic and stochastic travel time information. A multimodal network model is presented that makes it possible to model the travel time information of each transportation mode differently. This travel time information can either be static or dynamic, or either deterministic or stochastic. Next, a Dijkstra-based routing algorithm is presented that deals with this variety of travel time information in a uniform way. This research focuses on a practical implementation of the system, which means that a number of assumptions were made, like the modelling of the stochastic distributions, comparing these distributions, and so on. A tradeoff had to be made between the performance of the system and the accuracy of the results. Experiments have shown that the proposed system produces realistic routes in a short amount of time. It is demonstrated that routing dynamically indeed results in a travel time gain in comparison to routing statically. By making use of the additional stochastic travel time information even better (i.e. faster), more reliable routes can be calculated. Moreover, it is shown that routing in the multimodal network may have its advantages over routing in a unimodal network, especially during rush hours

Reliable network design under supply uncertainty with probabilistic guarantees

This paper proposes a bi-level risk-averse network design model for transportation networks with heterogeneous link travel time distributions. The objective of the network design is to minimise the total system travel time (TSTT) budget (TSTTB), which consists of the mean TSTT and a safety margin. The design is achieved by selecting optimal link capacity expansions subject to a fixed expansion budget. Users’ selfish behaviour and risk attitude are captured in the lower level traffic assignment constraints, in which travellers select routes to minimise their own path travel time budget. The properties of the design problem are analysed analytically and numerically. The analysis shows that despite the lack of knowledge of travel time distributions, the probabilities that the actual TSTT and the actual path travel time are, respectively, within the optimal TSTTB and the minimum path travel time budget under optimal design have lower bounds. The lower bounds are related to the system manager's and travellers’ risk aversion. The optimal TSTTB is proven to be bounded below even when the link expansion budget is unlimited.postprin

Time Series Analysis of Stochastic Networks with Correlated Random Arcs

While modern day weather forecasting is not perfect, there are many benefits given by the multitude and variety of predictive models. In the interest of routing airplanes, this paper uses time series analysis on successive weather forecasts to predict the optimal path and fuel burn of wind-based, fuel-burn networks with stochastic correlated arcs. Networks are populated with either deterministic or ensemble-based weather data, and the two data sources with and without time series analysis are compared. Methods were compared by fuel burn prediction accuracy and ability to predict a future optimal path. Of the four options, the ensemble-based methods were on average the least accurate. Using time series analysis on ensemble data gave a nominal change in correct future path prediction and an increase in fuel burn pre- diction accuracy. The deterministic method gave the most accurate results but the worst correct future path prediction rate. Time series analysis on deterministic data had a marginal decrease in accuracy but the highest correct future path prediction rate

INCORPORATING TRAVEL TIME RELIABILITY INTO TRANSPORTATION NETWORK MODELING

Travel time reliability is deemed as one of the most important factors affecting travelers’ route choice decisions. However, existing practices mostly consider average travel time only. This dissertation establishes a methodology framework to overcome such limitation. Semi-standard deviation is first proposed as the measure of reliability to quantify the risk under uncertain conditions on the network. This measure only accounts for travel times that exceed certain pre-specified benchmark, which offers a better behavioral interpretation and theoretical foundation than some currently used measures such as standard deviation and the probability of on-time arrival. Two path finding models are then developed by integrating both average travel time and semi-standard deviation. The single objective model tries to minimize the weighted sum of average travel time and semi-standard deviation, while the multi-objective model treats them as separate objectives and seeks to minimize them simultaneously. The multi-objective formulation is preferred to the single objective model, because it eliminates the need for prior knowledge of reliability ratios. It offers an additional benefit of providing multiple attractive paths for traveler’s further decision making. The sampling based approach using archived travel time data is applied to derive the path semi-standard deviation. The approach provides a nice workaround to the problem that there is no exact solution to analytically derive the measure. Through this process, the correlation structure can be implicitly accounted for while simultaneously avoiding the complicated link travel time distribution fitting and convolution process. Furthermore, the metaheuristic algorithm and stochastic dominance based approach are adapted to solve the proposed models. Both approaches address the issue where classical shortest path algorithms are not applicable due to non-additive semi-standard deviation. However, the stochastic dominance based approach is preferred because it is more computationally efficient and can always find the true optimal paths. In addition to semi-standard deviation, on-time arrival probability and scheduling delay measures are also investigated. Although these three measures share similar mathematical structures, they exhibit different behaviors in response to large deviations from the pre-specified travel time benchmark. Theoretical connections between these measures and the first three stochastic dominance rules are also established. This enables us to incorporate on-time arrival probability and scheduling delay measures into the methodology framework as well

통행시간 신뢰도의 개별 리스크 선호도를 고려한 경로선택행태 모형

학위논문 (박사)-- 서울대학교 대학원 : 공과대학 건설환경공학부, 2018. 2. 고승영.The route choice problem is an important factor in traffic operation and transportation planning. There have been many studies to analyze the route choice behavior using travel data. There was a limit in constructing a route choice model by generating an appropriate choice set due to the limitations of the data. In this study, we construct a choice set generation model and a stochastic route choice model using the observed data. This study estimates the parameters incorporating travelers heterogeneity according to the choice set from the choice set generation model and the route choice model. We define the individual confidence level according to perceived travel time distribution to reflect travelers heterogeneity on choice set generation model. In addition, the parameters were estimated using the mixed path-size correction logit model (MPSCL) considering the path overlapping and individual risk preference in the route choice model. We compare the experienced paths and the derived choice set to construct choice set generation model. In addition, it is possible to estimate better parameters incorporating travelers heterogeneity for choice set generation model and route choice model. We compare the choice set from the developed model with that of the conventional choice set generation model. This study shows the superior prediction result in route choice model reflecting the individual behaviors of the route choice in the urban area on the transportation demand forecasting and traffic operation.1. Introduction 1 1.1 Backgrounds 1 1.2 Research Purpose 4 1.3 Main contents 5 1.4 Research Scope 9 2. Literature Review 11 2.1 Choice Set Generation 13 2.2 Route Choice Model 30 2.3 Review result and limitation 58 2.4 Research Contributions 62 3. Modelling Framework 66 3.1 Overview 66 3.2 Terminology 68 3.3 Choice set generation model 76 3.4 Route choice model 92 4. Revealed Preference Routing Data 100 4.1 Data Characteristics 100 4.2 Data Collection & Description 106 4.3 Data Processing 109 4.4 Missing Data Correction 113 5. Model Estimation & Validation 120 5.1 Overview 120 5.2 Choice set generation 121 5.3 Model estimation & Validation 124 5.4 Model verification 135 5.5 Discussion 138 6. Conclusion 140 6.1 Conclusion 140 6.2 Further research 142 REFERENCES 145 APPENDIX 158Docto

Combinatorial optimization under ellipsoidal uncertainty

We study combinatorial problems with ellipsoidal uncertainty in the objective function concerning their theoretical and practical solvability. Ellipsoidal uncertainty is a natural model when the coefficients are normally distributed random variables. Robust versions of typical combinatorial problems can be very hard to solve compared to their linear versions. Complexity and approaches differ fundamentally depending on whether uncorrelated or correlated uncertainty occurs. We distinguish between these two cases and consider first the unconstrained binary optimization under uncorrelated ellipsoidal uncertainty. For this we develop an algorithm which computes an optimal solution by merely sorting the variables and, correspondingly, has a running time of O(n log n). The algorithm is based on the diminishing returns-property, which is characteristic for submodular functions. We introduce a new and a more general p-norm-uncertainty and show that with only slight modifications the sorting algorithm can be easily applied. We also extend the algorithm to general integer variables, which in this case only leads to a pseudo-polynomial time. The next step to the general case is investigation of problems with arbitrary combinatorial sets X ⊆ {0, 1}n under uncorrelated ellipsoidal uncertainty. For this case we embed the O(n log n)-algorithm for the unconstrained binary problems into a Lagrangean decomposition approach. The approach separates the objective function from the combinatorial structure applying Lagrangean relaxation to some artificial connecting constraints. This creates two subproblems, one of which is the linear version of the combinatorial problem and the other one is just the unconstrained binary uncorrelated problem, which can be solved using the O(n log n)-algorithm. The solutions of the subproblems are used to obtain primal and dual bounds which are used in a branch and bound-approach. The approach shows an excellent performance in practice. In the correlated case already the unconstrained binary problem turns out to be strongly NP-hard. Here we also define a branch and bound-approach, now with lower bounds determined by underestimation of the given ellipsoid with certainly defined axis-parallel ellipsoids. We use this idea to extend the decomposition approach to general combinatorial problems under correlated uncertainty. In contrast to the uncorrelated case the uncertain subproblem of the decomposition is here strongly NP-hard in itself. We solve it approximately using the developed underestimators which are determined in a preprocessing step. The approach offers room for improvement concerning in the primal extent a faster computation of the underestimators, which is done by solving semidefinite programs