A graphical approach to identify sensor locations for link flow inference

Information of link flows in a traffic network becomes increasingly critical in contemporary transportation practice and researches. The network sensor installation is carried out to supply such information. In this paper, we present a graphical approach to determine the smallest subset of links in a traffic network for counting sensor installation, so as to infer the flows on all remaining links. The elegant assumption-free character of the problem introduced by Hu, Peeta and Chu is still kept in this approach. This study points out the topological tree feature of solutions that makes it possible for traffic management agencies to easily and flexibly select links for sensor installation in practice. Addressing from the same graphical perspective, we provide solutions to four other important problems about sensor locations. The preceding two problems are, in traffic networks that already have sensors installed on some links, to identify the subset of links on which link flows can be inferred from sensor measurements and to determine the smallest subset of links on which counting sensors also need to be installed so as to infer link flows on all remaining non-equipped links. The third is to identify the optimal locations for a given number of sensors so as to infer flows on as many links as possible by gradually enlarging the number of links included in circuits. The last one is to determine the smallest subset of links on which to install sensors, in such a way that it becomes possible at the same time to satisfy prior requirements and infer the flows on all remaining links, through building a minimum spanning tree. These methods can be applied to all kinds of long-term planning and link-based applications in traffic networks.     

A generalized sensor location model for the estimation of network origin–destination matrices

This study examined the network sensor location problem by using heterogeneous sensor information to estimate link-based network origin–destination (O–D) demands. The proposed generalized sensor location model enables different sensors’ traffic monitoring capabilities to be used efficiently and the optimal number and deployment locations of both passive- and active-type sensors to be determined simultaneously without path enumeration. The proposed sensor location model was applied to solve the network O–D demand estimation problem. One unique aspect of the proposed model and solution algorithms is that they provide satisfactory network O–D demand estimates without requiring unreasonable assumptions of known prior information on O–D demands, turning proportions, or route choice probabilities. Therefore, the proposed model and solution algorithms can be practically used in numerous offline transportation planning and online traffic operation applications.     

Vehicle identification sensor models for origin–destination estimation

The traditional approach to origin–destination (OD) estimation based on data surveys is highly expensive. Therefore, researchers have attempted to develop reasonable low-cost approaches to estimating the OD vector, such as OD estimation based on traffic sensor data. In this estimation approach, the location problem for the sensors is critical. One type of sensor that can be used for this purpose, on which this paper focuses, is vehicle identification sensors. The information collected by these sensors that can be employed for OD estimation is discussed in this paper. We use data gathered by vehicle identification sensors that include an ID for each vehicle and the time at which the sensor detected it. Based on these data, the subset of sensors that detected a given vehicle and the order in which they detected it are available. In this paper, four location models are proposed, all of which consider the order of the sensors. The first model always yields the minimum number of sensors to ensure the uniqueness of path flows. The second model yields the maximum number of uniquely observed paths given a budget constraint on the sensors. The third model always yields the minimum number of sensors to ensure the uniqueness of OD flows. Finally, the fourth model yields the maximum number of uniquely observed OD flows given a budget constraint on the sensors. For several numerical examples, these four models were solved using the GAMS software. These numerical examples include several medium-sized examples, including an example of a real-world large-scale transportation network in Mashhad.     

A mixed-integer linear program for optimizing sensor locations along freeway corridors

How to optimally allocate limited freeway sensor resources is of great interest to transportation engineers. In this paper, we focus on the optimal allocation of point sensors, such as loop detectors, to minimize performance measurement errors. Although it has been shown that the minimization problem can be intuitively formulated as a nonlinear program, the formulation is so complex that only heuristic approaches can be used to solve the problem. In this paper, we transform the nonlinear program into an equivalent mixed-integer linear model. The linearized model is shown to have a graphical interpretation and can be solved using resource constrained shortest path algorithms. A customized Branch-and-Bound technique is then proposed to solve the resource constrained shortest path problem. Numerical experiments along an urban freeway corridor demonstrate that this sensor location model is successful in allocating loop detectors to improve the accuracy of travel time estimation.     

Analysis of factors that influence the sensor location problem for freeway corridors

The use of traffic sensors to acquire real‐time traffic information for intelligent transportation systems is becoming increasingly common. It is a challenge to determine where these sensors should be located to maximize the benefit of their use. This paper aims to illuminate the interaction of the sensor location problem (SLP) and its influencing factors, and to reveal the influencing mechanisms between those factors and the optimal sensor numbers. Firstly, we sum up the factors that influence the SLP for freeway corridors in detail and present the mathematical formulation of each factor. Then, given the parameters, which are derived from those influencing factors, the maximum integration value model (MIVM) and simplified MIVM are proposed for addressing the SLP. Finally, a real world case study, in which the simplified MIVM is used, is presented to illustrate how these factors influence the optimal sensor numbers and the maximum integration value, and also leads to the typical influencing patterns of those factors for freeway corridors. The results of the case study also demonstrate the effectiveness of the model and problem solving scheme. What is more, the suggestions for using the findings hereof in practical applications are put forward. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust network sensor location for complete link flow observability under uncertainty

The link observability problem is to identify the minimum set of links to be installed with sensors that allow the full determination of flows on all the unobserved links. Inevitably, the observed link flows are subject to measurement errors, which will accumulate and propagate in the inference of the unobserved link flows, leading to uncertainty in the inference process. In this paper, we develop a robust network sensor location model for complete link flow observability, while considering the propagation of measurement errors in the link flow inference. Our model development relies on two observations: (1) multiple sensor location schemes exist for the complete inference of the unobserved link flows, and different schemes can have different accumulated variances of the inferred flows as propagated from the measurement errors. (2) Fewer unobserved links involved in the nodal flow conservation equations will have a lower chance of accumulating measurement errors, and hence a lower uncertainty in the inferred link flows. These observations motivate a new way to formulate the sensor location problem. Mathematically, we formulate the problem as min–max and min–sum binary integer linear programs. The objective function minimizes the largest or cumulative number of unobserved links connected to each node, which reduces the chance of incurring higher variances in the inference process. Computationally, the resultant binary integer linear program permits the use of a number of commercial software packages for its globally optimal solution. Furthermore, considering the non-uniqueness of the minimum set of observed links for complete link flow observability, the optimization programs also consider a secondary criterion for selecting the sensor location scheme with the minimum accumulated uncertainty of the complete link flow inference.     

Network sensor health problem

Many existing studies on the sensor health problem determine an individual sensor’s health status based on the statistical characteristics of collected data by the sensor. In this research, we study the sensor health problem at the network level, which is referred to as the network sensor health problem. First, based on the conservation principle of daily flows in a network, we separate all links into base links and non-base links, such that the flows on the latter can be calculated from those on the former. In reality, the network flow conservation principle can be violated due to the existence of unhealthy sensors. Then we define the least inconsistent base set of links as those that minimize the sum of squares of the differences between observed and calculated flows on non-base links. But such least inconsistent base sets may not be unique in a general road network. Finally we define the health index of an individual sensor as the frequency that it appears in all of the least inconsistent base sets. Intuitively, a lower health index suggests that the corresponding sensor is more likely to be unhealthy. We present the brute force method to find all least inconsistent base sets and calculate the health indices. We also propose a greedy search algorithm to calculate the approximate health indices more efficiently. We solve the network sensor health problem for a real-world example with 16 nodes and 30 links, among which 18 links are monitored with loop detectors. Using daily traffic count data from the Caltrans Performance Measurement System (PeMS) database, we use both the brute-force and greedy search methods to calculate the health indices for all the sensors. We find that all the four sensors flagged as unhealthy (high value) by PeMS have the lowest health indices. This confirms that a sensor with a lower health index is more likely to be unhealthy. Therefore, we can use such health indices to determine the relative reliability of different sensors’ data and prioritize the maintenance of sensors.     

A day-to-day and within-day dynamic stochastic assignment model

In this article a doubly dynamis assignment model for a general network is presented. It is assumed that users' choices are based on information about travel times and generalized transportation costs occurred in a finite number of previous days and, possibly, in previous periods of the same day. The information may be supplied and managed by an informative system. In this context, path and link flows vary for different subperiods of the same day (within-day dynamics) and for different days (day-to-day dynamics). The proposed model follows a nonequilibrium approach in which both within-day and day-to-day flow fluctuations are modelled as a stochastic process. A model of dynamic network loading for computing within-day variable arc flows from path flows is also presented. The model deals explicitly with queuing at oversaturated intersections and can be formulated as a fixed point problem. A solution scheme for the doubly dynamic assignment model is presented embedding a solution algorithm for the fixed-point problem.     

Identification of vehicle sensor locations for link-based network traffic applications

Information on link flows in a vehicular traffic network is critical for developing long-term planning and/or short-term operational management strategies. In the literature, most studies to develop such strategies typically assume the availability of measured link traffic information on all network links, either through manual survey or advanced traffic sensor technologies. In practical applications, the assumption of installed sensors on all links is generally unrealistic due to budgetary constraints. It motivates the need to estimate flows on all links of a traffic network based on the measurement of link flows on a subset of links with suitably equipped sensors. This study, addressed from a budgetary planning perspective, seeks to identify the smallest subset of links in a network on which to locate sensors that enables the accurate estimation of traffic flows on all links of the network under steady-state conditions. Here, steady-state implies that the path flows are static. A “basis link” method is proposed to determine the locations of vehicle sensors, by using the link-path incidence matrix to express the network structure and then identifying its “basis” in a matrix algebra context. The theoretical background and mathematical properties of the proposed method are elaborated. The approach is useful for deploying long-term planning and link-based applications in traffic networks.     

Entropy weighted average method for the determination of a single representative path flow solution for the static user equilibrium traffic assignment problem

The formulation of the static user equilibrium traffic assignment problem (UETAP) under some simplifying assumptions has a unique solution in terms of link flows but not in terms of path flows. Large variations are possible in the path flows obtained using different UETAP solution algorithms. Many transportation planning and management applications entail the need for path flows. This raises the issue of generating a meaningful path flow solution in practice. Past studies have sought to determine a single path flow solution using the maximum entropy concept. This study proposes an alternate approach to determine a single path flow solution that represents the entropy weighted average of the UETAP path flow solution space. It has the minimum expected Euclidean distance from all other path flow solution vectors of the UETAP. The mathematical model of the proposed entropy weighted average method is derived and its solution stability is proved. The model is easy to interpret and generalizes the proportionality condition of Bar-Gera and Boyce (1999). Results of numerical experiments using networks of different sizes suggest that the path flow solutions for the UETAP using the proposed method are about identical to those obtained using the maximum entropy approach. The entropy weighted average method requires low computational effort and is easier to implement, and can therefore serve as a potential alternative to the maximum entropy approach in practice.     

Quasi-dynamic traffic assignment with residual point queues incorporating a first order node model

Static traffic assignment models are still widely applied for strategic transport planning purposes in spite of the fact that such models produce implausible traffic flows that exceed link capacities and predict incorrect congestion locations. There have been numerous attempts to constrain link flows to capacity. Capacity constrained models with residual queues are often referred to as quasi-dynamic traffic assignment models. After reviewing the literature, we come to the conclusion that an important piece of the puzzle has been missing so far, namely the inclusion of a first order node model. In this paper we propose a novel path-based static traffic assignment model for finding a stochastic user equilibrium in general transportation networks. This model includes a first order (steady-state) node model that yields more realistic turn capacities, which are then used to determine consistent capacity constrained traffic flows, residual point (vertical) queues (upstream bottleneck links), and path travel times consistent with queuing theory. The route choice part of the model is specified as a variational inequality problem, while the network loading part is formulated as a fixed point problem. Both problems are solved using existing techniques to find a solution. We illustrate the model using hypothetical examples, and also demonstrate feasibility on large-scale networks.     

Sustainable cold supply chain management under demand uncertainty and carbon tax regulation

Increasing awareness of sustainability in supply chain management has prompted organizations and individuals to consider environmental impacts when managing supply chains. The issues concerning environmental impacts are significant in cold supply chains due to substantial carbon emissions from storage and distribution of temperature-sensitive product. This paper investigates the impact of carbon emissions arising from storage and transportation in the cold supply chain in the presence of carbon tax regulation, and under uncertain demand. A two-stage stochastic programming model is developed to determine optimal replenishment policies and transportation schedules to minimize both operational and emissions costs. A matheuristic algorithm based on the Iterated Local Search (ILS) algorithm and a mixed integer programming is developed to solve the problem in realistic sizes. The performance and robustness of the matheuristic algorithm are analyzed using test instances in various sizes. A real-world case study in Queensland, Australia is used to demonstrate the application of the model. The results highlight that higher emissions price does not always contribute to the efficiency of the cold supply chain system. Furthermore, the analyses indicate that using heterogeneous fleet including light duty and medium duty vehicles can lead to further cost saving and emissions reduction.     

Sensor location problems in path-differentiated congestion pricing

Path-differentiated congestion pricing is a tolling scheme that imposes tolls on paths instead of individual links. One way to implement this scheme is to deploy automated vehicle identification sensors, such as toll tag readers or license plate scanners, on roads in a network. These sensors collect vehicles’ location information to identify their paths and charge them accordingly. In this paper, we investigate how to optimally locate these sensors for the purpose of implementing path-differentiated pricing. We consider three relevant problems. The first is to locate a minimum number of sensors to implement a given path-differentiated scheme. The second is to design an optimal path-differentiated pricing scheme for a given set of sensors. The last problem is to find a path differentiated scheme to induce a given target link-flow distribution while requiring a minimum number of sensors.     

A planning model for multiple‐mode transportation system operations

The problem of generating a set of “good” transportation alternatives during the early and intermediate stages of transportation planning is addressed in this paper. A linear programming model of a multi‐modal transportation system is developed. The model is run interactively to determine optimal operating levels for all modes for various transport policy decisions. The model described is a component of a composite network generation model incorporating dynamic changes. The linear programming component determines optimal operating policies for given points in time. The composite model incorporates these in a dynamic programming framework to determine optimal staged investment policies over several time periods.     

Optimal placement of omnidirectional sensors in a transportation network for effective emergency response and crash characterization

Rapid motor vehicle crash detection and characterization is possible through the use of Intelligent Transportation Systems (ITS) and sensors are an integral part of any ITS system. The major focus of this paper is on developing optimal placement of accident detecting omnidirectional sensors to maximize incident detection capabilities and provide ample opportunities for data fusion and crash characterization. Both omnidirectional sensors (placed in suitable infrastructure locations) and mobile sensors are part of our analysis. The surrogates used are acoustic sensors (omnidirectional) and Advanced Automated Crash Notification (AACN) sensors (mobile). This data fusion rich placement is achieved through a hybrid optimization model comprising of an explicit–implicit coverage model followed by an evaluation and local search optimization using simulation. The compound explicit–implicit model delivers good initial solutions and improves the detection and data fusion capabilities compared to the explicit model alone. The results of the studies conducted quantify the use of a data fusion capable environment in crash detection scenarios, and the simulation tool developed helps a decision maker evaluate sensor placement strategy.     

Hybrid model of taxonomy and genetic algorithms for finding shortest path in transportation systems

This is research is aimed at elaborating a new methodology of shortest path finding by utilizing the methods of taxonomy and genetic algorithms. Combination of the two is developed and called Genetic Taxonomy Evaluator (GTE) which is expected to be an alternative tool to solve shortest path finding problems within the transportation networks While keeping the properties of transportation networks Taxonomy Reconstructor (TR) transforms the network representation into taxonomic structure, which is hierarchically shaped, based on problem to be solved. In the process TR also creates classification of nodes in the network. This classification provides facilities to isolate the problem to the core, and the criteria that can be inserted in the Genetic Algorithm (GA). A package program for GTE is then developed in C-Language and performance of model is analyzed upon a medium scale of Sioux-Falls City Network. In conclusion, it is found that to achieve fairly quick convergence of GTE computation several optimal parameters of GA should be determined prior to searching for the shortest paths. And since GTE has only been applied to limited case, it is suggested that the findings could be a threshold for further researches.     

A regional railroad network optimization model for coal transportation

A regional railroad network is presented to evaluate the system's response to increased coal traffic. An optimal, multimodal, coal-shipping pattern is developed for the study region to minimize total costs and to efficiently use the existing network. A two-stage, general model allocates resources among demands and then assigns flows to the network according to efficiency criteria. The model is sufficiently general to permit modification for specific needs, assumptions and data. Government agencies and industries can apply the model in resource allocation decisions and transportation policy analysis.     

The design of capacitated intermodal hub networks with different vehicle types

In this study, we allow using alternative transportation modes and different types of vehicles in the hub networks to be designed. The aim of the problem is to determine the locations and capacities of hubs, which transportation modes to serve at hubs, allocation of non-hub nodes to hubs, and the number of vehicles of each type to operate on the hub network to route the demand between origin-destination pairs with minimum total cost. Total cost includes fixed costs of establishing hubs with different capacities, purchasing and operational costs of vehicles, transportation costs, and material handling costs. A mixed-integer programming model is developed and a variable neighborhood search algorithm is proposed for the solution of this problem. The heuristic algorithm is tested on instances from the Turkish network and CAB data set. Extensive computational analyzes are conducted in order to observe the effects of changes in various problem parameters on the resulting hub networks.     

Optimal toll locations and toll levels in congestion pricing schemes: a case study of Stockholm

As congestion pricing has moved from theoretical ideas in the literature to real-world implementation, the need for decision support when designing pricing schemes has become evident. This paper deals with the problem of finding optimal toll levels and locations in a road traffic network and presents a case study of Stockholm. The optimisation problem of finding optimal toll levels, given a predetermined cordon, and the problem of finding both optimal toll locations and levels are presented, and previously developed heuristics are used for solving these problems. For the Stockholm case study, the possible welfare gains of optimising toll levels in the current cordon and optimising both toll locations and their corresponding toll levels are evaluated. It is shown that by tuning the toll levels in the current congestion pricing cordon used in Stockholm, the welfare gain can be increased significantly, and furthermore improved by allowing a toll on a major bypass highway. It is also shown that, by optimising both toll locations and levels, a congestion pricing scheme with welfare gain close to what can be achieved by marginal social cost pricing can be designed with tolls being located on only a quarter of the tollable links.     

A multi-objective optimization approach to balancing economic efficiency and equity in accessibility to multi-use paths

Improving public health through active transpiration investments has increasingly become a new research focus in transportation planning. This study is to propose a multi-objective optimization modeling framework, through an optimal allocation of active transportation investments, to maximize the total accessibility while minimizing the total differences in accessibility over a city. Accessibility to multi-use paths is calculated for Fresno, California that measures the total length of multi-use paths a resident could reach with a 30-min cycling ride. Then, a geographically weighted regression (GWR) model is used to capture the local relationships between accessibility outcome and previous transportation investments. The marginal-effect analysis for the GWR results indicates economically efficient, inefficient, and indifferent locations for further investments. This study is one of the few to incorporate such a GWR model into a multi-objective optimization modeling framework to improve accessibility to multi-use paths and address inequality issues in transportation. Solving the multi-objective optimization model provides decision-makers a new insight into the making of an economically efficient and socially equal active transportation plan to improve public health.