[Show abstract][Hide abstract] ABSTRACT: Incorporating network configurations in bridge management problems is computationally difficult. Because of the interdependencies among bridges in a network, they have to be analyzed together. Simulation-based numerical optimization techniques adopted in past research are limited to networks of moderate sizes. In this paper, a simple framework is developed to determine optimal maintenance plans for large networks with many bridges. The objective is to minimize disruption, specifically, the extra travel distance caused by potential bridge failures over a planning horizon and under a budget constraint. It is conjectured and then verified that the expected increase in vehicle-miles traveled due to failures can be approximated by the sum of expected increases due to individual failures. This allows the network-level problem to be decomposed into single-bridge problems and tackled efficiently. The computational effort increases linearly with the number of bridges.
Transportation Research Part C Emerging Technologies 02/2015; 55. DOI:10.1016/j.trc.2015.01.008 · 2.82 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: According to Euler–Lagrange duality principle of kinematic wave (KW) theory any well-posed initial value traffic flow problem can be solved with the same methods either on the time–space (Euler) plane or the time vs vehicle number (Lagrange) plane. To achieve this symmetry the model parameters and the boundary data need to be expressed in a form appropriate for each plane. It turns out, however, that when boundary data that are bounded in one plane are transformed for the other, singular points with infinite density sometimes arise. Duality theory indicates that solutions to these problems must exist and be unique. Therefore, these solutions should be characterized.
The paper shows that the only added feature of these solutions is a new type of shock that can contain mass and we call a supershock. Nothing else is different. The evolution laws of these shocks are described. Solution methods based on these laws for problems with singularities are also presented. The methods apply to problems with monotone speed–density relations and not necessarily concave fundamental diagrams. In accordance with duality theory they can be used with both, the Euler and Lagrange versions of a problem.
Transportation Research Part B Methodological 11/2014; 69:50–59. DOI:10.1016/j.trb.2014.07.002 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: This paper extends Vickrey’s (1969) commute problem for commuters wishing to pass a bottleneck for both cars and transit that share finite road capacity. In addition to this more general framework considering two modes, the paper focuses on the evening rush, when commuters travel from work to home. Commuters choose which mode to use and when to travel in order to minimize the generalized cost of their own trips, including queueing delay and penalties for deviation from a preferred schedule of arrival and departure to and from work. The user equilibrium for the isolated morning and evening commutes are shown to be asymmetric because the schedule penalty in the morning is the difference between the departure and wished curves, and the schedule penalty in the evening is the difference between the arrival and wished curves. It is shown that the system optimum in the morning and evening peaks are symmetric because queueing delay is eliminated and the optimal arrival curves are the same as the departure curves.
The paper then considers both the morning and evening peaks together for a single mode bottleneck (all cars) with identical travelers that share the same wished times. For a schedule penalty function of the morning departure and evening arrival times that is positive definite and has certain properties, a user equilibrium is shown to exist in which commuters travel in the same order in both peaks. The result is used to illustrate the user equilibrium for two cases: (i) commuters have decoupled schedule preferences in the morning and evening and (ii) commuters must work a fixed shift length but have flexibility when to start. Finally, a special case is considered with cars and transit: commuters have the same wished order in the morning and evening peaks. Commuters must use the same mode in both directions, and the complete user equilibrium solution reveals the number of commuters using cars and transit and the period in the middle of each rush when transit is used.
Transportation Research Part B Methodological 11/2013; 57:286–299. DOI:10.1016/j.trb.2013.06.009 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The day-long system optimum (SO) commute for an urban area served by auto and transit is modeled as an auto bottleneck with a capacitated transit bypass. A public agency manages the system’s capacities optimally. Commuters are identical except for the times at which they wish to complete their morning trips and start their evening trips, which are given by an arbitrary joint distribution. They value unpunctuality – their lateness or earliness relative to their wish times – with a common penalty function. They must use the same mode for both trips. Commuters are assigned personalized mode and travel start times that collectively minimize society’s generalized cost for the whole day. This includes unpunctuality penalties, queuing delays, travel times and out-of-pocket costs for users, as well as travel supply costs and externalities for society.It is shown that in a SO solution there can be no queuing and that the set of SO solutions forms a convex set. Furthermore, if the schedule penalty that users suffer due to unpunctuality is separable into morning and evening components, then the set of commuters traveling by the same mode arrive at work and depart from work in the order of their wishes. These orders are in general different in the morning and the evening. It is also shown that there always is a SO solution in which users are at all times, and on both modes, either punctual or flowing at capacity. These problem properties are used to identify search methods, both, for SO solutions and for time-dependent tolls and transit fares that preserve the solutions as Nash equilibriums. In every case studied, these prices exist. They must peak concurrently for the two modes in both periods.In special cases involving only one mode, only one period or concentrated demand the solution to the complete problem decomposes by period conditional on the number of transit users, and this facilitates the solution. In these cases the day-long SO cost is the sum of the SO costs for the two peaks considered separately. However, this is not true in general – the solution obtained by combining the two single-period solutions can be infeasible. When this happens, the optimum day-long cost will exceed the sum of the single-period costs. The discrepancy is about 40% of the total schedule penalty for an example representing a large city. Thus, to develop realistic policies the day-long problem must be addressed head on. An approximate method that yields closed form formulas for the case with uniformly distributed wishes is presented.
Transportation Research Part B Methodological 09/2013; 55:98–117. DOI:10.1016/j.trb.2013.05.004 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Recently cities have been converting traditional one-way downtown street networks to two-way operation partly because one-way networks are seen as confusing and as less conducive to economic activity and a livable environment and they require vehicles to travel longer distances on average. However, one of the main disadvantages of such conversions is thought to be a reduction in the network's ability to serve vehicles. Intersections in two-way networks can serve fewer vehicles per unit time than their-one-way counterparts. Several studies have assessed the differences between these two types of networks, but most studies are site specific and do not consider the best possible two-way networks. This paper presents an analytical model that uses macroscopic analysis techniques to compare various one-way and two-way networks using their trip-serving capacities. This metric is a key indicator of network performance. Two-way networks can serve more trips per unit time than one-way networks when average trip lengths are short. This study also found that two-way networks in which left-turn movements were banned at intersections could always serve trips at a higher rate than one-way networks could, even long trips. Thus, the trip-serving capacity of a one-way network can actually be increased when it is converted to two-way operation if left turns are banned. In this way, livability and efficiency objectives can be achieved simultaneously. This framework can be used by planners and engineers to determine how much a network's capacity changes after a conversion, and also to unveil superior conversion options.
Transportation Research Record Journal of the Transportation Research Board 12/2012; 2301(-1):76-85. DOI:10.3141/2301-09 · 0.44 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In theory midblock presignals can be used to increase the capacity of signalized intersections [The authors define "presignal" as "a set of signal heads that are installed in the middle of a block upstream of an intersection."-Ed.]. The capacity is increased because presignals can reorganize how traffic is stored between a presignal and an intersection downstream. However, different vehicle classes have different acceleration characteristics, and the effectiveness of presignals hinges on the assumption of linear superposition; that is, the total time to discharge a mixture of distinct vehicle classes equals the sum of the times to discharge each vehicle class separately. This assumption has not been tested in the field. In this study, results from a natural experiment are used to validate the assumption for the case of cars and buses. The effectiveness of presignals to increase intersection capacity is also demonstrated.
Transportation Research Record Journal of the Transportation Research Board 12/2012; 2315(2315):191-196. DOI:10.3141/2315-20 · 0.44 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: This paper considers the optimization of public infrastructure systems, recognizing that these systems serve multiple user classes. Example application domains include: public transportation systems, electricity distribution grids, urban water distribution systems, and maintenance of pavement and bridge systems. Under the guidance of a policy-making body, the analyst chooses both the system design, including its layout and control, and the prices to be charged for the service. The goal of the optimization is to maximize society’s welfare recognizing that the system’s performance will in general depend on the system’s demand, and vice versa.The optimization problem is first formulated in its full complexity, where the prices, the demand and the system design are to be determined. It is then shown that if the user classes recognized in the analysis can be priced independently, and if the policy setting body specifies either the demand levels or the generalized prices experienced by each user group, then the resulting welfare maximization problem decomposes into three sub-problems that can be solved sequentially: demand estimation, system design and pricing. It also turns out that the optimum design can always be obtained by minimizing the generalized cost of the system to society for the known fixed demand, as is conventionally done in practice. The resulting design is independent of how net user benefits are measured and of the pricing scheme.If the policy-making body does not specify cost or demand targets, and instead assesses benefits by means of consumer surplus then the optimum design is still the solution of a conventional design problem with fixed demand. In this case, however, the demand has to be obtained iteratively using a marginal cost pricing rule.The paper finally shows how government can structure payments to a for-profit agency so it will be induced to design and operate the system optimally for society.
Transportation Research Part B Methodological 11/2012; 46(9):1288–1293. DOI:10.1016/j.trb.2012.06.005 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A model with few variables is said to be parsimonious. If it is also analytically tractable, physically realistic, and conceptually insightful, it is said to be effective. Effective parsimonious models have long been used in fields such as economics and applied physics to describe the aggregate behavior of systems as opposed to the behavior of their individual parts. In transportation, these models are particularly well suited to address big picture questions because they provide insights that might be lost when focusing on details. This paper presents an abbreviated history of effective parsimonious models in the transportation field, classified by sub-area: regional and urban economics, traffic flow, queuing theory, network dynamics, town planning, public transportation, logistics, and infrastructure management. The paper also discusses the benefits of these models—fewer data requirements, reduced computational complexity, improved system representation, insightfulness—and ways of constructing them. Two examples, one from logistics and one from urban transportation, are used to illustrate these points. Finally, the paper discusses ways of expanding the application of effective parsimonious models in the transportation field.
[Show abstract][Hide abstract] ABSTRACT: 8 shown, for example, in Figure 9a of the work by Geroliminis and Sun (7), Figure 2 of the work of Endo et al. (8), and Figure 8c of the work by Buisson and Ladier (9). This scatter was attributed largely to data included from periods during which parts of each freeway system were congested while other parts were not. Thus, the suffi-ciency condition for an MFD's existence was violated. Ji et al. also found that freeway data from multiple regimes contribute to the scat-ter observed in data plots (10). The data in that study were not mea-sured on real freeways but were instead generated from computer simulation. The present work proposes that the sufficiency condition of Daganzo can be generalized for freeway networks (3, 4). The new condition is that all lanes of all links throughout the network be either congested or uncongested, even if vehicle speeds vary con-siderably in time and space. (This is less stringent than the suffi-ciency condition previously proposed for surface street networks but still is not easily satisfied for large freeway systems.) It is shown with real and highly detailed trajectory data, and for a range of congested conditions, that well-defined relations arise for freeway stretches of moderate physical length if the new sufficiency con-dition is satisfied. These relations can also be observed with data from ordinary loop detectors, and the relations are found to be repro-ducible across many days. All this is shown to be true even for free-way stretches that comprise links with inhomogeneous geometries, including on ramps and off ramps with variable flows. THEORY This paper proposes that any freeway network with homogeneous but different links that include on ramps and off ramps has a triangular MFD that relates VHT to VKT, that this MFD is the outer envelope of all VHT versus VKT data pairs that are measured on the network, and that the data points lie near the triangular MFD when all lanes within the entire network are either congested or uncongested.
Transportation Research Record Journal of the Transportation Research Board 01/2012; 2260:8-15. · 0.44 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Through the use of a profit-maximizing continuum approximation model, this paper systematically analyzes the development and structure of informal transit systems as a function of the network, user, and modal characteristics. This study examines the evening commute problem along a linear corridor where passengers originate uniformly from a central business district and have destinations uniformly distributed along the corridor. Informal transit drivers who are profit-maximizing will be compared against the traditional case of coordinated, government service that aims to maximize the total welfare. Policies, such as fare regulation and vehicle licensing schemes, will be presented to help rationalize informal transit service using a government-operated service as the baseline.
Research in Transportation Economics 01/2012; 39(1). DOI:10.1016/j.retrec.2012.06.025
[Show abstract][Hide abstract] ABSTRACT: A simple symmetric network that consists of two tangent rings on which vehicles obey the kinematic wave theory of traffic flow and can switch rings at the point of tangency is studied. An online adaptive simulation reveals that if there is any turning whatsoever, the two-ring system becomes unevenly loaded for densities greater than the optimal density, and reduces traffic flow. Furthermore, the two-ring system jams at significantly lower densities than the maximum density possible.
Transportation Research Record Journal of the Transportation Research Board 12/2011; 2249(-1). DOI:10.3141/2249-03 · 0.44 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Macroscopic fundamental diagrams (MFDs), which relate the total time spent to the total distance traveled, are explored for freeway networks. It is proposed that these macrolevel relations should be observed if the data come from periods when all lanes on all links throughout the network are in either the congested or the uncongested regime. The theory pertains to freeway networks of any size, even when they are inhomogeneously congested and the data are variable in time. Analysis of vehicle trajectories from two freeway stretches of modest physical length supports this theory. Study further reveals that MFDs can be estimated with data from ordinary loop detectors, provided that every link in the network has at least one detector station and that the data are filtered to meet (approximately) the single-regime requirement. Detector data then confirm that well-defined MFDs exist for other freeway stretches and that the relations are reproducible across days. The results demonstrate that the stringent single-regime condition necessary to observe a freeway MFD does arise at times, even if only on shorter-length freeway stretches. The results also explain why previous efforts to observe freeway MFDs without filtering the data have been unsuccessful. Finally, the results suggest that policies to spread congestion evenly over a freeway network can be useful in maximizing the rate that trips are served.
Transportation Research Record Journal of the Transportation Research Board 12/2011; 2260(-1):8-15. DOI:10.3141/2260-02 · 0.44 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: As is well known, bus systems are naturally unstable. Without control, buses on a single line tend to bunch, reducing their punctuality in meeting a schedule. Although conventional schedule-based strategies that hold buses at control points can alleviate this problem these methods require too much slack, which slows buses. This delays on-board passengers and increases operating costs.It is shown that dynamic holding strategies based on headways alone cannot help buses adhere to a schedule. Therefore, a family of dynamic holding strategies that use bus arrival deviations from a virtual schedule at the control points is proposed. The virtual schedule is introduced whether the system is run with a published schedule or not. It is shown that with this approach, buses can both closely adhere to a published schedule and maintain regular headways without too much slack.A one-parameter version of the method can be optimized in closed form. This simple method is shown to be near-optimal. To put it in practice, the only data needed in real time are the arrival times of the current bus and the preceding bus at the control point relative to the virtual schedule. The simple method was found to require about 40% less slack than the conventional schedule-based method. When used only to regulate headways it outperforms headway-based methods.
Transportation Research Part B Methodological 12/2011; 45(10):1831-1845. DOI:10.1016/j.trb.2011.07.009 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: This paper presents and tests a method to design high-performance transit networks. The method produces conceptual plans for geometric idealizations of a particular city that are later adapted to the real conditions. These conceptual plans are generalizations of the hybrid network concept proposed in Daganzo (2010). The best plan for a specific application is chosen via optimization. The objective function is composed of analytic formulae for a concept‘s agency cost and user level of service. These formulae include as parameters key demand-side attributes of the city, assumed to be rectangular, and supply-side attributes of the transit technology. They also include as decision variables the system‘s line and stop spacings, the degree to which it focuses passenger trips on the city center, and the service headway. These decision variables are sufficient to define an idealized geometric layout of the system and an operating plan. This layout-operating plan is then used as a design target when developing the real, detailed master plan. Ultimately, the latter is simulated to obtain more accurate cost and level of service estimates.
Transportation Research Part A Policy and Practice 11/2011; 45(9):935-950. DOI:10.1016/j.tra.2011.04.006 · 2.79 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: This paper proposes a non-anticipative, adaptive, decentralized strategy for managing evacuation networks. The strategy is non-anticipative because it does not rely on demand forecasts, adaptive because it uses real-time traffic information, and decentralized because all the information is available locally. It can be used with a failed communication network.The strategy pertains to networks in which no links backtrack in the direction of increased risk. For these types of networks, no other strategy exists that can evacuate more people in any given time, or finish the evacuation in less time. The strategy is also shown to be socially fair, in the sense that the time needed to evacuate all the people exceeding any risk level is, both, the least possible, and the same as if less-at-risk individuals did not participate in the evacuation. The strategy can be proven optimal even when backflows happen due to driver gaming.Highlights► Considered are evacuation networks whose links point in the direction of decreasing risk. ► These networks can be optimally managed in real-time without demand information. ► The proposed strategy is adaptive and decentralized: it only uses locally available real-time data. ► The strategy is fair: all people within a given risk level are evacuated in the least possible time. ► The strategy works well even if people are allowed to choose their point of entry in real-time.
Transportation Research Part B Methodological 11/2011; 45(9):1424-1432. DOI:10.1016/j.trb.2011.05.015 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A separate turn phase is often used on the approach leg to an intersections with heavy left turns. This wastes capacity on the approach because some of its lanes cannot discharge during its green phases. The paper shows that the problem can be eliminated by reorganizing traffic on all the lanes upstream of an intersection using a mid-block pre-signal. If drivers behave deterministically, the capacity that can be achieved is the same as if there were no left turns. However, if the reorganization is too drastic, it may be counterintuitive to drivers. This can be remedied by reorganizing traffic on just some of the available lanes. It is shown that such partial reorganization still increases capacity significantly, even if drivers behave randomly and only one lane is reorganized. The paper shows how to optimize the design of a pre-signal system for a generic intersection. It also identifies both, the potential benefits of the proposed system for a broad class of intersections, and the domain of application where the benefits are most significant.
Transportation Research Part B Methodological 06/2011; 45(5):769-781. DOI:10.1016/j.trb.2011.02.009 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A simple model of traffic flow is used to analyze the spatio-temporal distribution of flow and density on closed-loop homogeneous freeways with many ramps, which produce inflows and allow outflows. As we would expect, if the on-ramp demand is space-independent then this distribution tends toward uniformity in space if the freeway is either: (i) uncongested; or (ii) congested with queues on its on-ramps and enough inflow to cause the average freeway density to increase with time. In all other cases, however, including any recovery phase of a rush hour where the freeway's average density declines, the distribution of flow and density quickly becomes uneven. This happens even under conditions of perfect symmetry, where the percentage of vehicles exiting at every off ramp is the same. The flow-density deviations from the average are shown to grow exponentially in time and propagate backwards in space with a fixed wave speed. A consequence of this type of instability is that, during recovery, gaps of uncongested traffic will quickly appear in the unevenly congested stream, reducing average flow. This extends the duration of recovery and invariably creates clockwise hysteresis loops on scatter-plots of average system flow vs. density during any rush hour that oversaturates the freeway. All these effects are quantified with formulas and verified with simulations. Some have been observed in real networks. In a more practical vein, it is also shown that the negative effects of instability diminish (i.e., freeway flows increase) if (a) some drivers choose to exit the freeway prematurely when it is too congested and/or (b) freeway access is regulated in a certain traffic-responsive way. These two findings could be used to improve the algorithms behind VMS displays for driver guidance (finding a), and on-ramp metering rates (finding b).
Transportation Research Part B Methodological 06/2011; 45(5):782-788. DOI:10.1016/j.trb.2011.02.001 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A recent study reported that the Macroscopic Fundamental Diagram of a medium size city exhibited a clockwise hysteresis loop on a day in which a major disturbance caused many drivers to use unfamiliar routes. It is shown below that, even in a perfectly symmetric network with uniform demand, clockwise loops are to be expected when there are disturbances, especially if the disturbances cause a significant fraction of the drivers to not change routes adaptively. It is also shown that when drivers are not adaptive networks are inherently more unstable as they recover from congestion than as they are loaded. In other words, during recovery congestion tends more strongly toward unevenness because very congested areas clear more slowly than less congested areas. Since it is known that uneven congestion distributions reduce network flows, it follows that lower network flows should arise during recovery, resulting in clockwise loops. Fortunately, the presence of a sufficient number of drivers that choose routes adaptively to avoid congested areas helps to even out congestion during recovery, increasing flow. Thus, clockwise loops are less likely to occur when driver adaptivity is high.
Transportation Research Part B Methodological 05/2011; 45(4):643-655. DOI:10.1016/j.trb.2010.11.006 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: This chapter summarizes recent findings on the bullwhip effect in decentralized multi-echelon supply chains based on a system-control
approach. The influence of the supply chain operation (e.g., ordering policy and lead time) is separated from that of the
customer demand. Robust results that hold for any customer demand are derived for both deterministically and stochastically
operated chains. We demonstrate the importance of robust analysis. It is shown that instability is an inherent property of
the system, e.g., of the ordering policies used by the suppliers, but it is independent of customer demand. We first present
analytical stability conditions for deterministically operated chains. The demand can be arbitrary and random. These chains
are modeled and their stability is evaluated in the frequency domain. We unify some techniques used in the literature, and
present analytical results with or without the knowledge of customer demand. We also allow additional randomness to arise
from unpredictably varying factors in the operating environment, such as supplier behavior and transportation lead times.
We then develop linear matrix inequality stability conditions to predict the bullwhip effect and bound its magnitude. Examples
are shown for both types of chains. We also show the effect of advance demand information on the bullwhip effect.