Showing papers in "Transportation Research Part B-methodological in 1993"
TL;DR: In this paper, it is shown how a formal solution for A ( x, t ) can be evaluated directly from boundary or initial conditions without evaluation at intermediate times and positions, and the correct solution, which is the lower envelope of all such formal solutions, will automatically have discontinuities in slope describing the passage of a shock.
Abstract: In the theory of “kinematic waves,” as described originally by Lighthill and Whitham in 1955, the evaluation of the shock path is typically rather tedious. Instead of using this theory to evaluate flows or densities, one can use it to evaluate the cumulative flow A ( x , t ) past any point x by time t . It is shown here how a formal solution for A ( x, t ) can be evaluated directly from boundary or initial conditions without evaluation at intermediate times and positions. If there are shocks, however, this solution will be multiple-valued. The correct solution, which is the lower envelope of all such formal solutions, will automatically have discontinuities in slope describing the passage of a shock. To evaluate A ( x, t ) at any particular location x , it is not necessary to follow the actual path of the shock. The solution can be evaluated directly in terms of the boundary data by either graphical or numerical techniques.
834 citations
TL;DR: In this article, the authors proposed a method to relate the cumulative flow curve at any junction to the net cumulative entrance flow at this junction, and the cumulative curve for the freeway at the next upstream junction and/or the next downstream junction.
Abstract: For a freeway having various entrance and exit ramps, the methods described in Part I are used to relate the cumulative flow curve at any junction to the net cumulative entrance flow at this junction, and the cumulative flow curves for the freeway at the next upstream junction and/ or the next downstream junction. If the type of flow-density relations typical of freeway traffic are idealized by a triangular shaped curve with only two wave speeds, one for free-flowing traffic (positive) and the other for congested traffic (negative), then the relationship is easy to evaluate. The cumulative flow curve at the junction is simply the lower envelope of a translation of the cumulative curve from upstream and a different translation of the cumulative curve from downstream. This relationship is the basic building block for a freeway flow prediction model described in Part III.
547 citations
TL;DR: In this paper, handling and storage strategies for export containers at marine terminals were described and quantified according to the amount of space and number of handling moves they require, and the optimal strategy was identified.
Abstract: This paper describes handling and storage strategies for export containers at marine terminals and quantifies their performance according to the amount of space and number of handling moves they require. Identifying a “best” strategy is complicated because the optimization problem is combinatorial in nature—strategies are characterized, among other things, by the order in which future ship arrivals claim preferential space in the storage area. Given a certain traffic, the paper first examines the minimal storage space needed to implement the recommended strategies. This analysis may be of use for long-term planning, helping, for example, with the selection of a handling technology, site locations, or proposed service expansions. At the operational level (i.e. for a given traffic and amount of storage space), the paper also describes how to minimize and predict the amount of handling work.
200 citations
TL;DR: In this article, the authors present methods for measuring the amount of handling effort required when two basic strategies are adopted, one that tries to keep all stacks the same size and another than segregates containers according to arrival time.
Abstract: Many types of storage systems require goods to be stacked in a storage area. The amount of handling effort required to retrieve individual items from the stacks depends on stack heights and on the adopted storage strategy. The paper focuses on container import operations at marine terminals. It presents methods for measuring the amount of handling effort required when two basic strategies are adopted, one that tries to keep all stacks the same size and another than segregates containers according to arrival time. The strategies are compared in an idealized situation. The methods should be easy to modify for the analysis of similar systems.
189 citations
TL;DR: It is proved that if this model is used to find route costs then a dynamic user equilibrium exists and a descent algorithm is suggested; there is, as yet, no proof that the algorithm converges to an equilibrium.
Abstract: This paper presents a new dynamic model of peak period traffic flows on congested capacity-constrained urban road networks. While respecting the first in, first out (FIFO) discipline of road traffic queues and the exit capacities of road links, the model determines the (time-varying) costs incurred in traversing the various routes when (time-varying) route inflows are specified. It is proved that if this model is used to find route costs then a dynamic user equilibrium exists. The paper also gives four optimisation formulations of the dynamic user equilibrium problem. A descent algorithm is suggested; there is, as yet, no proof that the algorithm converges to an equilibrium. Finally, the paper introduces a family of alternative methods of determining dynamic flows which (almost) satisfy FIFO, and specifies one member of this family in some detail. These alternative methods arise as a consequence of using different ways of specifying the priority of a vehicle or a group of vehicles.
181 citations
TL;DR: To solve the problem of determining the cumulative flows past various points of the freeway, trip times, etc, one must combine the equations of traffic dynamics for the total flow (for all origins and destinations) with equations specifying that the trip time of a vehicle between two successive junctions is independent of its origin or destination.
Abstract: Suppose that one specifies the times at which vehicles enter each freeway junction and where (but not when) they will exit. The problem is to determine the cumulative flows past various points of the freeway, trip times, etc. To solve this problem, one must combine the equations of traffic dynamics for the total flow (for all origins and destinations) as described in Part II, with equations specifying that the trip time of a vehicle between two successive junctions is independent of its origin or destination. One must evaluate not only the total flow past each point but the component flows past each point for each destination. A solution of this problem based on the theory in Part II is fairly straightforward.
158 citations
TL;DR: The viability of using cross-correlation techniques with inductance loop data to measure the propagation time of traffic is demonstrated and can be used to improve the volume/occupancy ratio estimate of speed from single loops.
Abstract: This paper demonstrates the viability of using cross-correlation techniques with inductance loop data to measure the propagation time of traffic. The propagation time between loops separated by 0.5 miles is measured by using time-average activation counts (“volume”) from inductance loops. The resulting time delay is used to estimate the mean speed. This independent speed estimate can be used to improve the volume/occupancy ratio estimate of speed from single loops.
152 citations
TL;DR: The existing high-order models are reviwed and discussed, and a new formulation is proposed which does not require the use of an equilibrium speed-density relationship, which suggests that the proposed mode is more accurate and computationally more efficient.
Abstract: This paper investigates advanced continuum models for describing traffic dynamics at congested flows. First, the existing high-order models are reviwed and discussed, and a new formulation is proposed which does not require the use of an equilibrium speed-density relationship. (A model is of high-order when it includes both mass and momentum conservation.) Traffic friction at interrupted flows and changing geometries is also addressed through the use of a viscosity term. The model is then discretized through two alternative numerical schemes to examine the effectiveness of the implementation. Stability analysis is performed to set up numerical limits of the model parameters. Finally, in two test cases with congested and uncongested field data, the new model is compared with the existing models; this comparison suggests that the proposed mode is more accurate and computationally more efficient.
124 citations
TL;DR: In this article, an accessibility index that captures the overall transportation access level of an area is proposed, which is formulated as a natural extension of the existing relative and integral accessibility measures.
Abstract: This paper constructs an accessibility index that captures the overall transportation access level of an area. This index is formulated as a natural extension of the existing relative and integral accessibility measures. Theoretical modelling and empirical tests demonstrate that the index has a convergence property and can be calculated accurately without incurring very high costs. Regression analyses show that the index captures the overall accessibility levels of areas very well. Using this index, the overall access levels of the sixty largest U.S. metropolitan areas are calculated.
121 citations
TL;DR: In this paper, a delay model for signalized intersections that is suitable for variable demand conditions is proposed, which is applicable to the entire range of expected operations, including highly oversaturated conditions with initial queues at the start of the analysis period.
Abstract: This paper proposes a delay model for signalized intersections that is suitable for variable demand conditions. The model is applicable to the entire range of expected operations, including highly oversaturated conditions with initial queues at the start of the analysis period. The proposed model clarifies several issues related to the determination of the peak flow period, as well as the periods immediately preceding and following the peak. Separate formulas are provided for estimating delay in each of the designated flow periods as well as in the total flow period. Formulas are also provided to estimate the duration of the oversaturation period where applicable. The strength of the model lies in the use of simple rules for determining flow rates within and outside the peak, using the peak flow factor, a generalization of the well-known peak hour factor parameter. Simple rules are also provided for the identification of the location and duration of the peak flow period from observations of the demand profile. Such information is considered vital from an intersection design and evaluation viewpoint. Application of the model to a variety of operating conditions indicates that the estimated delay for vehicles arriving in the peak flow period is an acceptable predictor of the average delay incurred during the total flow period, even when oversaturation persists beyond the total flow period. On the other hand, the use of the average degree of saturation with no consideration of peaking can lead to significant underestimation of delay, particularly when operating at or near capacity conditions. These findings were confirmed by comparing the model results with other models found in the literature. The significant contribution of this work is not simply in the development of improved delay estimates, but, more important, in providing an integrated framework for an estimation process that incorporates (a) the peaking characteristics in the demand flow pattern, (b) the designation of flow-specific periods within the total flow period in accordance with the observed peaking and (c) the estimation of performance parameters associated within each flow period and in combination with other periods. A revised delay formula for the U.S. Highway Capacity Manual (HCM) is proposed. The revised formula has no constraints on the peak flow period degree of saturation, unlike the current HCM formula. It is also recommended that a simple formula for estimating the duration of oversaturation be used in conjunction with the revised delay formula.
89 citations
TL;DR: In this article, the authors describe the estimation of a nested logit model of parking location choice using revealed preference data, which concerned the behavior of drivers going to work in a central business district.
Abstract: This paper describes the estimation of a nested logit model of parking location choice using revealed preference data. These data concerned the behavior of drivers going to work in a central business district. The model's nested structure acknowledges the relatively greater similarity among off-street and among on-street alternatives on their own. Each individual parking facility and surface lot is represented as a distinct off-street alternative. Areas of on-street parking constitute on-street alternatives. Special parking provided by employers is also represented separately. A variety of attributes other than money cost and separation from final destination were considered for the model's utility functions. Both the proposed nested structure and the inclusion of measures representing various attributes other than money cost and separation from final destination were found to be appropriate.
TL;DR: In this paper, a joint decision-making approach to minimize the sum of inspection and maintenance and rehabilitation (M&R) costs is presented, and the effect of forecast uncertainty on the minimum expected costs produced by each of them is investigated empirically.
Abstract: Pavement management systems need to address not only maintenance and rehabilitation (M&R) decisions, but also facility inspection decisions. The state of the art in pavement management is lacking of any consistent methodology for making such decisions on a cost-effectiveness basis. Such a methodology must recognize the presence of interactions between M&R and inspection decisions. These interactions argue for a joint decision-making approach, where the sum of inspection and M&R costs is minimized. This paper reviews different possible mathematical formulations to such a joint decision-making model, having various levels of restriction and computational complexity. These formulations are then compared and the effect of the forecast uncertainty on the minimum expected costs produced by each of them is investigated empirically. It is concluded that optimizing inspection decisions jointly with M&R decisions can lead to substantial cost savings, especially for high precisions of forecasting.
TL;DR: A rapid computational method of optimal control for vehicles and the software realizing it is described, finding that one can travel up to 20 to 80% faster than the most economical average speed without increasing fuel consumption more than an equal amount.
Abstract: This paper describes a rapid computational method of optimal control for vehicles and the software realizing it. The optimal control problem is solved with the dynamic programming technique. A traditional engineering simulator is used to predict the vehicle's performance and economy. An objective function is suggested that permits high-speed computation. Results show the dependence of optimal fuel consumption on average speed for various vehicle masses in a number of situations: acceleration from rest to cruising speed, driving between stop signs and driving on hilly terrain. Findings include that one can travel up to 20 to 80% (depending on the situation) faster than the most economical average speed without increasing fuel consumption more than an equal amount.
TL;DR: In this paper, a mathematical model of the management of a fleet of cars shared by autonomous profit maximizing managers faced with time-varying demands requiring shared service responsibility is presented.
Abstract: The paper presents the development and solution procedures of a mathematical model of the management of a fleet of cars shared by autonomous profit maximizing managers faced with time-varying demands requiring shared service responsibility. Motivation for the model development arises from the freight car management problem, in which many railroads independently manage an interchangeable fleet of cars that serve customers with time-dependent origin-destination patterns; this often requires the cooperative service of more than one railroad. The problem is formulated as an N -person, noncooperative game played on a temporal-spatial network. An iterative sequential procedure is developed for which car management decisions for each railroad over a specified time horizon are based on the previously calculated optimized decisions of car management decisions for all other railroads. Several realistic test case problems are reported that exhibit rapid convergence to an equilibrium solution. It is proposed that this modeling procedure be used as a basis for evaluating (and possibly generating optimal) interrailroad agreements for the exchange of empty freight cars.
TL;DR: In this paper, the nature of non-user insider benefits, particularly from job-creation, is discussed, while gains and losses to outsiders are ignored in an open-economy cost-benefit analysis.
Abstract: In a “closed-economy” cost-benefit analysis of a public investment, all affected economic agents matter. In such an analysis, if price equals marginal cost in all affected markets, accurately measuring benefits requires looking only at the use made of the improvement; “non-user” costs and benefits cancel out. Only if price is unequal to marginal cost in affected markets do unduplicated net nonuser benefits and costs exist. In an “open-economy” cost-benefit analysis, gains and losses to outsiders are ignored. The nature of nonuser insider benefits, particularly from “job-creation”, is discussed.
TL;DR: The paper deals specifically with the bus operators submodel, for which several algorithms are proposed to find equilibrium solutions, and various methods to deal with the problem posed by limited bus capacities.
Abstract: We study urban traffic equilibrium involving three classes of agents: car users, bus users or passengers and bus operators. A partially unregulated transit system is assumed, where bus fares are exogenously determined by municipal or transportation authorities, but bus operators are allowed to choose the routes where they offer service. The paper deals specifically with the bus operators submodel, for which several algorithms are proposed to find equilibrium solutions. Convergence properties of the proposed algorithms are analyzed and computational results, on both small test networks and the Santiago de Chile urban transit network, are reported. Various methods to deal with the problem posed by limited bus capacities are discussed.
TL;DR: In this paper, a trip distribution/assignment model is developed, which includes an endogenous destination cost for the conduct of a given activity at the destination, which is determined endogenously, as increasing functions of the number of trips to the destination.
Abstract: A “user-equilibrium” trip distribution/assignment model is developed, which includes an endogenous destination cost for the conduct of a given activity at the destination. Destination costs are determined endogenously, as increasing functions of the number of trips to the destination. Link travel costs are increasing functions of link volumes. Travelers are assumed to choose the itinerary of deterministically perceived least cost. Activity performers are assumed to choose among alternative destinations so as to minimize the randomly perceived total cost of activity and travel. It is shown that the model always possesses a unique solution, when destination costs reflect either positive or negative externalities. An algorithm for obtaining that solution is described. The model is well suited to the analysis of a variety of issues concerning the effects of road pricing policies on urban travel demand and, conversely, of toll-based traffic management strategies on economic performance.
TL;DR: The representation of the response to a change in transport costs is analyzed for three integrated land-use transport models in terms of such topics as modal choice, locational choice, car ownership and the effects on the location of physical infrastructure.
Abstract: It is widely accepted that there is a two-way relationship between land use and transport. The effects of land use on transport can be modeled at both aggregate and disaggregate levels using well-established methodologies. However, there is no established representation of the converse relationship. A number of models exist that represent this two-way relationship, and many of them have been compared within the research program of the International Study Group on Land-Use Transport Interaction (ISGLUTI). However, the results from that work suggest not only that many mechanisms represent the linkages, but also that their dynamic behavior is not well understood. This paper focuses on the analysis of these mechanisms, drawing on experience from the ISGLUTI study. The representation of the response to a change in transport costs is analyzed for three integrated land-use transport models in terms of such topics as modal choice, locational choice, car ownership and the effects on the location of physical infrastructure.
TL;DR: A normative transshipment problem for freight flows over a multimodal network, in which an origin/destination matrix which corresponds to the minimal cost flows must be computed as well is considered.
Abstract: We consider a normative transshipment problem for freight flows over a multimodal network. In addition to computing the flows, which minimize a convex cost objective function, an origin/destination matrix which corresponds to the minimal cost flows must be computed as well. The supply is given as totals at origins and the demand as totals at destinations. We formulate the problem and propose an algorithm for its solution. Finally, we describe an application carried out with data for the transportation of coal in Finland.
TL;DR: This paper compares rectilinear distance transportation costs for hub networks with two types of demand to investigate how well an idealized model predicts the cost for real-world demand.
Abstract: Hub and spoke designs have been adopted by many air carriers and motor carriers in recent years. This paper compares rectilinear distance transportation costs for hub networks with two types of demand to investigate how well an idealized model predicts the cost for real-world demand. The idealized model approximates the transportation cost for a hub network serving a continuous uniform distribution of demand in a square service region with equal origin-destination flows. The cost for the approximation formula is compared to the optimal cost for discrete demand hub location problems. The ability of the approximation formula to predict the optimal transportation cost is measured, and the quality of the prediction is related to characteristics of the discrete demand.
TL;DR: In this article, a flexible assignment approach is proposed to assign some seats exclusively to each single- or multi-leg itinerary as in fixed assignment and assign the remaining seats to groups of itineraries as in bucket control.
Abstract: This paper proposes a new approach to the optimal allocation of airline seats among itineraries in a network under stochastic demand. Current approaches to network seat inventory control are based on either full assignment or bucket control. Under full assignment, all seats on each flight leg are assigned to a specific single- or multi-leg itinerary. Under bucket control seats are assigned to groups of itineraries. The flexible assignment approach proposed in this paper assigns some seats exclusively to each single- or multi-leg itinerary as in fixed assignment and assigns the remaining seats to groups of itineraries as in bucket control. This paper formulates the flexible assignment approach, develops rules for optimal assignment for a single-fare-class network and proves the superiority of this approach to either fixed assignment or bucket control. A numerical simulation is ised to illustrate the differences in expected revenue among these three methods of seat inventory control for four different demand scenarios.
TL;DR: The problem of finding maximum entropy link uses (MELU) formulated herein is a multi-commodity optimum flow (max-flow at min-cost) problem with nonlinear flow-dependent link use costs.
Abstract: This paper formulates the problem of finding the most likely distribution of origin-destination (O-D) specific link volumes (called “link uses”) from equilibrium assignment. Although an equilibrium assignment is unique in terms of aggregate link volumes, trips between different O-D pairs assigned to alternative paths between any node pair can be swapped among these paths such that total link volumes remain unchanged. Alternative link uses that yield identical aggregate link volumes can affect O-D specific estimates of fuel consumption, pollution emissions or development impacts. Equilibrium assignments found by methods of linear combinations, such as the Frank-Wolfe algorithm, may not represent most likely link uses. The problem of finding maximum entropy link uses (MELU) formulated herein is a multi-commodity optimum flow (max-flow at min-cost) problem with nonlinear flow-dependent link use costs. MELU does not require path enumeration or knowledge of used paths between zones, but it is NP-hard to solve and very sizable for large networks. An approximate solution technique is presented that finds likely link uses for realistic size problems. The method is to linearly combine successive F-W solutions using step sizes that seek a maximum entropy mix. The examples include other comparisons of trial link uses that indicate the extent to which they differ.
TL;DR: In this paper, the authors developed generalized newsboy models for minimizing the expected sum of costs and penalties in a typical hub airport, where incoming flights from many origins feed outgoing flights to equally many destinations.
Abstract: In a typical hub airport, incoming flights from many origins feed outgoing flights to equally many destinations. If an incoming flight is late, outgoing flights that are fed by it may also be delayed. Alternatively, aircraft may leave before some feeding flights arrive, thereby incurring high misconnection penalties. By optimizing the scheduled ground time of each plane, we can minimize the expected sum of costs and penalties. In this paper we develop generalized newsboy models for this purpose. In particular, we investigate in detail a pure-waiting model in which no misconnections are allowed and discuss a no-waiting model in which aircraft that are ready to leave never wait for late-feeding flights. The models show that to maximize the system level of service at a given cost, the level of service of individual flights should be allowed to vary. The models can also be applied to similar problems such as express parcel deliveries and ground transportation hubs. The problems we address are nonlinear and highly combinatorial, so for life-size problems it is not practical to solve them to optimality. Therefore, an important part of the paper is devoted to heuristic solutions and the promising numerical experience achieved with them.
TL;DR: In this article, a link cost function is developed that incorporates a linear and an integer term, the latter representing excess cost due to incomplete utilization of vehicle capacity, and the model accounts for sorting and fixed costs at terminals.
Abstract: Local area freight networks (LANs) are used to collect and distribute freight within metropolitan regions. This paper classifies LAN topologies, then shows how the optimal topology for a common carrier depends on demand characteristics. A link cost function is developed that incorporates a linear and an integer term, the latter representing excess cost due to incomplete utilization of vehicle capacity. Continuous space models are used to approximate transportation distance. In addition, the model accounts for sorting and fixed costs at terminals. The star topology is found to be most attractive when a large proportion of shipments are external (i.e. originate or are destined outside the region), when many pickup and delivery routes are needed to distribute freight and when shipments are small. The best examples of systems with these characteristics are postal services. The complete topology is most attractive when shipments are large and primarily internal, as in many less-than-truckload (LTL) trucking companies.
TL;DR: In this paper, a model of competition between public transport services operating on a single route is developed and its properties explored analytically and numerically, and the sensitivity of the equilibrium configurations to changes in the parameters characterizing the demand for and cost of service provision is explored in a series of numerical studies.
Abstract: A model of competition between public transport services operating on a single route is developed and its properties explored analytically and numerically. The passenger demand function incorporates both substitution between services, expressed through a multinomial logit model, and elastic demand for the public transport market as a whole. Each operator is assumed to maximize its net revenue. Expressions are derived for the Nash-Cournot equilibrium fares and frequencies, which determine the resultant profits to suppliers and consumer benefits to users. The sensitivity of the equilibrium configurations to changes in the parameters characterizing the demand for and cost of service provision is explored in a series of numerical studies. The equilibrium analysis allows explicit conclusions to be drawn about the determinants of market concentration and the emergence of monopolies.
TL;DR: The paper shows that, conditional on a transportation schedule, lot sizes for the different items can be determined separately across items and independently for each store, suggesting the need for practical routing and inventory control procedures that recognize handling explicitly.
Abstract: This paper presents a handling cost model for a warehouse that supplies one or more stores with a large number of items and examines operating strategies whose objective is to minimize the sum of handling, transportation and inventory costs. Decisions must be made regarding the frequency of shipments to the store(s) (i.e. the transportation schedule) and the specific items and lot sizes included in each shipment. The paper shows that, conditional on a transportation schedule, lot sizes for the different items (i.e. their delivery frequency consistent with the transportation schedule) can be determined separately across items and independently for each store. The paper also examines how these lot sizes and the best transportation schedule can be identified. The results, unlike those of other inventory models such as the economic order quantity (EOQ) model, exhibit peculiarities caused by the nonsmooth nature of handling costs. For example, the optimal lot size for individual items sent to a specific store is not a continuous function of the value or size of the items. This suggests the need for practical routing and inventory control procedures that recognize handling explicitly.
TL;DR: In this paper, an extensive evaluation of alternative estimation methods for logistic binary choice probabilities when applied to binary frequency data with limit cases is presented, and the results indicate that the binomial logistic (BL) model is a practical tool that outperforms all the other methods examined in this study.
Abstract: An extensive evaluation of alternative estimation methods for logistic binary choice probabilities when applied to binary frequency data with limit cases is presented in this paper. The methods examined are binomial-logistic (BL) model, Berkson's (BK) method, and Haldane's (HL) method. These models are applied to weekly mode choice data that contained a substantial number of limit cases in which one of the alternatives was never chosen. The results indicate that the BL model is a practical tool that outperforms all the other methods examined in this study. The BL models accommodate limit cases without requiring any additional assumptions or approximations. The BK and HL methods have been shown to offer coefficient estimates similar to, and fits that are somewhat worse than, those obtained by the BL models. These methods remain to be useful tools for the analysis of binary frequency data, especially in initial phases of analysis. In this paper it is also shown that coefficient estimates of HL methods are sensitive to the value of the adjustment constant, Δ, used to incorporate limit cases, and its optimal value may depend on the data at hand.
TL;DR: A new mathematical formulation is proposed for the problem of optimal traffic assignment in dynamic networks with multiple origins and destinations that avoids complete microscopic detail by grouping vehicles into platoons irrespective of origin node and time of entry to network.
Abstract: We propose a new mathematical formulation for the problem of optimal traffic assignment in dynamic networks with multiple origins and destinations. This problem is motivated by route guidance issues that arise in an Intelligent Vehicle-Highway Systems (IVHS) environment. We assume that the network is subject to known time-varying demands for travel between its origins and destinations during a given time horizon. The objective is to assign the vehicles to links over time so as to minimize the total travel time experienced by all the vehicles using the network. We model the traffic network over the time horizon as a discrete-time dynamical system. The system state at each time instant is defined in a way that, without loss of optimality, avoids complete microscopic detail by grouping vehicles into platoons irrespective of origin node and time of entry to network. Moreover, the formulation contains no explicit path enumeration. The state transition function can model link travel times by either impedance functions, link outflow functions, or by a combination of both. Two versions (with different boundary conditions) of the problem of optimal traffic assignment are studied in the context of this model. These optimization problems are optimal control problems for nonlinear discrete-time dynamical systems, and thus they are amenable to algorithmic solutions based on dynamic programming. The computational challenges associated with the exact solution of these problems are discussed and some heuristics are proposed.
TL;DR: In this paper, the authors defined the index of spatial concentration as the maximum cumulative proportion of trips that are directly linked to a set of selected nodes, and the curve connecting the indexes of incremental nodes is approximated by the Gompertz function.
Abstract: The index of spatial concentration is defined as the maximum cumulative proportion of trips that are directly linked to a set of selected nodes. The curve connecting the indexes of incremental nodes is approximated by the Gompertz function. Estimated parameters of the function can be used to evaluate the spatial concentration of airline travel demand. The origin-destination data of airline traffic among 30 American cities in 1985 were examined in a case study.
TL;DR: In this paper, it is shown that only two equilibrium saddle points can be reached, one stable and the other unstable, and that traffic planning and control measures such as drastically increased metering and/or a metropolitan rail transit alternative must be in place so as to maintain equilibrium.
Abstract: Anthony Downs's (1962) traffic congestion analysis is given a generalized theoretical foundation. It is demonstrated that only two equilibrium saddle points—one stable, the other unstable—can be attained. Once the stable equilibrium is reached, traffic planning and control measures such as drastically increased metering and/or a metropolitan rail transit alternative must be in place so as to maintain equilibrium. If not, the expressway system eventually reaches gridlock. It is also shown that the analyses of Thomson (1977) and Mogridge (1986) parallel Downs's analysis and lead to the same conclusion.