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The Operations Research Society of America/Transportation Science Section's (ORSA/TSS) Workshop "Automated Techniques for Scheduling of Vehicle Operators for Urban Public Transportation Services," seals with the development and application of automated techniques for the scheduling of vehicle operators for urban public transportation services. The Urban Mass Transportation Administration, American Transit Association, and Union Internationale des Transports Publics are cooperating with ORSA/TSS to assure the workshop's success. Authors are invited to propose papers dealing principally with the following areas, heuristic and mathematical programming approaches to the assignment of vehicle operators; strategies for crew rotation schedules; interactive computer methods; reviews of implementations of automated scheduling systems; costs and benefits of automated techniques; and comparisons with manual scheduling techniques. Short abstracts should reach by November 1, 1974 and full manuscripts by January 1, 1975.

The paper presents a mathematical investigation into bus scheduling. The passenger arrival rate is supposed to be given; the problem is to determine the bus departure rate as a function of time. The primary objective is to minimize the number of buses that is needed. A secondary criterion is the minimization of the passenger waiting time, for which a calculus of variation technique is used. Although the paper deals mainly with a single busroute, it is also shown how the theory can be extended to the case of a pair of linked busroutes. The practical implications are illustrated by an example. The fleetsize formula that is used here is thought to be applicable to many transportation systems. [ABSTRACT FROM AUTHOR]

In a recent paper a traffic assignment model has been constructed in which the cost on a link may depend not only on its load, but also on the loads on other links of the network. In this paper it is shown that this model is also capable of handling the case of several classes of users in the same transportation network each of which has an individual cost function and, at the same time, contributes to its own and other classes' cost functions in an individual way. Typical applications arise not only in street networks where vehicles of different types share the same roads (e.g., trucks and passenger cars) but also in other types of transportation networks (e.g., telephone networks). An algorithm is constructed for finding the system-optimizing flow pattern for such a multiclass-user transportation network. [ABSTRACT FROM AUTHOR]

This paper presents a generalized analysis of the effects of on-ramp time varying flow on unidirectional n-lane freeways. The analysis incorporates the speed-density relations for every lane, which are then used to set up separate continuity equations for every lane and are coupled by some reasonable lane-changing hypotheses. The paper assumes the same wave velocities (uniform freeway) for the perturbed flow in each lane of a freeway. Using the generalized n-lane analysis, the paper then predicts the relative propagation of density perturbations in time and space in different lanes of a two-lane, three-lane, and four-lane freeway. The corresponding relaxation distances from the on-ramp, where the initial perturbation had started, have been defined and compared for the two-lane, three-lane, and four-lane freeway. The above studies have then incorporated the effects of con- trolled ramp flow by suitable mathematical expressions that simulate controlled ramp flow. [ABSTRACT FROM AUTHOR]

The article presents a paper, which shows how to determine the optimal number and routings of containers used to move mail among several cities. This paper extends the above system to more than two cities, with different schedules on different days and with transfer of containers permitted throughout the system. A mathematical formulation is developed that can be readily solved by known linear programming techniques. Critical assumptions are (a) periodic demand patterns and linear transportation costs between each city-pair, and (b) constant fixed cost per container in the system. The optimization problem is transformed into a network flow linear program for which efficient solution methods are known. The researchers have investigated a system where containerized mail would be sent between two cities. The problem solved in reference was that of determining the best number of containers to be sent each day between the two cities, based on (a) the distribution of mail volumes going between the cities each day and (b) the costs for sending containers, full or empty, and for sending mail by other means in case of container shortage. Thus the original convex programming problem has been converted to an especially tractable type of linear program, namely the optimization of a network flow.

In a previous paper, APPELGREN (1969), a decomposition algorithm for a class of vessel scheduling problems was presented. In some problems, the algorithm gives fractional solutions that cannot be interpreted as feasible schedules. This paper treats two integer programming methods that can be used to resolve these cases. The cutting plane method that was first tested was abandoned because it was not able to solve all the test problems. The second method is a branch-and- bound algorithm, where the branching is performed on one of the `essential' fractional variables and where the bounds are obtained by the decomposition algorithm. All fractional problems that have been found by simulation or in regular use of the algorithm have been solved, mostly with one branching only. There are fundamental difficulties in combining these integer programming methods with the DANTZIG-WOLFE decomposition, since the constraints generated in the master program have to be taken into account in the solution of the subprograms. The success in this case is due to the simple structure of the master LP problem. [ABSTRACT FROM AUTHOR]

The longitudinal vehicle control problem associated with any automated transportation scheme is discussed. The two fundamental aspects of the problem are the logical aspect and the control aspect. The logical aspect of the problem concerns the decision of where vehicles should be at a future time, based on present system conditions, so that the level of service delivered by the system is good. The control aspect is concerned with how to control vehicles to attain and maintain their desired positions while giving a comfortable ride, not taking too long, not exceeding car capabilities, and maintaining safety. Previous work dealing with both the logical and control aspects of the longitudinal vehicle control problem is briefly reviewed. One approach to handling the logical aspects of the merging problem in automated systems assumes that vehicles occupy positions on a guideway within hypothetical 'cells' that move at a constant velocity. This approach simplifies the logical aspect of the longitudinal control problem. The problem of controlling vehicles to attain and maintain an assigned cell on a guideway is modeled in the paper as a linear state regulator optimal control problem. The resulting vehicle control scheme requires less information feedback than alternative schemes, and exhibits good vehicle response characteristics. Alternative control strategies that lead to optimal control problems other than the linear state regulator are discussed, and the relative advantages of the scheme presented in the paper are pointed out. [ABSTRACT FROM AUTHOR]

This paper presents the motivation for the construction of a digital computer simulation of the American military's strategic airlift system, the author's analysis of that system preparatory to the simulation design, and the currently anticipated application of the model to studies of strategic mobility. Emphasis is placed on the estimation of the airlift productivity function for its subsequent utilization in appropriate strategic mobility models employed by the Joint Chiefs of Staff and by the Office of the Assistant Secretary of Defense (Systems Analysis). Those variables suspected of being primary contributors to gains in marginal airlift productivity are delineated in a description of the modules constituting the model. Finally, a sketch of an hypothetical experimental design, permitting the systems analyst to specify sequentially model iterations so as to obtain valid statistical estimates of desired marginal productivities, serves as a conclusion to the paper. [ABSTRACT FROM AUTHOR]

This paper investigates the welfare implication of changes in the transportation system in two special areas. The first is when the origin-destination demand for transportation may be assumed to be fixed and the second case is where, considering only work trips, origins may vary but destinations may not. A technique is described that could be used to forecast the new origin-destination demand resulting from a change in the transportation system. The technique also provides an appropriate measure of the welfare implications. A particular objective of the paper is to point out the pitfalls of using transportation (generalized) cost saving as a welfare measure whenever origin-destination demand may not be assumed fixed. In this situation it is shown that the welfare measure must take into consideration the benefit derived from the increased choice in available housing sites. [ABSTRACT FROM AUTHOR]

A wide range of signal switching policies may be adopted for control of traffic flow between a pair of intersections. One of the most import,ant traffic situations is that in which rush-hour commuter traffic travels towards or away from a city center along radial roads. Under these circumstances opposing and tangential flow may be light. Earlier papers have shown that a modified form of the Dunne-Potts switching policy might be applied to pairs of intersections carrying commuter flow. Efficient and flexible operation of the system under a wide variety of flow conditions, and with the minimum of computer surveillance, was demonstrated. The present paper reports the results of further simulation experiments and discussed tentative solutions of some of the practical problems associated with the proposed scheme. [ABSTRACT FROM AUTHOR]

In two papers by C. J. ANCKER, JR., A. F. GAFARIAN, AND R. K. GRAY, the structure of the headways at the passage of an oversaturated signalized intersection were studied. The statistical analysis performed by these authors seems to confirm the hypothesis that these headways are independent random variables. In this paper we consider the following simple model. Let the spacings and reaction times of the vehicles stopped at the intersection all be independent and let the trajectory relative to the start position and start time be the same for all stopped vehicles. It is shown that the head- ways at the intersection are independent if and only if this trajectory is linear in a certain region specified in the paper. [ABSTRACT FROM AUTHOR]

This paper describes an algorithm for a ship scheduling problem, obtained from a Swedish ship-owning company. The algorithm uses the Dantzig-Wolfe decomposition method for linear programming. The subprograms are simple network flow problems that are solved by dynamic programming. The master program in the decomposition algorithm is an LP problem with only zero-one elements in the matrix and the right-hand side. Integer solutions are not guaranteed, but generation and solution of a large number of problems indicates that the frequency of fractional solutions is as small as 1-2 per cent. Problems with about 40 ships and 50 cargoes are solved in about 2.5 minutes on an IBM 7090. In order to resolve the fractional cases, some integer programming experiments have been made. The results will be reported in a forthcoming paper. [ABSTRACT FROM AUTHOR]

This paper describes the examination of an oversaturated signalized intersection with no turning permitted. During the green phase, data on the time between arrivals of successive vehicles at an intersection with no downstream bottleneck have been collected and analyzed. Measurements were made of only the vehicles in queue, i.e., vehicles that were stopped during the red phase and those that were stopped during the green phase because the starting wave had not traveled back far enough. Measurements were made only on weekdays from approximately 7:00 A.M. to 8:45 A.M. in order to restrict the sample, as far as possible, to commuters. It is shown that shifted Erlang density functions fit the data satisfactorily and that all vehicles from the third on may be considered as members of the same population with different means. The mean arrival times decrease from front to rear with all from the seventh on being the same. In addition, our statistical analysis leads us to accept the hypothesis that all interarrival times are independent. Experimental techniques and statistical methods are described. Two uses of these results are (1) to provide in- formation for Monte Carlo simulations of traffic phenomena in which oversaturated situations are being considered, and (2) to develop, as will be done in a subsequent paper, a renewal model that takes account of variability in the empyting process, and that may be used in formulating control policies for the oversaturated situation. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model for the behavior of right- turning (left-hand drive is the convention observed) vehicles at an uncontrolled intersection. The model is a development of the one proposed for this situation in a previous paper by the author. It relates to the intersection of a two-lane major road with a minor road at which vehicles on the major road have absolute priority. Completely random traffic is postulated on the major road, and congestion is caused by drivers of vehicles on the major road who wish to turn right and are unable to do so immediately because of oncoming traffic. It is not possible for following vehicles to filler to the left of a delayed vehicle. The delay distribution for vehicles in each lane of the major road is determined for the case of stochastically stationary behavior, and sonic numerical results for the mean and variance of this distribution are given. The gap acceptance mechanism used in this paper is similar to the one proposed by GAVER. Further references for this paper are discussed in the Introduction to the author's previous paper. [ABSTRACT FROM AUTHOR]

This paper gives a description of how to find the 'best' sequence of allocation of resources to projects. The method handles simultaneously a great number of projects. The expression 'best' sequence means here the priority-rating that optimizes some chosen measure for the efficiency of the system. This optimization is done within the limits of the total resources available for allocation to projects. The problem is solved for whatever dependency there may be between resource quantity and system efficiency for the single projects. It works for the 'difficult' case of discontinuous efficiency functions as well. It is shown that in order to handle a great number of projects, one can divide the projects into groups, apply the method within each group of projects, then consider each group as a super project, and finally solve the whole problem by using the same method on groups. The problem is solved by a combination of the dynamic programming method, Lagrange's multiplier method, and numerical calculations on an electronic computer. The main part of the method is shown in a flow-diagram form. In the last sections of this paper practical examples are given, where the method is applied on investment problems. [ABSTRACT FROM AUTHOR]

This paper provides a simple test for the statistical significance of accident reductions. Such a test is applicable when some change has occurred at a highway location and we wish to know whether or not the difference between the number of accidents 'before' and 'after' represents a statistically significant reduction. In arriving at a decision based on random data we run the risk of occasionally (a) claiming a reduction in accidents when there is none (i.e., type I error), or (b) failing to claim a reduction when it exists (i.e., type II error). A decision procedure is proposed that considers these errors and their costs, and provides curves that indicate trade-offs in the probabilities of making each of the two types of error. Most of the statistical theory used in this paper is generally well known. However, the selection of significance levels based on economic considerations represents an improvement over the all too common practice of arbitrarily selecting significance levels for type I errors and ignoring type II errors altogether. [ABSTRACT FROM AUTHOR]

The article presents a list of papers published in the 1973 issue of the periodical. Some papers are "Announcements," "API Method Extended," "Airline Crew-Scheduling," "Air-Cargo Deployment Combat Personnel," "Aircraft Average Number Collisions," "Collision Probabilities," "Large Relative Velocity," "Special Cases, Velocity," "Air Fleet Evaluation Model (AFEM)," "Airports, Parallel Runways," "Air Routes, Potential Conflict," "Air-Route Network Planning," "Augmented Predecessor Indexing Method," "Books of Interest," "Brisbane City Council Transport Services, Note," "Broken Shifts, Bus Scheduling," "Bus Crew Scheduling," "Chesapeake Bay Bridge Traffic Control," "Column Generation Algorithm," "Combat Personnel, Equipment, Deployment," "Comparison, Steady-State and Simulation Methods," "Designing Transportation Networks," "Digital Simulation, Freeway Traffic, Long Island Expressway, New York," "Facility Location Algorithm," "Feeder Transit Lines," "Freeway Traffic, Digital Simulation," "General Networks Lemmas," "Generalized Network Problems," and "Generalized Transportation Problems."

The automatic control of a string of high-speed, densely-packed vehicles is studied in a unified approach. Various input structures for the control schemes and their stability are studied and compared. The optimal decentralized regulation theory developed in a previous paper is applied to seek the best feedback control gains for various input structures. Value of information is defined to evaluate the relative merit of these inputs. The results can be easily applied for on-board computer designs in developing new transportation technology such as `personal rapid transit' systems. [ABSTRACT FROM AUTHOR]

The traffic assignment problem associated with a given transportation network is the process of distributing zone-to-zone trips on links of the network. A number of methods have been proposed to solve this problem, but none have been found to be entirely satisfactory. This paper is concerned with the nonlinear mathematical model of the problem, where the link-traveling costs are increasing functions of the link flows and no explicit capacity constraint is imposed on individual links. An efficient algorithm is developed, using a node-arc formulation of the problem. It is an adaptation of the convex-simplex method that takes advantage of the very special network structure of the traffic assignment problem formulated in this way. Numerical results obtained with a moderate size street network are presented. [ABSTRACT FROM AUTHOR]

In many transit systems, vehicles depart their originating stops at fixed intervals, but headways become increasingly irregular as they move along the line. This paper considers how best to control such randomness through a strategy based on holding individual vehicles at a chosen control stop. An algorithm is presented for constructing an approximate optimal dispatching strategy from the control point, where optimal is defined both in terms of average passenger wait at the control stop and average delay for riders already aboard the vehicle. The algorithm is used on actual operations data from a Boston subway line to propose service improvements. [ABSTRACT FROM AUTHOR]

This paper develops an analytic model of the mean running time for trains on a single track railway. Trains operating at several different speeds in each direction are permitted. Priority systems are included in the model to control train behavior when meets and overtakes occur and delay times due to implementing these priority schemes are calculated. It is assumed that the departing times for trains are independent random variables that are uniformly distributed over the time period of interest. The resulting mean running times, including delays, for each speed class in each direction are found by solving a set of linear equations. [ABSTRACT FROM AUTHOR]

One of the best descriptors of traffic in a town is its speed and some knowledge of the way that it varies is clearly of interest and importance. This paper compares the suitability of five formulas that relate journey speed to distance from a town center for six towns in England and Wales. The formula that gives the most consistently good fit to the data from the towns studied here is of the form v = a - be-cr, where v is journey speed at radial distance r, and a, b, c, are constants. However, a form ala of the power form v= arb also provides a reasonable description of the data from the towns studied. Although not necessarily being the best fitting formula for individual towns, the ease of use and interpretation of this power function and the fact that it requires only two constants may make it preferable for many studies of the variation of speed within towns. The disadvantage that this formula predicts zero speed at a town center is of little practical importance, since in practice, it can give fairly good estimates of the time taken to reach points in the neighborhood of the town center. It is also concluded that the wide variation of speeds at any particular distance from the center of the one town for which this was examined can be partly explained by the variation between radial routes. [ABSTRACT FROM AUTHOR]

This paper presents a method for serial combination of truck trips to minimize the total cost of deadheading, subject to constraints on the allowed combinations. The problem is initially formulated as an integer transportation problem with extra compatibility constraints, and then reduced to a classical transportation problem. Modifications of the classical algorithm led to a fifty-fold reduction in computer time, and permit solution of a 1000 × 1000 problem in less than two minutes of computer time. Implementation of the method led to considerable cost savings over the older manual procedure. [ABSTRACT FROM AUTHOR]

The railway bridge at Dordrecht (Holland) can be raised to let big ships pass through. This takes place according to a fixed daily time schedule derived from the railway timetable. The waiting times of the ships depend on the number and the duration of these openings, the headway of the unraised bridge (changing on account of tidal effects), and the traffic supply. In this paper the dependence of the waiting times on the above-mentioned factors is quantified by means of a Monte Carlo simulation procedure. [ABSTRACT FROM AUTHOR]

The basic limitation on air traffic compression, from the safety point of view, is the increased risk of collision due to reduced separations. In order to evolve new procedures, and eventually a fully automatic system, it is desirable to have a means of calculating the collision probability for any prescribed flight paths. This paper extends the statistical-probabilistic method of collision probability calculation, which has been limited to parallel, straight line flight paths, to arbitrary flight paths and vehicle shapes. The general formula is specialized to the cases of large relative velocity, nonzero relative velocity, zero relative velocity, and spherical collision surface. The formulas are applied to independent curved landing approaches to parallel runways. [ABSTRACT FROM AUTHOR]

This paper is addressed to the problem of locating the absolute and vertex centers (minimax criterion) of an undirected tree graph. Based upon a convexity property of the criterion function a very simple and efficient algorithm is offered that locates the minimax point by locating first a maximax point. The minimax is at the mid-point of the maximum path from the maximax point. The vertex center is located simultaneously. [ABSTRACT FROM AUTHOR]

This paper develops the dual program of the constrained multifacility location problem in which total transportation cost in the system is proportional to the sum of the weighted Euclidean distances between facilities. A decomposition solution method is presented in which the master program is linear and each subprogram is a nonlinear programming problem. Computation results are presented and discussed. [ABSTRACT FROM AUTHOR]

In this paper we apply the following general scheme to determine toll patterns for multiclass-user transportation networks: we modify the travel cost as perceived by the individual traveler by charging him a 'toll.' Then we try to determine the toll pattern in such a way that the system-optimizing flow pattern becomes at the same time user- optimizing. We discuss two toll policies: (a) Tolls are collected on a link basis. (b) Tolls are collected on a path basis. The study shows that there is a degree of freedom in the path-toll collection policy. Alternative criteria are proposed for the exploitation of the degree of freedom such as: (i) that the tolls collected be nonnegative; (ii) that the personal cost of travelers, before and after the imposition of tolls, remains the same; (iii) that certain classes are treated discriminately in order to attain some social good. [ABSTRACT FROM AUTHOR]

This paper outlines an approach to analyzing the safety characteristics of vehicular ground transportation systems operated under computer surveillance and control. A quantitative index of safety is formulated, and a procedure is developed for analyzing the dependence of system safety on the significant design parameters and performance attributes. Lower bounds on the permissible minimum headway are established on the assumption of instantaneous and perfect control, so that the effects of various sensing, communication, control and actuation subsystems can be assessed independently. Time delays in emergency control-resulting from discrete sensor spacing, finite sampling time, and loss of telemetered data-are analyzed and expressions for the attendant increase in the minimum headway are developed. The general approach and the specific techniques are illustrated with numerical examples. [ABSTRACT FROM AUTHOR]

The paper considers the location of centers (e.g., plants, warehouses) on a network. Necessary conditions and sufficient conditions for optimal solutions to occur at nodes in the network are determined. The conditions include consideration of capacity constraints and the possibility that not all shipments are made via the `shortest route.' The cost functions may differ from arc to arc. A proof is given for the sufficiency of node locations in situations of multistage processing when transport costs are concave over each arc. Three sets of con conations under which it is necessary for an optimal solution to occur at a node are investigated. One set of conditions involves a production function characterization of the centers being located. [ABSTRACT FROM AUTHOR]

This paper deals with a car-following model relating driver reaction time, temporal headway and deceleration response to accident frequency. The central goal is to assess the sensitivity of collision probability to a shift in expected reaction time. This problem reduces to determining the sensitivity of the probability of ruin to changes in the drift of the process of cumulative differences between reaction times and temporal headways. A diffusion-type approximation is used and it is shown that additive changes in mean reaction time correspond to multiplicative changes in collision probability. A numerical example is given to illustrate the potential effects of a mere 0.1 sec decrease in mean reaction time. [ABSTRACT FROM AUTHOR]

The various theoretical analyses that have been made of delay to traffic at a fixed time traffic signal are critically reviewed. The more practicably applicable expressions for the average delay per vehicle, especially those derived by Webster, Miller, and Newell, are examined in some detail, and this paper provides an introduction to numerical comparisons to be reported by Hutchinson in the sequel. [ABSTRACT FROM AUTHOR]

In this paper, different empirical models for explaining car travel to Canadian provinces by American citizens are estimated. The results indicate interesting substitution and complementarities in travel that have important policy implications. Furthermore, the results have implications for future travel to Canada given rising incomes and the shifting of the United States' population center. [ABSTRACT FROM AUTHOR]

This paper describes an aircraft scheduling model which accounts for indivisibilities in production (airplanes, flights), capacity costs due to peak demand, and consumer preferences regarding the time of day flights are scheduled. Application of the model to real-world routing problems is not intended, as the scope is limited to a system comprised of a single city pair. However, the model does make possible a detailed examination of the economic welfare aspects of various routing criteria and the degree of realism in the assumptions made. Cost functions formulated from CAB data, along with hypothesized characteristics of air travel demand, form a data base for the model. Results are included to show the effect on economic welfare of utilizing a model which fails to incorporate passenger preferences as to the time of day flights are scheduled. [ABSTRACT FROM AUTHOR]

Various versions of the Weber problem deal with the location of facilities in a system with fixed destinations or customers. The object is to minimize the sum of transportation costs, which is represented as the sum of the weighted distances in the system. This paper finds the optimum location for facilities where the object is to minimize the maximum weighted distance in the system. Rectangular distances, which are more appropriate for urban transportation than straight line distances, are used in the model. Optimization is achieved through parametric linear programming. [ABSTRACT FROM AUTHOR]

This paper concerns itself with the kinematic analysis of traffic flow on a signalized one-way artery. Using as mathematical model the continuum flow theory of LIGHTHILL -WHITHAM-RICHAJWS, the flow pattern is carefully investigated under the assumptions of parabolic volume-density diagram and constant flow on the artery. The interesting symmetry existing between fluid and congested regimes is noted and used in proving various results. The delay caused by an interruption of arbitrary regimes is analyzed as a function of space and time. It is shown that an interruption of an arbitrary regime is equivalent to a particular interruption of a corresponding uniform regime: this provides a very simple and general method for delay computation. The delay caused by a periodic interruption (traffic signal) is bounded by and is asymptotically equal to the duration of the red signal; more- over, both the maximum and the average delay at fixed distance from the signalized intersection are increasing functions of the cycle time. It is further shown that the results concerning the delay function apply to all convex volume-density diagrams. [ABSTRACT FROM AUTHOR]

This paper illustrates the simulation method of evaluating the effect of system component changes on highway crash reduction. The evaluation procedure presented uses operating characteristics of a component as input, and compares the performance of alternative components in emergency traffic conflict situations. It is shown that Monte Carlo simulation of the model may he an efficient technique for comparing component alternatives. The examples presented involve (1) the emergency braking capabilities of two populations of vehicles in emergency car-following situations, and (2) two different rear lighting systems. [ABSTRACT FROM AUTHOR]

The article presents an analytical derivation of mean speed in the "Boltzmann-Like" traffic theory. In order to determine the speed distribution, it is, therefore, necessary to first determine the mean speed of the distribution. In this paper, the mean speed of the steady-state speed distribution is investigated. The mean speed is determined on the basis of the intersection of two functions; one of the functions is given by the desired speed distribution, which is a description of the goals that drivers want to attain in traffic; the other function is given by the concentration-dependent traffic parameters of the model. These parameters give a description of the restrictions that drivers exert on each other in the process of attaining their individual goals. Since the model is basically a description of the interaction between these two conflicting traffic characteristics, the effect on the mean speed due to each characteristic can hence be investigated separately through the properties of the corresponding function.

The article focuses on models of fleet routing and scheduling problems for transportation systems, which are formulated as integer linear programs with 0-1 variables. The topics discussed in this paper are concerned with important operational problems confronting the management of the competitive air transportation system. Some of these problems are significant for other transportation systems, including those with public-service rather than profit objectives. The problems are those connected with fleet utilization, fleet size, routing, and scheduling. Work that is related to some of these problems has been carried out by operations researchers and has been limited because, when optimal solutions were sought, computation times were excessive. The principal method of attack has been dynamic programming, which usually involves a very large state space for any real-life transportation system. The basic models are of the discrete-time rather than of the continuous-time variety. This property permits the formulation of the optimization problems as integer linear programs. The aim is to formulate a realistic model and to obtain its optimal solution

As large medical centers become ever more capable, the existence of well equipped, well staffed and rapid emergency ambulance service becomes increasingly important. This paper presents a method for determining the optimum location of ambulance stations to minimize the average response time to emergency calls. A new point-to-point driving time model is introduced, and a computer optimization algorithm used to determine the optimum locations. A constraint that the average response time to any point in the service area be less than some specified minimum is also considered. The method is applied to Washtenaw County, Michigan. [ABSTRACT FROM AUTHOR]

The traffic assignment and distribution problems are customarily treated as though they were independant rather than related and interacting. In this paper a combined traffic distribution-assignment model is formulated as a mathematical program, based on the equilibrium traffic distribution model and a linear programming assignment model. The behavior of this model using the DANZIG- WOLFE decomposition principle is investigated and illustrated by means of an example. A number of areas for extension are indicated and an alternative formulation that has certain advantages is also [ABSTRACT FROM AUTHOR]

The general problem is that of locating a central facility in a network so as to minimize the sum of its distances from the sources of flow to it, each distance being appropriately weighted to reflect the associated flow volume and/or cost. In this paper, simple one-pass solution algorithms are given for two classes of topologically simple networks, namely those which are either acyclic or contain exactly one cycle. The first algorithm is based on a reduction procedure that may also yield useful simplification of problems involving general networks. [ABSTRACT FROM AUTHOR]

This paper shows how the problem of predicting traveler behavior may be approached in terms of economic utility theory. A general utility maximization model on the level of individual trip-making decisions is developed from basic hypotheses regarding the costs and benefits attributed to travel disaggregated into individual trips. For predictive purposes the form of the utility functions involved must be specified, and several possibilities are explored. The functional forms of the resulting travel demand functions are then derived. In order to pursue an analysis of variations in traveler behavior and in order to perform aggregation over individuals, disturbances in the parameters of the utility functions are considered. The parameters investigated are marginal utilities and the distributions used are normal distributions. In considering binary choices, a trip demand model, a modal split model, and a destination split model are obtained from the same basic methodology. Finally, possible approaches to testing the functional relations involved and to measuring marginal utilities are discussed. [ABSTRACT FROM AUTHOR]

The Dantzig and Fulkerson Tanker Scheduling Problem is concerned with the determination of the minimum size and optimal routing of a fleet of homogeneous tankers needed to meet a prescribed schedule of deliveries. This problem has been formulated as a network flow problem. Later formulations consider an existing nonhomogeneous tanker fleet and relax the fixed shipping schedule. These problems are treated as multicommodity minimal cost flow problems. This paper further extends the problem to consider differing carrying capabilities of the vehicles and formulates a mixed integer linear program that permits partially loaded tankers. A branch-and-bound enumerative scheme in conjunction with a decomposed linear program with network sub-problem is presented. [ABSTRACT FROM AUTHOR]

A method for estimating costs and benefits to commuters, over a period of time, is developed in this paper. The method will account for the variation of traffic volumes over the period of time considered. The cost structure of a transport mode is taken as a function of the volume of traffic on that mode. The distribution of traffic volumes is then used to measure the costs and benefits to the user and the state over a year. Commuters are divided into different social classes according to the value they place on the attributes of the different transport modes. Next the method is used to evaluate different road pricing schemes. Finally the road system is examined both as a public utility and as a public enterprise. [ABSTRACT FROM AUTHOR]

This paper describes a heuristic method for sequencing barge Unloadings at terminals that have regulated unloading rates or flows with the objective of minimizing the variation of a common constituent in the final combined output. The work was undertaken in response to the desire of a steel manufacturer to minimize the maximum sulfur content in coal entering the coking ovens after being mixed by the simultaneous unloading of barges onto a common conveyor. Although the problem may be given an integer programming formulation, the solution method we propose enables one to obtain optimal or near optimal solutions by hand. A hypothetical problem is solved to illustrate the procedure. [ABSTRACT FROM AUTHOR]

This paper presents an explicit procedure for finding improving cycles or paths in the distribution model. The procedure developed may be incorporated in the row-column sum method. When this is done, both the row and column numbers and the predecessor index numbers may be determined simultaneously, a fact which contributes to the rapidity of the method. The chief difference between our method and other labeling procedures derives from the fact that the ordinary procedures are implemented in a 'dual' framework and are concerned with identifying a flow augmenting path that maintains dual feasibility. [ABSTRACT FROM AUTHOR]

This paper presents a method for developing efficient timetables for the operation of fixed schedule common-carrier passenger transportation systems. The ability to compute such timetables is needed in the consideration of planning alternatives for future transportation systems and/or the efficient operation of existing systems. Here, time- table optimization is accomplished by maximizing an objective function consisting of three basic components: operating costs, revenues, and traveler benefits. Traveler benefits are computed using a consumer preference model that specifies a traveler's willingness to pay for alternative trips, based on the scheduling of those trips. The optimization is based on successive iterations of a dynamic programming algorithm that develops timetables for each vehicle in the system. Solutions are termed optimal to within a 'first-order passenger exchange! Examples are presented to illustrate the utilization of the methodology for computing information relevant to the development of system operating policies and to the consideration of planning alternatives. [ABSTRACT FROM AUTHOR]

Alternative methods of analysing gap acceptance data are considered with a view to removing the bias implicit in the situation in which minor road vehicle drivers exhibit consistent behavior and all accepted and rejected gaps are taken into account. Simulation techniques are used to show that some of these suggested methods are invalid, but verification is obtained for a method derived by the author in an earlier paper that simply requires the displacement of the gap acceptance curve time scale by an amount equal to the product of the variance of the observed gap acceptance distribution (sec²) and the major road volume (veh/sec). This, it is contended, is easier to apply than an alternative method of estimating the critical gap distribution parameters given by MCNEIL AND MORGAN. A theoretical relation is determined between the mean of the critical gap distribution and the Raff critical lag that shows the two to be equal only when the gap acceptance curve takes the form of a step function. [ABSTRACT FROM AUTHOR]

Before we can construct models for multilane traffic flow, we must be able to describe single-lane traffic. This paper considers some of these methods of description including the use of headway and counting distributions. Another method of describing point processes is by means of product densities. These are essentially joint probabilities of two or more vehicles passing a point at different specified times. Product densities have been used in many fields including particle physics, ecology, and road traffic. The idea of using product densities is simple and attractive, but they do have two major disadvantages: (i) except in simple cases, headway distributions are very difficult to derive from product densities, and (ii) product density estimates for different time lags are cor- related, so that tests of hypotheses are not easy to perform. An alternative to product densities is proposed. For want of a better name these are called termination rates. The termination rate after lag τ is the probability of a vehicle passing a point in a small interval of time, divided by the length of the small interval and conditional upon the last vehicle having passed a time τ previously. These are very similar to mortality rates for humans or scrap page rates for commodities with limited life-times. The interrelations between these statistics are quoted but not derived. Various sets of data are used to illustrate the less common statistics. Some analysis is given of a sample of data from the Congress (now Eisenhower) Expressway in Chicago. Variance to mean ratios are used to show that there is a strong correlation between lanes even though the autocorrelations of headways within lanes are very small. Bivariate termination rates have been estimated for each lane. Given a vehicle in one lane, it was found that the expected number of vehicles in a neighboring lane within 2 or 3 sec was enhanced by about 10-15 percent. [ABSTRACT FROM AUTHOR]