Carlos F. Daganzo

THE CELL TRANSMISSION MODEL: A DYNAMIC REPRESENTATION OF HIGHWAY TRAFFIC CONSISTENT WITH THE HYDRODYNAMIC THEORY

This paper presents a simple representation of traffic on a highway with a single entrance and exit. The representation can be used to predict traffics evolution over time and space, including transient phenomena such as the building, propagation, and dissipation of queues. The easy-to-solve difference equations used to predict traffics evolution are shown to be the discrete analog of the differential equations arising from a special case of the hydrodynamic model of traffic flow. The proposed method automatically generates appropriate changes in density at locations where the hydrodynamic theory would call for a shockwave; i.e., a jump in density such as those typically seen at the end of every queue. The complex side calculations required by classical methods to keep track of shockwaves are thus eliminated. The paper also shows how the equations can mimic the real-life development of stop-and-go traffic within moving queues.

The cell transmission model, part II: Network traffic

This article shows how the evolution of multi-commodity traffic flows over complex networks can be predicted over time, based on a simple macroscopic computer representation of traffic flow that is consistent with the kinematic wave theory under all traffic conditions. The method does not use ad hoc procedures to treat special situations. After a brief review of the basic model for one link, the article describes how three-legged junctions can be modeled. It then introduces a numerical procedure for networks, assuming that a time-varying origin-destination (O-D) table is given and that the proportion of turns at every junction is known. These assumptions are reasonable for numerical analysis of disaster evacuation plans. The results are then extended to the case where, instead of the turning proportions, the best routes to each destination from every junction are known at all times. For technical reasons explained in the text, the procedure is more complicated in this case, requiring more computer memory and more time for execution. The effort is estimated to be about an order of magnitude greater than for the static traffic assignment problem on a network of the same size. The procedure is ideally suited for parallel computing. It is hoped that the results in the article will lead to more realistic models of freeway flow, disaster evacuations and dynamic traffic assignment for the evening commute.

Distribution Strategies that Minimize Transportation and Inventory Costs

This paper develops an analytic method for minimizing the cost of distributing freight by truck from a supplier to many customers. It derives formulas for transportation and inventory costs, and determines the optimal trade-off between these costs. The paper analyzes and compares two distribution strategies: direct shipping i.e., shipping separate loads to each customer and peddling i.e., dispatching trucks that deliver items to more than one customer per load. The cost trade-off in each strategy depends on shipment size. Our results indicate that, for direct shipping, the optimal shipment size is given by the economic order quantity EOQ model, while for peddling, the optimal shipment size is a full truck. The peddling cost trade-off also depends on the number of customers included on a peddling route. This trade-off is evaluated analytically and graphically. The focus of this paper is on an analytic approach to solving distribution problems. Explicit formulas are obtained in terms of a few easily measurable parameters. These formulas require the spatial density of customers, rather than the precise locations of every customer. This approach simplifies distribution problems substantially while providing sufficient accuracy for practical applications. It allows cost trade-offs to be evaluated quickly using a hand calculator, avoiding the need for computer algorithms and mathematical programming techniques. It also facilitates sensitivity analyses that indicate how parameter value changes affect costs and operating strategies.

The crane scheduling problem

This paper examines crane scheduling for ports. It starts with a simple static case and uses it as a building block to develop a better understanding of the dynamic problem with berth length limitations. The paper assumes that ships are divided into holds and that (usually) only one crane can work on a hold at a time. Cranes can be moved freely from hold to hold, and ships cannot depart until all their holds have been handled. In the most general case, ships arrive at different times and must queue for berthing space if the berths are full. The objective is to turn around (serve) all the ships, while minimizing their aggregate cost of delay. The paper presents exact and approximate solution methods for crane scheduling. The approximation methods are based on optimality principles and are easy to implement. The exact methods can only be used for a few ships. The paper includes examples, performance tests, and a discussion of port operations and further work.

ANALYZING TRADE-OFFS BETWEEN TRANSPORTATION, INVENTORY AND PRODUCTION COSTS ON FREIGHT NETWORKS

The purpose of this paper is to determine optimal shipping strategies (i.e. routes and shipment sizes) on freight networks by analyzing trade-offs between transportation, inventory, and production set-up costs. Networks involving direct shipping, shipping via a consolidation terminal, and a combination of terminal and direct shipping are considered. This paper makes three main contributions. First, an understanding is provided of the interface between transportation and production set-up costs, and of how these costs both affect inventory. Second, conditions are identified that indicate when networks involving direct shipments between many origins and destinations can be analyzed on a link-by-link basis. Finally, a simple optimization method is developed that simultaneously determines optimal routes and shipment sizes for networks with a consolidation terminal and concave cost functions. This method decomposes the network into separate sub-networks, and determines the optimum analytically without the need for mathematical programming techniques.

A behavioral theory of multi-lane traffic flow. Part I: Long homogeneous freeway sections

In this paper, the author presents a macroscopic behavioral theory of traffic dynamics for multi-lane freeways. The theory offers predictions for separate groups of lanes. A model is specified using eight observable parameters. The author discusses reversed lambda patterns, the hysteresis phenomenon, lane-specific patterns, and queued and unqueued traffic regimes.

Handling strategies for import containers at marine terminals

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.

The Distance Traveled to Visit N Points with a Maximum of C Stops per Vehicle: An Analytic Model and an Application

The purpose of this paper is to develop a simple formula to predict the distance traveled by fleets of vehicles in physical distribution problems involving a depot and its area of influence. Since the transportation cost of operating a break-bulk terminal or a warehouse is intimately related to the distance traveled, the availability of such a simple formula should facilitate the study of more complex logistics problems. A simple manual dispatching strategy intended to mimic what dispatchers do, but simple enough to admit analytical modeling is presented. Since the formulas agree rather well with the length of nearly optimal computer built tours, the predictions should approximate distances achievable in practice; the formulas seem realistic. The technique is a variant of the classical “cluster-first, route-second” approach to vehicle routing problems. In these approaches, the depot influence area is first partitioned into districts containing clusters of stops; one vehicle route is then constructed to serve each cluster. Our procedure is characterized by the way district shapes are chosen; ignoring shape during the clustering step can increase significantly travel distances. The technique is simple. To exercise it, one needs only a pencil, eraser, and a scale map showing the destinations. Once mastered, the technique takes only a few minutes. This time should increase only linearly with the number of destinations. For repetitive problems, the technique can be enhanced with the help of interactive computer graphics. A newspaper delivery problem for the city of San Francisco is used as an illustration.

The length of tours in zones of different shapes

The object of this paper is to explain how the expected length of traveling salesman tours changes with zone shape. To do this, a simple strategy that yields good traveling salesman tours is presented. The resulting tours are suboptimal but appear to be close to those that can be obtained by hand. Thus, the formulas that are provided may also be indicative of the length of tours built with better strategies. The results of this paper are useful for the design of distribution systems.

Possible explanations of phase transitions in highway traffic

It is shown that all the phase transitions in and out of freely flowing traffic reported earlier for a German site could be caused by bottlenecks, as are all the transitions observed at two other sites examined here. The evidence suggests that bottlenecks cause these transitions in a predictable way, and does not suggest that stoppages (jams) appear spontaneously in free flow traffic for no apparent reason. It is also shown that many of the complicated instability phenomena observed at all locations can be explained qualitatively in terms of a simple Markovian theory specific to traffic that does not necssarily include spontaneous transitions into the queued state as a feature.