Hub location with flow economies of scale

A characteristic feature of hub and spoke networks is the bundling of flows on the interhub links. This agglomeration of flows leads to reduced travel costs across the interhub links. Current models of hub location do not adequately model the scale economies of flow that accrue due to the agglomeration of flows. This paper shows that current hub location models, by assuming flow-independent costs, not only miscalculate total network cost, but may also erroneously select optimal hub locations and allocations. The model presented in this paper more explicitly models the scale economies that are generated on the interhub links and in doing so provides a more reliable model representation of the reality of hub and spoke networks.     

Junction interactions and monotonicity in traffic assignment

We consider the traffic equilibrium problem when the travel demand is inelastic and stationary in time. Junction interactions, which abound in urban road networks, are permitted. We prove that the set of equilibria (solutions to the assignment problem) is convex when certain monotonicity and continuity conditions are statisfied at each junction.     

Evaluation of forced flows on freeways with single‐loop detectors

This paper documents the development of a simple method for identifying and/or predicting freeway congestion using single loop detection systems. The proposed algorithm is simple and easy to incorporate into most freeway management systems. The Washington State Department of Transportation's Traffic Systems Management Center (TSMC) sponsored the original study. The investigation also led to a recommendation to replace the original TSMC definition of congestion or forced flow conditions with a more reliable indicator. Although, the TSMC has recently implemented a more advanced prediction system based on fuzzy set theory and neural networks to further identify patterns and rules for ramp metering strategies, the findings presented here continue to be constructive to freeway managers looking for quick and easy analyses that rely solely on single‐loop detection systems. The Seattle Area freeway study section used for the original study was the portion of mainline 1–5 northbound starting at the downtown Seattle Station 108 and ending at the Mountlake Terrace Station 193. Several days' worth of volume and lane‐occupancy data were collected for the afternoon time period from 2:30 p.m. to 6:30 p.m. Time intervals of 20 seconds were chosen for each data collection period. Important products of this research include the following:

• simple, and more reliable criterion for the definition of “bottleneck” or forced flow conditions than that originally used by the TSMC.
• simple, and reliable criterion for predicting impending “bottlenecks” or forced flow conditions.
• A proposed variable for improved selection of the appropriate metering rate. (Further analysis of the use of this variable for determining metering rates is recommended for future studies.

The proposed criteria are simple and easy to incorporate into current freeway management computer systems. Further investigation of freeway performance measurement using volume and occupancy data obtained from single‐loop systems is currently being performed.     

Spatial price equilibrium sensitivity analysis

A direct approach to performing sensitivity analysis for a spatial price equilibrium problem with nonlinear transportation cost, commodity supply and commodity demand functions is presented. The first order derivatives of all decision variables with respect to parameter perturbations are shown to be expressable in a simple from which requires inversion of a matrix whose rank is the number of regions considered. A typical network usually involves several hundred regions and several thousand links; thus, by working with a matrix whose rank depends only on the number of regions rather than the number of links, computer storage is minimized and the necessary matrix inversion is made feasible, enabling us to perform the sensitivity analyses of very large nonlinear equilibrium problems. An example is presented to demonstrate application of the method. The approach taken here is also adaptable to the sensitivity analysis of Wardropian equilibrium problems.     

The stability of stochastic equilibrium in a two-link transportation network

Most research and applications of network equilibrium models are based on the assumption that traffic volumes on roadways are virtually certain to be at or near their equilibrium values if the equilibrium volumes exist and are unique. However, it has long been known that this assumption can be violated in deterministic models. This paper presents an investigation of the stability of stochastic equilibrium in a two-link network. The stability of deterministic equilibrium also is discussed briefly. Equilibrium is defined to be stable if it is unique and the link volumes converge over time to their equilibrium values regardless of the initial conditions. Three models of route choice decision-making over time are formulated, and the stability of equilibrium is investigated for each. It is shown that even when equilibrium is unique, link volumes may converge to their equilibrium values, oscillate about equilibrium perpetually, or converge to values that may be considerably different from the equilibrium ones, depending on the details of the route choice decision-making process. Moreover, even when convergence of link volumes to equilibrium is assured, the convergence may be too slow to justify the standard assumption that these volumes are usually at or near their equilibrium values. When link volumes converge to non-equilibrium values, the levels at which the volumes stabilize typically depend on the initial link volumes or perceptions of travel costs. Conditions sufficient to assure convergence to equilibrium in two of the three models of route choice decision-making are presented, and these conditions are interpreted in terms of the route choice decision-making process.     

The dynamics of traffic assignment and traffic control: A theoretical study

The paper considers traffic assignment, with traffic controls, in an increasingly dynamic way. First, a natural way of introducing the responsive policy, P_o, into steady state traffic assignment is presented. Then it is shown that natural stability results follow within a dynamical version of this static equilibrium model (still with a constant demand). We are able to obtain similar stability results when queues are explicitly allowed for, provided demand is constant. Finally we allow demand to vary with time; we consider the dynamic assignment problem with signal-settings now fixed. Here we assume that vehicles are very short and that deterministic queueing theory applies, and show that the time-dependent queueing delay at the bottleneck at the end of a link is a monotone function of the time-dependent input profile to the bottleneck. We have been unable to obtain results when dynamic demand and responsive signal control are combined.     

The design of bus route systems — An interactive location-allocation approach

An interactive modelling approach is developed to solve the practical problem of bus route network design. Possible bus routes are identified with facilities which can be located. Zones or pairs of zones in the urban area are identified with customers who will be allocated to the established facilities. It is shown that the classical Set Covering Problem is useful under the assumption of fixed demand; the Simple Plant Location Problem is effective under the assumption of demand which is sensitive to the level of bus service provided.