Two approaches to modeling peak-period congestion that account for travelers' scheduling behavior have made their way into the economics literature. On the demand side of both approaches, travelers trade off a cost of travel delay against a cost of being early or late at destination in scheduling their trip. On the supply side, the Vickrey approach uses a queuing-congestion technology; the Henderson approach uses a flow-congestion technology, assuming that the travel time for any traveler is determined by the departure flow he departs with at origin. But the Henderson approach is found to have problems. This paper illustrates these problems; shows that they can be eliminated by assuming that the travel time for any traveler is determined by the arrival flow he arrives with at destination; and compares the behavior of the Vickrey and reformulated Henderson approaches both analytically and using simulations. The paper finds that the behavior of the reformulated Henderson approach varies with its elasticity of travel delay with respect to traffic flow, while the Vickrey approach lacks such a flexibility; and that the behavior of the Vickrey approach is the limit of that of the reformulated Henderson approach as the elasticity of travel delay goes to infinity.Two approaches to modeling peak-period congestion that account for travelers' scheduling behavior have made their way into the economics literature. One approach, developed by Vickrey [17], models congestion as queuing behind a single bottleneck. It has subsequently been elaborated in Arnott, de Palrna, and Lindsey (ADL) [1, 2], Braid[3], and Small [14]. I will refer to it as the Vickrey approach. The other approach, developed by Henderson [6, 7], models congestion in a flow form by applying a speed-flow function at each instant. I will refer to it as the Henderson approach.Both approaches focus on the journey to work with a fixed number of commuters traveling on the same highway between home and work. All commuters wish to arrive at work at the same time. This is physically impossible. As a result, each commuter schedules the trip to minimize his trip cost, including a cost of travel delay and a cost of schedule delay (time early or late for work). Both approaches use simplified congestion technologies. In the Vickrey approach, a bottleneck of fixed capacity is assumed along the highway. If the departure flow from home is below capacity, travel is at the free-flow speed; otherwise, a queue develops. In the Henderson approach, speed for any commuter is constant throughout the journey and his travel time is determined solely by the departure flow he departs together. It is implicitly assumed that traffic flows departing at different times are independent. In both approaches, equilibrium obtains 1 Let R be the road capacity, Sm~ the free-flow speed, and F(t) the departure rate at time t. Henderson [7] assumes a power speed-flow function given by

We present a simulation model designed to determine the impact on congestion of policies for dealing with travel time uncertainty. The model combines a supply side model of congestion delay with a discrete choice econometric demand model that predicts scheduling choices for morning commute trips. The supply model describes congestion technology and exogenously specifies the probability, severity, and duration of non-recurrent events. From these, given traffic volumes, a distribution of travel times is generated, from which a mean, a standard deviation, and a probability of arriving late are calculated. The demand model uses these outputs from the supply model as independent variables and choices are forecast using sample enumeration and a synthetic sample of work start times and free flow travel times. The process is iterated until a stable congestion pattern is achieved. We report on the components of expected cost and the average travel delay for selected simulations.

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The new millennium provides a good time to reflect on transportation-industry trends in some fundamental external factors that influence transportation behavior and planning response. In the public-transit industry, urban density and transit captivity have long been fundamental conditions driving transit planning and service and facility investment decisions. In light of demographic and economic changes, it is useful to revisit the issue of the importance of these factors to the transit market. Findings from a comprehensive analysis of the 1995 Nation-wide Personal Transportation Study (NPTS), which explored current transit-travel behavior, are reported. Two key findings reflect on two historical axioms in transit: ( a) the extent to which density influences transit use and ( b) the importance of the transit-dependent market. The research findings reiterate the significant influence that development density has on public transit mode share and bring to light some revealing data on the influence of urban-area size on transit use. The importance of transit dependency on transit use is documented, and trends in transit dependency over the past few decades are revealed. Finally, the implications of these trends for the public-transit industry are discussed.

The role of the street environment in the way people cross roads in urban settings is modeled. Respondents were placed in real traffic conditions at the curbside of street blocks in the Tampa Bay, Florida, area for 3-min observations of the street environments. Without crossing the blocks, respondents stated their crossing preference at each of six blocks. The origin and destination of each crossing were hypothetically set and varied across the blocks. So were the options available: two options for crossing at an intersection and up to four options for crossing at midblock locations. Within the framework of discrete choice models, the stated preferences are explained with the street environment, including traffic conditions, roadway characteristics, and signal-control characteristics. All three components of the street environment are considered: midblock locations, intersections, and roadside environment. The data are described; a nested logit model of pedestrian street-crossing behavior is estimated; and its implications to researchers and practitioners are discussed.