Michael J. Cassidy

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.

Bivariate relations in nearly stationary highway traffic

This paper demonstrates that reproducible bivariate relations exist among traffic variables, such as flow and occupancy, when traffic conditions are approximately stationary. The inspection of cumulative curves of vehicle arrival number and vehicle occupancy has revealed that sustained periods of nearly stationary conditions do arise in the traffic stream. By plotting average values of the data corresponding to each nearly stationary condition, well-defined relations are observed. These scatterplots of near-stationary data are contrasted with plots of data that were measured over consecutive time intervals of fixed duration and this reveals that data from certain conditions do not necessarily fall on a curve describing near-stationary traffic.

Vehicle reidentification and travel time measurement on congested freeways

Abstract The paper presents an algorithm for matching individual vehicles measured at a freeway detector with the vehicles’ corresponding measurements taken earlier at another detector located upstream. Although this algorithm is potentially compatible with many vehicle detector technologies, the paper illustrates the method using existing dual-loop detectors to measure vehicle lengths. This detector technology has seen widespread deployment for velocity measurement. Since the detectors were not developed to measure vehicle length, these measurements can include significant errors. To overcome this problem, the algorithm exploits drivers’ tendencies to retain their positions within dense platoons. The otherwise complicated task of vehicle reidentification is carried out by matching these platoons rather than individual vehicles. Of course once a vehicle has been matched across neighboring detector stations, the difference in its arrival time at each station defines the vehicle’s travel time on the intervening segment. Findings from an application of the algorithm over a 1/3 mile long segment are presented herein and they indicate that a sufficient number of vehicles can be matched for the purpose of traffic surveillance. As such, the algorithm extracts travel time data without requiring the deployment of new detector technologies. In addition to the immediate impacts on traffic monitoring, the work provides a means to quantify the potential benefits of emerging detector technologies that promise to extract more detailed information from individual vehicles.

Freeway Traffic Oscillations: Observations and Predictions

Freeway traffic was observed over multiple days and was found to display certain regular features. Oscillations arose only in queues; they had periods of several minutes; and their amplitudes stabilized as they propagated upstream. They propagated at a nearly constant speed of about 22 to 24 kilometers per hour, independent of the location within the queues and the flow measured there; this was observed for a number of locations and for queued flows ranging from about 2,000 to 850 vehicles per hour per lane. The effects of the oscillations were not felt downstream of the bottleneck. Thus, the only effect on upstream traffic was that a queues tail meandered over time by small amounts. (For the long queues studied here, the tails deviated by no more than about 16 vehicle spacings, as compared with predictions that ignored the oscillations). Notably, the character of queued traffic at fixed locations did not change with time, despite the oscillations; i.e., traffic did not decay. There were changes over space, however. New oscillations formed in moderately dense queues near ramp interchanges and then grew to their full amplitudes while propagating upstream, even though the range of wave speeds was narrow. The formations of these new oscillations are strongly correlated with vehicle lane changing. But this pattern of formation and growth was less evident in a very dense queue (caused by an incident), although frequent lane changing occurred near the interchanges. It thus appears that the oscillations were triggered by random lane changing in moderately dense queues more than by car-following effects. Finally, kinematic wave theory was found to describe the propagation of the oscillations to within small errors. For distances approaching one kilometer, and for 2-hour periods, the theory predicted the locations of vehicles to within about 5 vehicle spacings. Further analysis showed that some of these small discrepancies are explained by differences in car-following behavior across drivers.

Some observed details of freeway traffic evolution

Certain details of traffic evolution were studied along a 2 km, homogenous freeway segment located upstream of a bottleneck. By comparing (transformed) cumulative curves constructed from the vehicle counts measured at neighboring loop detectors, it was found that waves propagated through queued traffic like a random walk with predictable statistical variation. There was no observed dependency of wave speed on flow. As such, these waves neither focused nor fanned outward and shocks arose only at the interfaces between free-flowing traffic and the back of queues. Although these traffic features may have long been suspected, actual observations of this kind have hitherto not been documented. Also of note, the shocks separating queued and unqueued traffic sometimes exhibited unexpectedly long transitions between these two states. Finally, some observations presented here corroborate earlier reports that, in unqueued traffic, vehicle velocity is insensitive to flows and that forward-moving changes in traffic states therefore travel with vehicles. Taken together, these findings suggest that certain rather simple models suffice for describing traffic on homogeneous freeway segments; brief discussion of this is offered in Section 5.

VERIFICATION OF A SIMPLIFIED CAR-FOLLOWING THEORY

A simple car-following rule proposed by G.F. Newell was verified by measuring vehicles discharging from long queues at signalized intersections. Observations indicated that the time-space trajectory of a jth vehicle discharging on a homogeneous intersection approach was essentially the same as the j-1th vehicle except for a translation in time and space. These fixed translations are merely the time and distance required for driver j to reach the spacings she chooses for following vehicle j-1 as a function of j-1s velocities. This description is far simpler, and uses fewer parameters, than other car-following models.

AN OBSERVED TRAFFIC PATTERN IN LONG FREEWAY QUEUES

A simple exercise in data analysis showed that, in queued traffic, a well-defined relation exists between the flow on a homogeneous freeway segment and the segments vehicle accumulation. The exercise consisted of constructing cumulative vehicle arrival curves to measure the flows and densities on multiple segments of a queued freeway. At this particular site, each interchange enveloped by the queue exhibited a higher on-ramp flow than off-ramp flow and as a consequence, motorists encountered a steady improvement in traffic conditions (e.g., reduced densities and increased speeds) as they traveled from the tail of the queue to the bottleneck. This finding has practical implications for freeway traffic planning and management. Perhaps most notably, it suggests that the first-order hydrodynamic theory of traffic is adequate for describing some of the more relevant features of queue evolution. This and other practical issues are discussed in some detail.

STUDY OF FREEWAY TRAFFIC NEAR AN OFF-RAMP

A bottleneck with a diminished capacity is shown to have arisen on a freeway segment whenever queues from the segments off-ramped spilled over and occupied its mandatory exit lane. It is also shown that longer exit queues from the over-saturate off-ramp were accompanied by lower discharge rates for non-exiting vehicles. The explanation appears to be rubber-necking on the part of the non-exiting drivers. Whenever the of-ramp queues were prevented from spilling over to the exit lane (by changing the logic of a nearby traffic signal), much higher flows were sustained on the freeway segment and a bottleneck did not arise there. These observations underscore the value of control strategies that enable diverging vehicles to exit a freeway unimpeded. Key words: Freeway Traffic Control, Off-Ramps, Bottlenecks

Relation Among Average Speed, Flow, and Density and Analogous Relation Between Density and Occupancy

To counter the growing body of literature disputing that average vehicle speed is the ratio of flow to density, the relation is shown to hold as an identity when the variables are defined in the manner described by Edie. In similar fashion, the analogous relation between density and occupancy is shown to be true. These identities are illustrated with data measured by paired loop detectors, which underscores that Edie’s definitions are natural ways to treat the variables. The detector data are further used to show that any disputes surrounding the validity of these identities are largely the result of having defined (i.e., measured) the traffic variables in some other ways.

Impacts of Lane Changes at Merge Bottlenecks: A Theory and Strategies to Maximize Capacity

Recent empirical observations at freeway merge bottlenecks have revealed (i) a drop in the bottleneck discharge rate when queues form upstream, (ii) an increase in lane-changing maneuvers simultaneous with this “capacity drop”, and (iii) a reversal of the drop when the ramp is metered.