Recent studies have proposed using person-based traffic signal timing optimization frameworks to minimize total passenger delay experienced by passenger cars and transit vehicles at signalized intersections. However, the efficiency and the practical application of existing efforts is limited by the assumption of fixed cycle lengths and deterministic bus arrival times. This paper extends the algorithms developed in previous work for isolated intersections to accommodate flexible cycle lengths and uncertain bus arrivals. Flexible cycle lengths are accommodated by minimizing total passenger delay within some fixed planning horizon that allows cycle lengths to vary within a feasible range. Two methods are proposed to accommodate uncertain bus arrival times: 1) a robust optimization approach that seeks to achieve a \“best\” worst-case scenario; and, 2) a rule-based strategy that applies green extension to signal timings obtained from deterministic optimization. The proposed strategies are tested using numerical simulations of an intersection in State College, PA. The results reveal that the flexible cycle length algorithm can significantly reduce bus passenger and total passenger delay with negligible increases in car passenger delay. These results are robust to both the bus and car flow expected at the intersection. The robust optimization strategy appears to reduce the additional passenger delay generated by bus arrival uncertainty for low uncertainty levels, while the rule-based strategy performs better for larger uncertainty levels when intersection flow ratios are low. The anticipated benefits decrease with the intersection flow ratio due to the inflexibility of signal timings at the intersection.

}, keywords = {Algorithms, Arrivals and departures, Bus transit, Green interval (Traffic signal cycle), Programming (Mathematics), Traffic delays, Traffic signal cycle, Traffic signal priority}, author = {Yu, Zhengyao and Gayah, Vikash V. and Christofa, Eleni} } @article {11107, title = {The potential of parsimonious models for understanding large scale transportation systems and answering big picture questions}, journal = {EURO Journal on Transportation and Logistics}, volume = {1}, year = {2012}, month = {06/2012}, pages = {47-65}, chapter = {47}, abstract = {A model with few variables is said to be parsimonious. If it is also analytically tractable, physically realistic, and conceptually insightful, it is said to be effective. Effective parsimonious models have long been used in fields such as economics and applied physics to describe the aggregate behavior of systems as opposed to the behavior of their individual parts. In transportation, these models are particularly well suited to address big picture questions because they provide insights that might be lost when focusing on details. This paper presents an abbreviated history of effective parsimonious models in the transportation field, classified by sub-area: regional and urban economics, traffic flow, queuing theory, network dynamics, town planning, public transportation, logistics, and infrastructure management. The paper also discusses the benefits of these models\—fewer data requirements, reduced computational complexity, improved system representation, insightfulness\—and ways of constructing them. Two examples, one from logistics and one from urban transportation, are used to illustrate these points. Finally, the paper discusses ways of expanding the application of effective parsimonious models in the transportation field.

}, keywords = {Continuum approximations, Effective parsimonious models, Logistics, Macroscopic modeling, Urban mobility}, doi = {10.1007/s13676-012-0003-z}, author = {Daganzo, Carlos F. and Gayah, Vikash V. and Gonzales, Eric J.} } @article {11109, title = {Macroscopic relations of urban traffic variables: bifurcations, multivaluedness, and instability}, journal = {Transportation Research Part B: Methodological}, volume = {45}, year = {2011}, month = {01/2011}, pages = {278-288}, chapter = {278}, abstract = {Recent experimental work has shown that the average flow and average density within certain urban networks are related by a unique, reproducible curve known as the Macroscopic Fundamental Diagram (MFD). For networks consisting of a single route this MFD can be predicted analytically; but when the networks consist of multiple overlapping routes experience shows that the flows observed in congestion for a given density are less than those one would predict if the routes were homogeneously congested and did not overlap. These types of networks also tend to jam at densities that are only a fraction of their routes\’ average jam density.

This paper provides an explanation for these phenomena. It shows that, even for perfectly homogeneous networks with spatially uniform travel patterns, symmetric equilibrium patterns with equal flows and densities across all links are unstable if the average network density is sufficiently high. Instead, the stable equilibrium patterns are asymmetric. For this reason the networks jam at lower densities and exhibit lower flows than one would predict if traffic was evenly distributed.

Analysis of small idealized networks that can be treated as simple dynamical systems shows that these networks undergo a bifurcation at a network-specific critical density such that for lower densities the MFDs have predictably high flows and are univalued, and for higher densities the order breaks down. Microsimulations show that this bifurcation also manifests itself in large symmetric networks. In this case though, the bifurcation is more pernicious: once the network density exceeds the critical value, the stable state is one of complete gridlock with zero flow. It is therefore important to ensure in real-world applications that a network\’s density never be allowed to approach this critical value.

Fortunately, analysis shows that the bifurcation\’s critical density increases considerably if some of the drivers choose their routes adaptively in response to traffic conditions. So far, for networks with adaptive drivers, bifurcations have only been observed in simulations, but not (yet) in real life. This could be because real drivers are more adaptive than simulated drivers and/or because the observed real networks were not sufficiently congested.

}, keywords = {Macroscopic fundamental diagram, Traffic congestion, Urban mobility}, doi = {10.1016/j.trb.2010.06.006}, author = {Daganzo, Carlos F. and Gayah, Vikash V. and Gonzales, Eric J.} }