Path-based traffic assignment algorithms and models to enhance deployment robustness

Amit Kumar, Purdue University

Abstract

The domain of traffic assignment algorithms has been an active area of research for more than five decades and still continues to be so for two important reasons. First, it estimates traffic flow pattern and determines the levels of service, and help in predicting the need for improvements in the transportation network. Second, estimated traffic flow pattern forms the basis for cost benefit analysis, and helps to decide the best alternative of network improvement. Static deterministic Wardropian user equilibrium (UE) is the widely used technique in practice for solving the traffic assignment problem (TAP) due to its simplicity in implementation and modest data needs. But, there are three issues related to UETAP algorithms namely, solution stability, consistency and convergence which are problematic from both theoretical and practical perspectives. In addition to this, UE condition is not sufficient to determine path flow solution uniquely and multiple path flow solutions are possible with large variations. These issues related to UETAP raises questions of confidence in the comparison of alternatives based on the UETAP solution outcomes. This research proposes path-based traffic assignment algorithms and models that endeavor to achieve the deployment robustness. This research also proposes a post-processing technique that incorporates these algorithms and models into the widely used four-step planning process using a feedback loop. The deployment robustness here is characterized by three important model properties namely, the solution stability, consistency and stable convergence. The solution stability here implies that small changes in input to the model lead to small changes in model output. The consistency implies that the model output in terms of network flows reasonably reflects the changes in the input. The inconsistency in path flow solution of traffic assignment problem can arise due to two reasons; first, the solution noise and second, the non-uniqueness of solution which is an inherent property of path-based traffic assignment formulation. Past studies have sought to determine a unique path flow solution using the concept of maximum entropy user equilibrium (MEUE). But, MEUE is difficult to implement for large networks. In addition, there are issues related to the representativeness of MEUE solution from theoretical point of view. This research proposes a new approach to determine a unique path flow solution from the set of multiple UETAP path flow solutions, based on the method of mean values from statistical thermodynamics. The proposed method determines a unique path flow solution, labeled the entropy weighted user equilibrium (EWUE), as the entropy-weighted average of the path flow solution vectors in the entire UE solution space. The EWUE has the minimum expected deviation from all possible solution vectors in the UETAP solution space; hence it is a better representation of solution space. The EWUE solution is theoretically stable. Proposed EWUE model is easier to implement for practice than MEUE models proposed in past. The EWUE model needs precise UE link flows and set of UE paths. This research develops two path-based algorithm for generating the UE link flows and UE path set. First algorithm is labeled as slope-based multi-path algorithm (SMPA) and has been developed to achieve stable convergence. Further, a hybrid version of SMPA is developed by combining the merits of sequential approach and simultaneous approach of solution algorithms. This hybrid approach facilitates applicability to large size networks and tends to eliminate order-bias in the solution. The order-bias can be a potential reason for solution noise leading to inconsistency in solution. The second algorithm labeled slope-based path shift-propensity algorithm (SPSA) inherits merits of SMPA-hybrid and endeavors to incorporate behavioral consistency in the flow update process. SPSA is simpler to implement and can act as potential substitute of SMPA for practice. In addition, this research proposes a day-to-day (DTD) dynamical model to represent the path-shift behavior of network users under the disequilibrium of traffic networks. Path-flow evolutions from this model can be used to evaluate the impact of transportation intervention projects and to mitigate their impact using strategic management. There are two key aspects of this model that bridges two important gaps in literature in this domain. First, it introduces the concept of variance band. The variance band allows modeling the variation in the perception of drivers shifting paths. Second, proposed model incorporates the sensitivity of path costs with respect to flows in modeling the DTD dynamics. These two factors help to enhance real-world consistency in the modeling and smoothens the trajectory of flow evolution profile. Contributions of this research are important from both theoretical and practical viewpoints. (Abstract shortened by UMI.)

Degree

Ph.D.

Advisors

Peeta, Purdue University.

Subject Area

Civil engineering|Transportation planning

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