# Network routing and equilibrium models for urban parking search

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This dissertation focuses on modeling parking search behavior in traffic assignment models. Parking contributes greatly to urban traffic congestion. When the parking supply is scarce, it is very common for a vehicle to circle around for a considerable period just for an open parking spot. This circling or "cruising" add additional traffic flow onto the network. However, traditional traffic assignment models either ignore parking completely or simply treat it in limited ways. Most traffic assignment models simply assume travelers just directly drive from their origin to their destination without considering the parking search behavior. This would result in a systematic underestimation of road traffic flows and congestion which may mislead traffic managers to give inappropriate planning or control strategies. Models which do incorporate parking effects either constrain their implementation in limited small networks or ignore the stochasticity of parking choice by drivers. This dissertation improves upon previous research into network parking modeling, explicitly capturing drivers' behavior and stochasticity in the parking search process, and is applicable to general networks. This dissertation constructs three types of parking search models. The first one is to model a single driver's parking search process, taking into account the likelihood of finding parking in different locations from past experience as well as observations gained during the search itself. This model uses the a priori probability of finding parking on a link, which reflects the average possibility of finding a parking space based on past experience. This probability is then adjusted based on observations during the current search. With these concepts, the parking search behavior is modeled as a Markov decision process (MDP). The primary contribution of the proposed model is its ability to reflect history dependence which combines the advantages of assuming "full reset" and "no reset" . "Full reset" assumes the probability of finding a parking space on a link is independent of any observations in the current search, while "no reset" assumes the state of parking availability is completely determined by past observations, never changing once observed. For instance, assume that the a priori probability of finding parking on a link is 30%. "Full reset" implies that if a driver drives on this link and sees no parking available, if he or she immediately turns around and drives on the link again, the probability of finding parking is again 30% independent of the past observation. By contrast, "no reset" implies that if a parking space is available on a link, it will always be available to return to in the future at any point. This dissertation develops an "asymptotic reset" principle which generalizes these principles and allows past observations to affect the probability of finding parking on a link and this impact weakens as time goes by. Both full reset and no reset are shown to be special cases of asymptotic reset. The second problem is modeling multiple drivers through a parking search equilibrium on a static network. Similar to the first type of problem, drivers aim to minimize their total travel costs. Their driving and parking search behaviors depend on the probabilities of finding parkings at particular locations in the network. On the other side, these probabilities depend on drivers' route and parking choices. This mutual dependency can be modeled as an equilibrium problem. At the equilibrium condition no driver can improve his or her expected travel cost by unilaterally changing his or her routing and parking search strategy. To accomplish this, a network transformation is introduced to distinguish between drivers searching for parking on a link and drivers merely passing through. The dependence of parking probability on flow rates results in a set of nonlinear flow conservation equations. Nevertheless, under relatively weak assumptions the existence and uniqueness of the network loading can be shown, and an intuitive 'flow-pushing" algorithm can be used to solve for the solution of this nonlinear system. Built on this network loading algorithm, travel times can be computed. The equilibrium is formulated as a variational inequality, and a heuristic algorithm is presented to solve it. An extensive set of numerical tests shows how parking availability and traffic congestion (flows and delays) vary with the input data. The third problem aims at developing a dynamic equivalent for the network parking search equilibrium problem. This problem attempts to model a similar set of features as the static model, but aims to reflect changes in input demand, congestion, and parking space availability over time. The approach described in the dissertation is complementary to the static approach, taking on the flavor of simulation more than mathematical formulation. The dynamic model augments the cell transmission model with additional state variables to reflect parking availability, and integrates this network loading with an MDP-based parking search behavior model. Finally, case studies and sensitivity analysis are taken for each of the three models. These analyses demonstrate the models' validity and feasibility for practice use. Specifically, all the models show excess travel time and flow on the transportation networks because of taking into account the "parking search cruising" and can show the individual links so affected. They all reflect the scattered parking distribution on links while traditional traffic assignment models only assign vehicles onto specified destination nodes.