A Parking-state-based Transition Matrix of Traffic on Urban Networks

The urban parking and the urban traffic systems are essential components of the overall urban transportation structure. The short- term interactions between these two systems can be highly significant and influential to their individual performance. The urban parking system, for example, can affect the searching-for-parking traffic, influencing not only overall travel speeds in the network (traffic performance), but also total driven distance (environmental conditions). In turn, the traffic performance can also affect the time drivers spend searching for parking, and ultimately, parking usage. In this study, we propose a methodology to model macroscopically such interactions and evaluate their effects on urban congestion. The model is built on a transition matrix describing how, over time, vehicles in an urban area transition from one parking-related state to another. With this model it is possible to estimate, based on the traffic and parking demand as well as the parking supply, the amount of vehicles searching for parking, the amount of vehicles driving on the network but not searching for parking, and the amount of vehicles parked at any given time. More importantly, it is also possible to estimate the total (or average) time spent and distance driven within each of these states. Based on that, the model can be used to design and evaluate different parking policies, to improve (or optimize) the performance of both systems. A simple numerical example is provided to show possible applications of this type. Parking policies such as increasing parking supply or shortening the maximum parking duration allowed (i.e., time controls) are tested, and their effects on traffic are estimated. The preliminary results show that time control policies can alleviate the parking-caused traffic issues without the need for providing additional parking facilities. Results also show that parking policies that intend to reduce traffic delay may, at the same time, increase the driven distance and cause negative externalities. Hence, caution must be exercised and multiple traffic metrics should be evaluated before selecting these policies. Overall, this paper shows how a parking-state-based transition matrix, despite its simplicity, can be used to efficiently evaluate the urban traffic and parking systems macroscopically. The proposed model can be used to estimate both, how parking availability can affect traffic performance (e.g., average time searching for parking, number of cars searching for parking); and how different traffic conditions (e.g., travel speed, density in the system) can affect drivers ability to find parking. Moreover, the proposed model can be used to study multiple strategies or scenarios for traffic operations and control, transportation planning, land use planning, or parking management and operations.