Planning service facilities and infrastructures under continuous traffic equilibrium

Facility location design;continuous traffic equilibrium;partial differential equations;conformal mapping

Wang, Zhaodong

关键词: Facility location design;    continuous traffic equilibrium;    partial differential equations;    conformal mapping;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/101283/WANG-DISSERTATION-2018.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

The transportation community has long recognized the need to address congestion and equilibrium while planning service facilities to serve spatially distributed customers. The customers' choices on service facility and access path may be coupled with one another due to induced or altered traffic congestion near these facilities. Disregarding the congestion effect while planning facility locations may not only lead to unnecessarily high transportation cost and low facility patronage, but also impose a negative socioeconomic impact on the general public. In a broader sense, the societal cost includes not only wasted time due to extra delay, but also security and safety hazards.Examples of such problems can be found in many contexts that involve a continuous space. Personal air vehicles (i.e., ``flying cars'' that can take off and land ``outside of a house or in a garden'') are being considered as an option to allow future travelers to utilize low-altitude air space. The freight industry (e.g., Amazon, DHL) has been exploring the possibility of using short-range unmanned aerial vehicles (i.e., drones) to deliver parcels from a mobile dispatch base near customer neighborhoods. The concentration of air-vehicle or drone traffic in certain air space (e.g., near the city center or dispatch base) may cause delay and mandate traffic diversion. Similar issues would appear in military operations associated with stationing of air craft carriers in hostile environments. Even in a seemingly unrelated context, deployment of surveillance sensors (e.g., those based on radiation) in open or constrained spaces (e.g., airports or city squares) may be formulated into a similar problem, if sensor detection effectiveness is affected by not only distance but also blockage effects from a dense crowd. Perhaps the most extreme manifestation of such negative consequences of congestion is through the series of devastating stampede incidents in recent years.Many studies have addressed the impact of traffic congestion on service network planning, but most of the existing models were developed over an underlying discrete transportation network. Using discrete network flow (even on a very dense network) to approximate traffic concentration and congestion in a continuous space may not always be satisfactory due, in part, to difficulties associated with (i) the coupling of congestion experienced by neighboring travelers in different travel directions, and (ii) clustering of two-dimensional fluxes into one-dimensional link flows and characterization of link capacities, among others. As a result, alternative modeling approaches that can directly describe traffic in a two-dimensional continuous space have gained attention. A series of continuous user traffic equilibrium problems in the form of two-dimensional partial differential equations (PDE) were developed to quantitatively describe the congestion effect in traffic systems. Some numerical based methods are developed for facility location planning under the continuous traffic equilibrium. However, those models are only suitable for small scale problem instances due to excessive computational burden.In this Ph.D. research, we conduct an indepth investigation on the continuous traffic equilibrium. To improve computational efficiency, we first propose a continuum approximation (CA) model to find approximated solutions for large-scale instances. In contrast to most CA models which study uncapacitated fixed-charge location problems, we choose to focus on developing a solution approach for median-type problems. We further developed analytical solution methods for a class of continuous traffic equilibrium problems. We showed that under certain conditions the above PDE can be solved accurately in closed forms, for specially and generally shaped service regions. The latter case requires an additional conformal mapping treatment that can also be expressed in closed forms. Our PDE solution will not only serves as an efficient way to compute congestion effects in various application contexts, but also shed light on some basic properties of continuous traffic equilibrium in a two-dimensional space.The proposed analytical framework enables us to extend it in multiple directions. By paying attention to the shape design of facilities and infrastructures, we developed an infrastructure design framework which would be used to provide channelization of pedestrian flows in a congested area. We also extracted the optimal layout of facilities under some hypothetical situations and extending the model to incorporate the transshipment problem. As another direction of extension, we integrated the disruption risks into the facility location design.