Asymptotic Behavior of Queueing Networks and Interacting Particle Systems

9971248虽然排队网络和相互作用粒子系统的领域通常吸引不同的研究人员群体，但它们都处理大型对象系统，如顾客或粒子，它们通过某种相互作用规则连接在一起。适用于这两个领域的技术通常是相关的。Bramson教授打算研究第一类模型的稳定性问题和扩散标度下的行为；在这种分析中，流体模型的使用是一个重要的工具。第二类包括选民模型等模型，以及具有湮灭和质量产生的两型粒子系统。平衡态和极限浓度是这类模型的研究对象。排队网络和相互作用粒子系统是概率论领域的两个研究课题。这两个领域的目标都是理解大型对象系统的长期行为，例如客户或粒子，因为系统中存在随机性。在这里，“客户”不仅指个人，也指产品或需要执行的某些任务，例如在半导体晶圆的制造中。在排队理论中，人们分析了这类系统的效率和稳定性。建议集中讨论后一个问题，以及这类系统所固有的统计波动。在相互作用的粒子系统中，人们研究发生在物理、化学和生物学背景下的复杂随机系统，其组成部分代表例如粒子、细胞或各种生物体。例如，研究化学反应结果的模型，或者研究种群的遗传多样性。该提案调查了这类系统的长期平衡的性质。

9971248Although typically appealing to different groups of researchers, the areas of queueing networks and interacting particle systems both deal with large systems of objects, such as customers or particles, which are connected together by some interaction rule. The techniques that are applicable to the two areas are often related. Professor Bramson intends to study stability questions and the behavior under diffusive scaling for the first class of models; the use of fluid models is an important tool in such analysis. The second class includes models such as the voter model, and two-type particle systems with the annihilation and creation of mass. The equilibria and the limiting concentrations are the objects of investigation for such models.Queueing networks and interacting particle systems are two subjects within the field of probability theory. The goal in both areas is to understand the long-term behavior of large systems of objects, such as customers or particles, for which there is randomness in the system. Here, "customers" need not denote just individuals, but also products or some task to be performed, such as in the manufacture of semiconductor wafers. In queueing theory, one analyzes the efficiency and stability of such systems. The proposal concentrates on the latter topic, and on the statistical fluctuations that are inherent in such systems. In interacting particle systems, one studies complex random systems that occur in the context of physics, chemistry and biology, whose components represent, for example, particles, cells, or various organisms. For instance, one studies models for the outcome of a chemical reaction, or the genetic diversity of a population. The proposal investigates the nature of the long-term equilibria of such systems.