Limiting Behavior of Queueing Networks and Interacting Particle Systems

布拉姆森教授对随机过程的主要研究仍集中在排队网络和相互作用粒子系统领域。第一个主题的两个主要主题是排队网络的稳定性和它们的大流量限制。当相关的马尔可夫过程是正循环时，我们说一个排队网络是稳定的。队列网络序列的大流量限制是应用通常的中心极限缩放得到的扩散极限。过去十年的研究结果使人们对排队网络有了更好的理解，尽管还缺乏一个通用的理论。研究人员计划在某些众所周知的原则下研究排队网络的行为，如处理器共享和最早到期日，先服务。排队理论中的其他相关主题包括大流量下的动态调度和互联网自管理模型的稳定性。相互作用粒子系统是由许多粒子组成的系统，这些粒子按照某种相互作用规律演化。这样的系统通常是由物理和生物科学的模型驱动的。研究人员计划研究具有质量产生和湮灭的模型，以及某些排斥过程的固定测量。布拉姆森教授目前的研究方向是概率论的两个领域：排队网络和相互作用粒子系统。在第一个领域，人们研究由个人组成的大型系统的行为，这些人从一个服务器转到另一个服务器，直到他们的需求得到满足并离开系统。这里的“个人”应该在一般意义上解释，可能是等待服务的客户（例如，在银行或服务柜台），在某些制造过程中的工作（如半导体晶圆的生产）或互联网上的信息包。在实践中，人们常常面临先为谁服务的选择。这种选择会极大地影响系统的效率，有时甚至会影响系统的稳定性。也就是说，根据给定设置中的服务规则有多好，排队等候的客户数量通常会在较长时间内保持较小，或者可能会无限制地增长。过去十年的研究表明，由于意想不到的原因，这样的系统可能会不稳定。研究人员计划继续他在这一领域的工作，并研究在某些已知的服务规则下网络的稳定性。相互作用粒子系统的领域是由物理和生物科学的模型驱动的，这些模型由大量的“个体”组成，它们根据某种规则相互作用。例如，个体可能是按照某种规则移动的分子，也可能是沿着表面扩散的癌细胞。这些系统的行为在很大程度上取决于它们相互作用的性质。研究人员计划继续对其中的某些模型进行研究。

Professor Bramson's main research on stochastic processes continues to be in the areas of queueing networks and interacting particle systems. Two major themes in the first topic are the stability of queueing networks and their heavy traffic limits. A queueing network is said to be stable when the associated Markov process is positive recurrent. The heavy traffic limit of a sequence of queueing networks is the diffusive limit obtained by applying the usual central limit scaling. Results over the last decade have led to a better understanding of queueing networks, although a general theory is lacking. The researcher plans to investigate the behavior of queueing networks under certain well-known disciplines, such as processor sharing and earliest-due-date, first-served. Other related topics in queueing theory include dynamic scheduling in heavy traffic and the stability of self-managed models for the internet. Interacting particle systems consist of systems of many particles that evolve according to some interaction law. Such systems are frequently motivated by models from the physical and biological sciences. The researcher plans to investigate models that have creation and annihilation of mass, as well the stationary measures of certain exclusion processes. Professor Bramson's current research is in two areas of probability theory, queueing networks and interacting particle systems. In the first area, one studies the behavior of large systems of individuals who proceed from one server to the next, until their needs are satisfied and they leave the system. "Individuals" here should be interpreted in a general sense, and may be customers waiting to be served (for instance, at a bank or at a service counter), jobs in some manufacturing process (such as the production of semiconductor wafers) or information packets on the internet. In practice, one is often faced with the choice of whom to serve first. This choice can substantially affect the efficiency of a system, and sometimes even its stability. That is, based on how good a service rule is in a given setting, the number of customers waiting in line may typically remain small over extended periods of time, or may tend to grow without bound. Work over the last decade has shown that such systems can be unstable for unexpected reasons. The researcher plans to continue his work in this area and investigate the stability of the network under certain well-known service rules. The area of interacting particle systems is motivated by models from the physical and biological sciences consisting of large numbers of "individuals" who interact according to some rule. For instance, individuals might be molecules moving about according to some rule or cancer cells spreading along a surface. The behavior of these systems can depend strongly on the nature of their interactions. The researcher plans to continue his research on certain of these models.