Limiting Behavior of Queueing Networks and Interacting Particle Systems

Bramson教授对随机过程的主要研究仍然是在网络和相互作用的粒子系统领域。第一个主题中的两个主要主题是路由网络的稳定性和它们的高流量限制。当相关的马尔可夫过程是正常返的时，一个马尔可夫网络被认为是稳定的。一系列排队网络的重流量极限是通过应用通常的中心极限标度得到的扩散极限。在过去的十年中的结果导致了更好地理解网络，虽然缺乏一个一般的理论。研究人员计划研究在某些众所周知的规则下，如处理器共享和最早到期日，先服务的网络行为。其他相关的主题包括动态调度在繁忙的交通和稳定的自我管理模型的互联网。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。此类系统通常受到物理和生物科学模型的激励。研究人员计划研究具有质量的创造和湮灭的模型，以及某些排斥过程的静态测量。Bramson教授目前的研究是在概率论的两个领域，网络和相互作用的粒子系统。在第一个领域中，人们研究的是由个体组成的大型系统的行为，这些个体从一个服务器到下一个服务器，直到他们的需求得到满足并离开系统。这里的“个人”应该从一般意义上解释，可以是等待服务的客户（例如，在银行或服务柜台），某些制造过程中的工作（例如半导体晶片的生产）或互联网上的信息包。在实践中，一个人经常面临着选择谁先服务。这种选择会极大地影响系统的效率，有时甚至影响系统的稳定性。也就是说，基于服务规则在给定设置中的良好程度，排队等待的客户的数量通常可以在延长的时间段内保持较小，或者可以倾向于无限制地增长。过去十年的工作表明，这种系统可能会因意想不到的原因而不稳定。研究人员计划继续他在这一领域的工作，并调查在某些众所周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所激发的，这些模型由大量根据某种规则相互作用的“个体”组成。例如，个体可能是按照某种规则运动的分子，或者是沿着沿着扩散的癌细胞。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.