Limiting Behavior of Queueing Networks and Interacting Particle Systems

限制排队网络和交互粒子系统的行为

• 批准号: 0226245
• 负责人: Maury Bramson
• 金额: $ 24.38万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-07-01 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0226245&HistoricalAwards=false
• 关键词: Limiting; Behavior; Queueing; Networks; Interacting

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.

布拉姆森教授对随机过程的主要研究仍然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及其大流量限制。当相关的马尔可夫过程是正循环时，排队网络被认为是稳定的。排队网络序列的大流量限制是通过应用通常的中心限制缩放而获得的扩散限制。尽管缺乏一般理论，但过去十年的结果使人们更好地理解了排队网络。研究人员计划研究某些众所周知的学科下的排队网络行为，例如处理器共享和最早到期、先服务。排队论中的其他相关主题包括大流量中的动态调度和互联网自我管理模型的稳定性。相互作用的粒子系统由许多根据某种相互作用定律演化的粒子系统组成。此类系统通常受到物理和生物科学模型的启发。研究人员计划研究具有质量产生和湮灭的模型，以及某些排除过程的固定测量。布拉姆森教授目前的研究集中在概率论、排队网络和相互作用粒子系统两个领域。在第一个领域，研究人员从一个服务器移动到下一个服务器的大型系统的行为，直到他们的需求得到满足并离开系统。这里的“个人”应作一般意义上的解释，可以是等待服务的顾客（例如在银行或服务柜台）、某些制造过程中的工作（例如半导体晶圆的生产）或互联网上的信息包。在实践中，人们常常面临着首先为谁服务的选择。这种选择会极大地影响系统的效率，有时甚至影响系统的稳定性。也就是说，根据服务规则在给定环境中的良好程度，排队等候的顾客数量通常可能在较长时间内保持较少，或者可能趋于无限制地增长。过去十年的工作表明，此类系统可能会因意想不到的原因而不稳定。研究人员计划继续该领域的工作，研究网络在某些众所周知的服务规则下的稳定性。相互作用粒子系统领域是由物理和生物科学模型驱动的，该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移动的分子，或者是沿着表面扩散的癌细胞。这些系统的行为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。