Performance Analysis of Closed Queueing Networks with Subexponential Processing Times

本研究的目的是研究一类普遍存在于电信系统中的闭合排队网络。特别是，我们将考虑具有次指数处理时间的系统，因为有强有力的证据表明，在许多电信应用中，处理时间具有次指数分布。这意味着概率分布的尾部比指数衰减慢得多，这意味着极大观测的概率是不可忽略的。该项目的智能优点包括分析两个关键性能指标的某些特征：周期时间(在系统中花费的时间)和等待时间(从到达到在每个节点加入服务器)。在电信系统中，人们感兴趣的是这些性能度量中的任何一个大于一个被称为尾渐近的大值的概率。目标是了解瞬变和平稳周期时间以及等待时间的尾部渐近性。这两个性能指标的上下界以及利用这些上下界获得尾概率表达式的方法将被采用。尽管人们对具有非指数处理时间的排队系统越来越感兴趣，但现有的大多数研究都集中在单级排队上。因此，可以使用现有分析模型建模的电信系统类型与电信环境中出现的电信系统类型之间存在差距。如果成功，这项研究的结果将弥合这一差距。此外，这项研究项目是长期的。在这一阶段开发的分析模型将(最终)用于设计电信系统的控制战略，这些战略最终将导致这些系统的运作得到改善。

The objective of this research is to study a class of closed queueing networks that are prevalent in telecommunication systems. In particular, we will consider systems with subexponential processing times since there is strong evidence that in many telecommunications applications, processing times have subexponential distributions. This means that the tail of the probability distributions decay much slower than exponential implying that the probability of extremely large observations is non-negligible. The intellectual merit of this project involves analyzing certain characteristics of two key performance measures: cycle times (time spent in the system) and waiting times (from arrival until joining the server at each node). In telecommunication systems, one is interested in the probability that any one of these performance measures is greater than a large value which is referred as tail asymptotics. The objective is to understand the tail asymptotics of transient and stationary cycle times and waiting times. An approach that involves developing upper and lower bounds on these two performance measures and obtaining expressions on the tail probabilities using these bounds will be employed.Even though there has been a growing interest in queueing systems with subexponential processing times, most of the existing research has focused on single stage queues. Thus, there is a gap between the types of telecommunication systems that can be modeled using the existing analytical models and those that arise in telecommunication settings. If successful, the results of this research will bridge this gap. Moreover, this research project is long term. The analytical models developed during this phase will be (eventually) used to design control strategies for telecommunication systems that will ultimately lead to improvements in the operations of these systems.