Performance Analysis of Closed Queueing Networks with Subexponential Processing Times

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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.