Fluid modeling and analysis of some queueing and network issues
In the past decade, communication networks have experienced dramatic growth in all dimensions: size, speed, heterogeneity, applications and users, etc. They have posed greater challenges to researchers working on modelling and analysis of the networks. In this dissertation, we investigate some queueing and network issues using stochastic fluid models.
Fluid queueing models are models in which traffic enters and leaves a buffer continuously, like fluid. Many examples demonstrated that fluid models are good approximation of information flow of discrete units, e.g. packets, cells, whenever processing time of each individual unit is small compared with the time scale we are interested in. The continuous nature of fluid model enables us to obtain some analytical results for some fluid queueing systems, including multi-class fluid queue, tandem fluid queues and priority fluid queueing system. Sample path description tools, such as Poisson driven stochastic differential equations, are shown to be powerful in studying fluid queueing system.
In order to optimize the performance of a queueing system, we need to obtain derivative information of the performance function. Infinitesimal Perturbation Analysis (IPA) is successful in gradient estimation for classical queueing systems. But it is biased for multi-class queues. We extend the application of IPA to fluid queueing system. We are able to show it can provide unbiased gradient estimation for both single-class fluid queue and multi-class fluid queues.
Network behavior changes with the evolution of communication applications running over it. As an emerging trend in web access applications, concurrent downloading raises new issues for network congestion control. We study the issue of fairness among users with different download concurrency using a fluid network model. We also investigate its impact on network congestion and transient behavior. Its challenges to end system congestion control schemes and active queueing management mechanism are discussed.