| Queueing systems have long been used to model many discrete event systems, such as communication networks, flexible manufacturing and production systems, and traffic systems. However, it has become more and more difficult to use classical queueing theories to deal with most real-world discrete event systems because of the increasing complexity of those systems. For example, communication networks often have very large traffic volume, so it is unrealistic and unnecessary to capture each packet's behavior in such systems based on their queueing models. One way to overcome this difficult is to use fluid models in which the traffic is modeled as continuous flow instead of discrete parts.; In this thesis, we study multiclass fluid models, particularly, those with first-come-first-served (FCFS) and dynamic priority service policies. Two different applications are considered: one is call center and the other is the Resilient Packet Ring (RPR) protocol in communication networks. For the call center, a fluid model with a mix of FCFS and dynamic priority service policies is proposed. For this model, we derive infinitesimal perturbation analysis (IPA) derivative estimators of its performance measures with respect to parameters that control the dynamic priority service policy and also use these IPA estimators to optimize the system. We also provide numerical results and discuss implications of some of our results on the operation and management of the call center. For the RPR protocol, in which a feedback mechanism is used for the purpose of global fairness and congestion control, we propose a fluid model with a dynamic priority service policy based on this feedback mechanism. We again derive IPA sensitivity estimates and apply them to the problem of online control and optimization. This work is then extended to fluid networks with feedback based dynamic priority service policies. |
