Thesis (Ph.D.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / This dissertation is dedicated to optimization of Stochastic Hybrid Systems (SHS). The concentration is on both online optimization of these systems and extending the known optimal policies in Discrete-Event Systems (DES) to a broader context of SHS. A SHS involves both continuous and discrete dynamics and is suitable for modeling almost any physical system of interest.
The first part of this dissertation focuses on applications of SHS and, particularly, a subclass known as Stochastic Flow Models (SFM) used in fluid scheduling. To this end, a classic problem for optimally allocating a resource to multiple competing user queues is considered in the DES context and placed in the framework of SFMs. Infinitesimal Perturbation Analysis (IPA) is used to calculate the gradient estimates for the average holding cost of this system with respect to resource allocation parameters. The monotonicity property of these estimates allows us to prove the optimality of a well-known rule called the "c - mu-rule" under non-idling policies. Furthermore, nonlinear cost functions are considered, yielding simple distribution-free cost sensitivity estimates.
Next, we take the first step in using IPA for optimally calculating timeout thresholds in SHS. A Transmission Control Protocol (TCP) communication link is used to examine the effectiveness of SHS and IPA in calculating derivative estimates of a goodput objective with respect to a timeout parameter. The analysis is also extended to the case of multinode communications. Our results reveal a great potential in using IPA to control delay thresholds and motivate more investigations in future.
Finally, we propose a general framework for analysis and on-line optimization of SHS which facilitates the use of IPA. In doing so, we modify the previous structure of a Stochastic Hybrid Automaton (SHA) and show that every transition is associated with an explicit event which is defined through a "guard function." This enables us to uniformly treat all events observed on the sample path of the SHS. As a result, a unifying matrix notation for IPA equations is developed which eliminates the need for the case-by-case analysis of event classes as usually done in prior works involving IPA for SHS. / 2031-01-01
| Identifer | oai:union.ndltd.org:bu.edu/oai:open.bu.edu:2144/31576 |
| Date | January 2012 |
| Creators | Kebarighotbi, Ali |
| Publisher | Boston University |
| Source Sets | Boston University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
Page generated in 0.0025 seconds