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oai:www.ideals.illinois.edu:2142/24155 2023-07-10 col_2142_10761 col_2142_5131 com_2142_10755 com_2142_234 com_2142_5130

Sanders, William H. Sanders, William H. Agha, Gul A. Meseguer, José Nicol, David M. Buchholz, Peter Lam, Vinh V. 2011-05-25T15:03:21Z 2011-05-25T15:03:21Z 2011-05-25T15:03:21Z 2011-05 Reliability and dependability modeling can be employed during many stages of analysis of a computing system to gain insights into its critical behaviors. To provide useful results, realistic models of systems are often necessarily large and complex. Numerical analysis of these models presents a formidable challenge because the sizes of their state-space descriptions grow exponentially in proportion to the sizes of the models. On the other hand, simulation of the models requires analysis of many trajectories in order to compute statistically correct solutions. This dissertation presents a novel framework for performing both numerical analysis and simulation. The new numerical approach computes bounds on the solutions of transient measures in large continuous-time Markov chains (CTMCs). It extends existing path-based and uniformization-based methods by identifying sets of paths that are equivalent with respect to a reward measure and related to one another via a simple structural relationship. This relationship makes it possible for the approach to explore multiple paths at the same time,· thus significantly increasing the number of paths that can be explored in a given amount of time. Furthermore, the use of a structured representation for the state space and the direct computation of the desired reward measure (without ever storing the solution vector) allow it to analyze very large models using a very small amount of storage. Often, path-based techniques must compute many paths to obtain tight bounds. In addition to presenting the basic path-based approach, we also present algorithms for computing more paths and tighter bounds quickly. One resulting approach is based on the concept of path composition whereby precomputed subpaths are composed to compute the whole paths efficiently. Another approach is based on selecting important paths (among a set of many paths) for evaluation. Many path-based techniques suffer from having to evaluate many (unimportant) paths. Evaluating the important ones helps to compute tight bounds efficiently and quickly. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2011-04-18T13:15:14Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Lam_Vinh.pdf: 3532138 bytes, checksum: 70b75331efacd1c4471ab08e09a4ae06 (MD5) Made available in DSpace on 2011-05-25T15:03:21Z (GMT). No. of bitstreams: 2 Lam_Vinh.pdf: 3532138 bytes, checksum: 70b75331efacd1c4471ab08e09a4ae06 (MD5) license.txt: 4057 bytes, checksum: 19713078629f0a663a703e36fa94da1c (MD5) http://hdl.handle.net/2142/24155 en Copyright 2011 Vinh V. Lam Numerical analysis Markov chains System modelling A path-based framework for analyzing large markov models Computer Science 1434 Computer Science 0112 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Computer Science -UIUC 10KS0112PHD