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Kronecker products are used to define the underlying Markov chain (MC) in various modeling formalisms, including compositional Markovian models, hierarchical Markovian models, and stochastic process algebras. The motivation behind using a Kronecker structured representation rather than a flat one is to alleviate the storage requirements associated with the MC. With this approach, systems that are an order of magnitude larger can be analyzed on the same platform. The developments in the solution of such MCs are reviewed from an algebraic point of view and possible areas for further research are indicated with an emphasis on preprocessing using reordering, grouping, and lumping and numerical analysis using block iterative, preconditioned projection, multilevel, decompositional, and matrix analytic methods. Case studies from closed queueing networks and stochastic chemical kinetics are provided to motivate decompositional and matrix analytic methods, respectively.
Select your format based upon: 1) how you want to read your book, and 2) compatibility with your reading tool. To learn more about using Bookshare with your device, visit the "Using Bookshare" page in the Help Center.
Here is an overview of the specialized formats that Bookshare offers its members with links that go to the Help Center for more information.
- Bookshare Web Reader - a customized reading tool for Bookshare members offering all the features of DAISY with a single click of the "Read Now" link.
- DAISY (Digital Accessible Information System) - a digital book file format. DAISY books from Bookshare are DAISY 3.0 text files that work with just about every type of access technology that reads text. Books that contain images will have the download option of ‘DAISY Text with Images’.
- BRF (Braille Refreshable Format) - digital Braille for use with refreshable Braille devices and Braille embossers.
- MP3 (Mpeg audio layer 3) - Provides audio only with no text. These books are created with a text-to-speech engine and spoken by Kendra, a high quality synthetic voice from Ivona. Any device that supports MP3 playback is compatible.
- DAISY Audio - Similar to the Daisy 3.0 option above; however, this option uses MP3 files created with our text-to-speech engine that utilizes Ivona's Kendra voice. This format will work with Daisy Audio compatible players such as Victor Reader Stream and Read2Go.