{"product_id":"introduction-to-matrix-analytic-methods-in-queues-1-analytical-and-simulation-approach-basics-hardback-9781786307323","title":"Introduction to Matrix Analytic Methods in Queues 1; Analytical and Simulation Approach - Basics (Hardback) 9781786307323","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eIntroduction to Matrix Analytic Methods in Queues 1\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eAnalytical and Simulation Approach - Basics\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eSrinivas R. Chakravarthy (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781786307323, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 8 November 2022\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e368 pages\u003cbr\u003e1 x 1 x 1 cm, 0.454 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eMatrix-analytic methods (MAM) were introduced by Professor Marcel Neuts and have been applied to a variety of stochastic models since. In order to provide a clear and deep understanding of MAM while showing their power, this book presents MAM concepts and explains the results using a number of worked-out examples.\u003cbr\u003e\u003cbr\u003eThis book’s approach will inform and kindle the interest of researchers attracted to this fertile field. To allow readers to practice and gain experience in the algorithmic and computational procedures of MAM, \u003ci\u003eIntroduction to Matrix Analytic Methods in Queues 1\u003c\/i\u003e provides a number of computational exercises. It also incorporates simulation as another tool for studying complex stochastic models, especially when the state space of the underlying stochastic models under analytic study grows exponentially.\u003cbr\u003e\u003cbr\u003eThe book’s detailed approach will make it more accessible for readers interested in learning about MAM in stochastic models.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eList of Notations ix\u003c\/p\u003e \u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1. Probability concepts 2\u003c\/p\u003e \u003cp\u003e1.1.1. Random variables 5\u003c\/p\u003e \u003cp\u003e1.1.2. Discrete probability functions 6\u003c\/p\u003e \u003cp\u003e1.1.3. Probability generating function 7\u003c\/p\u003e \u003cp\u003e1.1.4. Continuous probability functions 7\u003c\/p\u003e \u003cp\u003e1.1.5. Laplace transform and Laplace-Stieltjes transform 9\u003c\/p\u003e \u003cp\u003e1.1.6. Measures of a random variable 10\u003c\/p\u003e \u003cp\u003e1.2. Renewal process 11\u003c\/p\u003e \u003cp\u003e1.2.1. Renewal function 12\u003c\/p\u003e \u003cp\u003e1.2.2. Terminating renewal process 15\u003c\/p\u003e \u003cp\u003e1.2.3. Poisson process 16\u003c\/p\u003e \u003cp\u003e1.3. Matrix analysis 18\u003c\/p\u003e \u003cp\u003e1.3.1. Basics 18\u003c\/p\u003e \u003cp\u003e1.3.2. Eigenvalues and eigenvectors 23\u003c\/p\u003e \u003cp\u003e1.3.3. Partitioned matrices 27\u003c\/p\u003e \u003cp\u003e1.3.4. Matrix differentiation 28\u003c\/p\u003e \u003cp\u003e1.3.5. Exponential matrix 30\u003c\/p\u003e \u003cp\u003e1.3.6. Kronecker products and Kronecker sums 32\u003c\/p\u003e \u003cp\u003e1.3.7. Vectorization (or direct sums) of matrices 33\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2 Markov Chains 35\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1. Discrete-time Markov chains (DTMC) 36\u003c\/p\u003e \u003cp\u003e2.1.1. Basic concepts, key definitions and results 36\u003c\/p\u003e \u003cp\u003e2.1.2. Computation of the steady-state probability vector of DTMC 43\u003c\/p\u003e \u003cp\u003e2.1.3. Absorbing DTMC 45\u003c\/p\u003e \u003cp\u003e2.1.4. Taboo probabilities in DTMC 47\u003c\/p\u003e \u003cp\u003e2.2. Continuous-time Markov chain (CTMC) 48\u003c\/p\u003e \u003cp\u003e2.2.1. Basic concepts, key definitions and results 48\u003c\/p\u003e \u003cp\u003e2.2.2. Computation of exponential matrix 52\u003c\/p\u003e \u003cp\u003e2.2.3. Computation of the limiting probabilities of CTMC 57\u003c\/p\u003e \u003cp\u003e2.2.4. Computation of the mean first passage times 58\u003c\/p\u003e \u003cp\u003e2.3. Semi-Markov and Markov renewal processes 61\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3 Discrete Phase Type Distributions 71\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1. Discrete phase type (DPH) distribution 72\u003c\/p\u003e \u003cp\u003e3.2. DPH renewal processes 92\u003c\/p\u003e \u003cp\u003e3.3. Exercises 97\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4 Continuous Phase Type Distributions 101\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1. Continuous phase type (CPH) distribution 101\u003c\/p\u003e \u003cp\u003e4.2. CPH renewal process 120\u003c\/p\u003e \u003cp\u003e4.3. Exercises 137\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5 Discrete-Batch Markovian Arrival Process 143\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1. Discrete-batch Markovian arrival process (D-BMAP) 144\u003c\/p\u003e \u003cp\u003e5.2. Counting process associated with the D-BMAP 152\u003c\/p\u003e \u003cp\u003e5.3. Generation of D-MAP processes for numerical purposes 162\u003c\/p\u003e \u003cp\u003e5.4. Exercises 165\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6 Continuous-Batch Markovian Arrival Process 171\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1. Continuous-time batch Markovian arrival process (BMAP) 171\u003c\/p\u003e \u003cp\u003e6.2. Counting processes associated with BMAP 177\u003c\/p\u003e \u003cp\u003e6.3. Generation of MAP processes for numerical purposes 198\u003c\/p\u003e \u003cp\u003e6.4. Exercises 206\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 7 Matrix-Analytic Methods (Discrete-Time) 213\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1. M\/G\/1-paradigm (scalar case) 215\u003c\/p\u003e \u003cp\u003e7.2. M\/G\/1-paradigm (matrix case) 224\u003c\/p\u003e \u003cp\u003e7.3. GI\/M\/1-paradigm (scalar case) 244\u003c\/p\u003e \u003cp\u003e7.4. GI\/M\/1-paradigm (matrix case) 252\u003c\/p\u003e \u003cp\u003e7.5. QBD process (scalar case) 268\u003c\/p\u003e \u003cp\u003e7.6. QBD process (matrix case) 269\u003c\/p\u003e \u003cp\u003e7.7. Exercises 278\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 8. Matrix-Analytic Methods (Continuous-time) 291\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1. M\/G\/1-type (scalar case) 291\u003c\/p\u003e \u003cp\u003e8.2. M\/G\/1-type (matrix case) 295\u003c\/p\u003e \u003cp\u003e8.3. GI\/M\/1-type (scalar case) 297\u003c\/p\u003e \u003cp\u003e8.4. GI\/M\/1-type (matrix case) 300\u003c\/p\u003e \u003cp\u003e8.5. QBD process (scalar case) 304\u003c\/p\u003e \u003cp\u003e8.6. QBD process (matrix case) 305\u003c\/p\u003e \u003cp\u003e8.7. Exercises 308\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 9. Applications 321\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1. Production and manufacturing 322\u003c\/p\u003e \u003cp\u003e9.2. Service sectors 323\u003c\/p\u003e \u003cp\u003e9.2.1. Healthcare 324\u003c\/p\u003e \u003cp\u003e9.2.2. Artificial Intelligence and the Internet of Things 324\u003c\/p\u003e \u003cp\u003e9.2.3. Biological and medicine 325\u003c\/p\u003e \u003cp\u003e9.2.4. Telecommunications 325\u003c\/p\u003e \u003cp\u003e9.2.5. Supply chain 325\u003c\/p\u003e \u003cp\u003e9.2.6. Consumer issues 326\u003c\/p\u003e \u003cp\u003eReferences 327\u003c\/p\u003e \u003cp\u003eIndex 335\u003c\/p\u003e \u003cp\u003eSummary of Volume 2 339\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Education [\u003ca title=\"See our other books on Education\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Education%20%5BJN%5D%22\"\u003eJN\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley-ISTE","offers":[{"title":"Brand New","offer_id":52446763352344,"sku":"9781786307323","price":94.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781786307323.jpg?v=1785113145","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/introduction-to-matrix-analytic-methods-in-queues-1-analytical-and-simulation-approach-basics-hardback-9781786307323","provider":"Freshly Printed Books","version":"1.0","type":"link"}