LEADER 04329nam 2200637Ia 450 001 9910829880103321 005 20230721005807.0 010 $a1-282-16515-1 010 $a9786612165153 010 $a0-470-61134-0 010 $a0-470-39395-5 035 $a(CKB)2550000000005862 035 $a(EBL)477650 035 $a(OCoLC)593311017 035 $a(SSID)ssj0000343434 035 $a(PQKBManifestationID)11286416 035 $a(PQKBTitleCode)TC0000343434 035 $a(PQKBWorkID)10289874 035 $a(PQKB)11065037 035 $a(MiAaPQ)EBC477650 035 $a(EXLCZ)992550000000005862 100 $a20080227d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSwitching processes in queueing models$b[electronic resource] /$fVladimir V. Anisimov 210 $aLondon ;$aISTE ;$aHoboken, NJ $cJohn Wiley & Sons$d2008 215 $a1 online resource (347 p.) 225 1 $aISTE ;$vv.47 300 $aDescription based upon print version of record. 311 $a1-84821-045-0 320 $aIncludes bibliographical references and index. 327 $aSwitching Processes in Queueing Models; Contents; Preface; Definitions; Chapter 1. Switching Stochastic Models; 1.1. Random processes with discrete component; 1.1.1. Markov and semi-Markov processes; 1.1.2. Processes with independent increments and Markov switching; 1.1.3. Processes with independent increments and semi-Markov switching; 1.2. Switching processes; 1.2.1. Definition of switching processes; 1.2.2. Recurrent processes of semi-Markov type (simple case); 1.2.3. RPSM with Markov switching; 1.2.4. General case of RPSM; 1.2.5. Processes with Markov or semi-Markov switching 327 $aChapter 3. Processes of Sums of Weakly-dependent Variables3.1. Limit theorems for processes of sums of conditionally independent random variables; 3.2. Limit theorems for sums with Markov switching; 3.2.1. Flows of rare events; 3.2.1.1. Discrete time; 3.2.1.2. Continuous time; 3.3. Quasi-ergodic Markov processes; 3.4. Limit theorems for non-homogenous Markov processes; 3.4.1. Convergence to Gaussian processes; 3.4.2. Convergence to processes with independent increments; 3.5. Bibliography; Chapter 4. Averaging Principle and Diffusion Approximation for Switching Processes; 4.1. Introduction 327 $a4.2. Averaging principle for switching recurrent sequences4.3. Averaging principle and diffusion approximation for RPSMs; 4.4. Averaging principle and diffusion approximation for recurrent processes of semi-Markov type (Markov case); 4.4.1. Averaging principle and diffusion approximation for SMP; 4.5. Averaging principle for RPSM with feedback; 4.6. Averaging principle and diffusion approximation for switching processes; 4.6.1. Averaging principle and diffusion approximation for processes with semi-Markov switching; 4.7. Bibliography 327 $aChapter 5. Averaging and Diffusion Approximation in Overloaded Switching Queueing Systems and Networks 330 $aSwitching processes, invented by the author in 1977, is the main tool used in the investigation of traffic problems from automotive to telecommunications. The title provides a new approach to low traffic problems based on the analysis of flows of rare events and queuing models. In the case of fast switching, averaging principle and diffusion approximation results are proved and applied to the investigation of transient phenomena for wide classes of overloading queuing networks. The book is devoted to developing the asymptotic theory for the class of switching queuing models which covers mode 410 0$aISTE 606 $aTelecommunication$xSwitching systems$xMathematical models 606 $aTelecommunication$xTraffic$xMathematical models 606 $aQueuing theory 615 0$aTelecommunication$xSwitching systems$xMathematical models. 615 0$aTelecommunication$xTraffic$xMathematical models. 615 0$aQueuing theory. 676 $a519.8/2 676 $a519.82 700 $aAnisimov$b V. V$g(Vladimir Vladislavovich)$01713524 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910829880103321 996 $aSwitching processes in queueing models$94106570 997 $aUNINA