6631

6182

كارشناسي ارشد

آمار رياضي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1390

127ص.: مصور، نمودار

ص.ع. به فارسي و انگليسي

صفيه محمودي

محمد سعيد صباغ

4/2/91

افشين پرورده، علي رجالي

1396/10/12

كتابنامه

علوم رياضي

رياضي

ID6182

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Abstract Matrix analytic methods initiated by Marcel Neuts serve as a powerful framework toanalyze large classes of stochastic processes in a unified manner and one can extend it forprocesses with infinite dimensions and inhomogeneous cases The study of manystochastic models is made possible by the presence of embedded Markov chains whichhave particular structures This is well recognized in the theory of queues and also ininventory models and branching processes One particular rich class of Markov chainmodels is the class with marix analytic models which includes GI M 1 and M G 1 modelsand introduced by Neuts in 1981 and 1989 These are Markov processes in twodimensions the level and the phase Matrix analytic methods themselves are presentedwithin the simpler framework of quasi birth and death processes QBDs In fact aMarkov process which is of GI M 1 and M G 1 type is a quasi birth and death process Since many stochastic models are extention of GI M 1 and M G 1 models we presentmatrix analytic methods based on these models and also we will give a probabilisticanalysis and algorithmic solutions for them and their related stochastic models One advantage in presenting probabilistic results separate from the algorithms is that wemake is clearly appear that the structural properties don t depend on whether there arefinitely or infinitely many values for the phase dimension Only when doing actual matrixcomputations does it become necessary to deal with a finite state space for the phase Markov processes appear in two cases discrete time and continuous time Any analysisin which the system is observed for analysis only at specific points in time is a discretetime system is observed for analysis only at specific points in time is a discrete timesystem As telecommunication systems are based more on digital technology these daysthan analog the need to use discrete time analysis only at specific points in time is adiscrete time system As telecommunication systems are based more on digitaltechnology these days than analog the need to use discrete time analysis for queues hasbecome more important In this thesis by considering discrete time Markov chains andusing some results related to terminating renewal processes we investigate the structureof stationary distributions for GI M 1 and M G 1 type models and the structure oftransient distributions only for GI M 1 type models We also present the necessaryconditions for existence of stationary distributions or ergodicity of chains and finally weinvestigate the relations between those two models and existence of some dualitybetween them using Taylor and Van Houdt 2010

صفيه محمودي

محمد سعيد صباغ

افشين پرورده، علي رجالي