Download or read book Sample Path Analysis of Stochastic Processes written by Chaitanya N. Garikiparthi and published by . This book was released on 2008 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: A number of processes that occur in nature as well as those that are manifestations of human activities are correlated in nature and can be describe by stochastic non-Markovian processes. Most known theoretical results for these systems are in the steady state domain, assuming that the system has been in operation for a long enough time, and that the state in which the system starts has no effect on the current behavior of the system. Nevertheless steady state assumptions do not hold in many applied situations. In this thesis we provide a framework to stochastically track these processes. Application of this theory provide valuable insights into the transient behavior of these stochastic processes and allows us to model and study the effect of auto-correlations in the driving processes on transient probabilistic (performance) metrics of interest. In order to develop accurate models to represent these systems, we allow the arrival and the service processes that characterize the system to be both general and correlated. We specifically study the busy period and other first passages of and auto-correlated MEP/MEP/1 single server queue to demonstrate the application of tracking these memory-full processes. Analysis presented here is the transient domain and does not require the underlying processes to be in a steady state. In the first part of the thesis we provide solutions to compute the probabilities for exactly 'n' customers being served in a busy period of MEP/MEP/1 queueing system. We then present matrix exponential representations to characterize the lengths of sample paths during these busy periods and derive expressions to compute moments for length of the busy period as well as for the number of customers served during the busy period. In the second part of the thesis, we study the effect of increase in threshold level and the correlations in the arrival and service processes on the mean first passage time to go below a given threshold. Finally we study the busy periods for finite queueing systems, and again study both the length of the busy period and the number of customers served during such a time.