OBDs with marked time epochs : a framework for transient performance measures
Faculty of Sciences. Mathematics and Computer Science
Los Alamitos, Calif. :IEEE, 2005
2nd International Conference on Quantitative Evaluation of Systems, September 19-22, 2005, Torino, Italy
University of Antwerp
A framework to assess transient performance measures is introduced by generalizing the theory of the quasi Birth-and-Death (QBD) paradigm to QBDs with marked time epochs (QBD(m)). The distinction with the classical QBD process is that certain time epochs get marked according to a specific set of Markovian rules. Our interest lies in obtaining the system state at the n-th marked time epoch. The steady state vector of a so-called reset Markov chain is used to obtain the above-mentioned system state (either by approximation or in an exact manner). A fast algorithm, with limited memory usage, based on solving a single quadratic matrix equation, a set of Sylvester matrix equations and fast Fourier transforms is proposed The generality and flexibility of our framework is demonstrated on a set of queueing systems and applied to dimensioning a video playout buffer and studying the transient throughput of a wireless random access algorithm.