Transient analysis of tree-Like processes and its application to random access systems
SIGMETRICS '06/Performance '06 Proceedings of the joint international conference on Measurement and modeling of computer systems
Uniformization with representatives: comprehensive transient analysis of infinite-state QBDs
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
CSL model checking algorithms for QBDs
Theoretical Computer Science
An analytical model for end-to-end communication channel over PLCN based on QBDs
Information Processing Letters
Time to buffer overflow in an MMPP queue
NETWORKING'07 Proceedings of the 6th international IFIP-TC6 conference on Ad Hoc and sensor networks, wireless networks, next generation internet
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A framework to assess transient performance measures is introduced by generalizing the theory of the quasi Birthand- 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.