Data networks
The MMAP[K]/PH[K]/1 queues with a last-come-first-served preemptive service discipline
Queueing Systems: Theory and Applications
Delay models for contention trees in closed populations
Performance Evaluation
Acyclic discrete phase type distributions: properties and a parameter estimation algorithm
Performance Evaluation
Robustness of Q-ary collision resolution algorithms in random access systems
Performance Evaluation
On the asymptotic behavior of some algorithms
Random Structures & Algorithms
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
QBDs with Marked Time Epochs: a Framework for Transient Performance Measures
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)
Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)
A review of contention resolution algorithms for IEEE 802.14 networks
IEEE Communications Surveys & Tutorials
Analysis of contention tree algorithms
IEEE Transactions on Information Theory
Time-bounded reachability in tree-structured QBDs by abstraction
Performance Evaluation
Triangular M/G/1-Type and Tree-Like Quasi-Birth-Death Markov Chains
INFORMS Journal on Computing
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A new methodology to assess transient performance measures of tree-like processes is proposed by introducing the concept of tree-like processes with marked time epochs. As opposed to the standard tree-like process, such a process marks part of the time epochs by following a set of Markovian rules. Our interest lies in obtaining the system state at the n-th marked time epoch as well as the mean time at which this n-th marking occurs. The methodology transforms the transient problem into a stationary one by applying a discrete Erlangization and constructing a reset Markov chain. A fast algorithm, with limited memory usage, that exploits the block structure of the reset Markov chain is developed and is based, among others, on Sylvester matrix equations and fast Fourier transforms. The theory of tree-like processes generalizes the well-known paradigm of Quasi-Birth-Death Markov chains and has various applications. We demonstrate our approach on the celebrated Capetanakis-Tsybakov-Mikhailov (CTM) random access protocol yielding new insights on its initial behavior both in normal and overload conditions.