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A duality theorem for the matrix paradigms in queueing theory

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References

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2003Fluid Flow Models and Queues—A Connection by Stochastic Coupling90 cited
1996Some properties of the rate perators in level dependent uasi-birth-and-death processes with countable number of phases89 cited
1990Probabilistic interpretations of some duality results for the matrix paradigms in queueing theory58 cited
2003Phase-type distributions and representations: Some results and open problems for system theory55 cited
1999The quasi-birth-death type markov chain with a tree structure46 cited
1990From the matrix-geometric to the matrix-exponential44 cited
2006Sojourn time distributions in the queue defined by a general QBD process41 cited
2003Markov chain representations of discrete distributions applied to queueing models

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34 cited

2015Beyond the mean in fork-join queues: Efficient approximation for response-time tails32 cited

1998Invariant measures for quasi-birth-and-death processes31 cited

1990Phase-type representations for matrix-geometric solutions30 cited

2002A CONSTRUCTIVE METHOD FOR FINDING β-INVARIANT MEASURES FOR TRANSITION MATRICES OF M/G/1 TYPE27 cited

1993On the duality between routing and scheduling systems with finite buffer space26 cited

2022Reliable design of a congested disaster relief network: A two-stage stochastic-robust optimization approach18 cited

1998Representations for matrix-geometric and matrix-exponential steady-state distributions with applications to many-server queues16 cited

2004On the Time Reversal of Markovian Arrival Processes14 cited