Solution of the Sylvester matrix equation AXBT + CXDT = E
ACM Transactions on Mathematical Software (TOMS)
On the Solution of a Nonlinear Matrix Equation arising in Queueing Problems
SIAM Journal on Matrix Analysis and Applications
On approximating higher order MAPs with MAPs of order two
Queueing Systems: Theory and Applications
Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)
Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)
A matrix-analytic solution for the DBMAP/PH/1 priority queue
Queueing Systems: Theory and Applications
Exploiting Restricted Transitions in Quasi-Birth-and-Death Processes
QEST '09 Proceedings of the 2009 Sixth International Conference on the Quantitative Evaluation of Systems
Quasi-birth-and-death processes with restricted transitions and its applications
Performance Evaluation
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We consider M/G/1-type Markov chains where a transition that decreases the value of the level triggers the phase to a small subset of the phase space. We show how this structure-referred to as restricted downward transitions-can be exploited to speed up the computation of the stationary probability vector of the chain. To this end we define a new M/G/1-type Markov chain with a smaller block size, the G matrix of which is used to find the original chain's G matrix. This approach is then used to analyze the BMAP/PH/1 queue and the BMAP[2]/PH[2]/1 preemptive priority queue, yielding significant reductions in computation time.