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
The solution of quasi birth and death processes arising from multiple access computer systems
The solution of quasi birth and death processes arising from multiple access computer systems
Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)
Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)
Structured Markov chains solver: software tools
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
Phase-Type Approximations for Message Transmission Times in Web Services Reliable Messaging
SIPEW '08 Proceedings of the SPEC international workshop on Performance Evaluation: Metrics, Models and Benchmarks
NET-COOP '09 Proceedings of the 3rd Euro-NF Conference on Network Control and Optimization
Triangular M/G/1-Type and Tree-Like Quasi-Birth-Death Markov Chains
INFORMS Journal on Computing
Packet level performance analysis in wireless user-relaying networks
IEEE Transactions on Wireless Communications - Part 2
Probability in the Engineering and Informational Sciences
A compressed cyclic reduction for QBDs with low rank upper and lower transitions
ACM SIGMETRICS Performance Evaluation Review
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In this paper, we identify a class of quasi-birth-and-death (QBD) processes where the transitions to higher (respectively lower) levels are restricted to occur only from (respectively to) a subset of the phase space. These restrictions induce a specific structure in the R or G matrix of the QBD process, which can be exploited to reduce the time required to compute these matrices. We show how this reduction can be achieved by first defining and solving a censored process, and then solving a Sylvester matrix equation. To illustrate the applicability and computational gains obtained with this approach, we consider several examples where the referred structures either arise naturally or can be induced by adequately modeling the system at hand. The examples include the general MAP/PH/1 queue, a priority queue with two customer classes, an overflow queueing system and a wireless relay node.