On the Solution of a Nonlinear Matrix Equation arising in Queueing Problems
SIAM Journal on Matrix Analysis and Applications
Efficient descriptor-vector multiplications in stochastic automata networks
Journal of the ACM (JACM)
A Toolbox for Functional and Quantitative Analysis of DEDS
TOOLS '98 Proceedings of the 10th International Conference on Computer Performance Evaluation: Modelling Techniques and Tools
Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)
Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)
Service-Level Differentiation in Call Centers with Fully Flexible Servers
Management Science
Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling
Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling
A matrix continued fraction algorithm for the multiserver repeated order queue
Mathematical and Computer Modelling: An International Journal
Analyzing Markov Chains using Kronecker Products: Theory and Applications
Analyzing Markov Chains using Kronecker Products: Theory and Applications
An improved truncation technique to analyze a Geo/PH/1 retrial queue with impatient customers
Computers and Operations Research
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Infinite level-dependent quasi-birth-and-death (LDQBD) processes can be used to model Markovian systems with countably infinite multidimensional state spaces. Recently it has been shown that sums of Kronecker products can be used to represent the nonzero blocks of the transition rate matrix underlying an LDQBD process for models from stochastic chemical kinetics. This paper extends the form of the transition rates used recently so that a larger class of models including those of call centers can be analyzed for their steady-state. The challenge in the matrix analytic solution then is to compute conditional expected sojourn time matrices of the LDQBD model under low memory and time requirements after truncating its countably infinite state space judiciously. Results of numerical experiments are presented using a Kronecker-based matrix-analytic solution on models with two or more countably infinite dimensions and rules of thumb regarding better implementations are derived. In doing this, a more recent approach that reduces memory requirements further by enabling the computation of steady-state expectations without having to obtain the steady-state distribution is also considered.