Handbook of theoretical computer science (vol. A)
SIGMETRICS '94 Proceedings of the 1994 ACM SIGMETRICS conference on Measurement and modeling of computer systems
Simple and Fast Algorithms for Linear and Integer Programs with Two Variables Per Inequality
SIAM Journal on Computing
Probability, stochastic processes, and queueing theory: the mathematics of computer performance modeling
Stochastic analysis of gang scheduling in parallel and distributed systems
Performance Evaluation
Processor Saving Scheduling Policies for Multiprocessor Systems
IEEE Transactions on Computers
Deciding Linear Inequalities by Computing Loop Residues
Journal of the ACM (JACM)
MAMSolver: A Matrix Analytic Methods Tool
TOOLS '02 Proceedings of the 12th International Conference on Computer Performance Evaluation, Modelling Techniques and Tools
Algorithms for shortest paths.
Algorithms for shortest paths.
Analytic modeling of load balancing policies for tasks with heavy-tailed distributions
Proceedings of the 2nd international workshop on Software and performance
Efficient analysis of the queue length moments of the MMAP/MAP/1 preemptive priority queue
Performance Evaluation
Journal of Network and Computer Applications
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We extend the ETAQA approach, initially proposed for the efficient numerical solution of a class of quasi-birth-death processes, to a more complex class of M/G/1-type Markov processes where arbitrary forward transitions are allowed but backward transitions must be to a single state to the previous level. The new technique reduces the exact solution of this class of M/G/1-type models to that of a finite linear system. We demonstrate the utility of our method by describing the exact computation of an extensive class of Markov reward functions that include the expected queue length or its higher moments. We also provide an algorithm that finds an appropriate state reordering satisfying our applicability conditions, if one such order exists. We illustrate the method, discuss its complexity and numerical stability, and present comparisons with other traditional techniques.