Probability, stochastic processes, and queueing theory: the mathematics of computer performance modeling
MAMSolver: A Matrix Analytic Methods Tool
TOOLS '02 Proceedings of the 12th International Conference on Computer Performance Evaluation, Modelling Techniques and Tools
M/G/1-Type Markov Processes: A Tutorial
Performance Evaluation of Complex Systems: Techniques and Tools, Performance 2002, Tutorial Lectures
MAMSolver: A Matrix Analytic Methods Tool
TOOLS '02 Proceedings of the 12th International Conference on Computer Performance Evaluation, Modelling Techniques and Tools
An aggregation-based method for the exact analysis of a class of GI/G/1-type processes
ACM SIGMETRICS Performance Evaluation Review - Special issue on the fifth workshop on MAthematical performance Modeling and Analysis (MAMA 2003)
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 10 - Volume 11
Models of the departure process of a BMAP/MAP/1 queue
ACM SIGMETRICS Performance Evaluation Review - Special issue on the workshop on MAthematical performance Modeling And Analysis (MAMA 2005)
Bridging ETAQA and Ramaswami's formula for the solution of M/G/1-type processes
Performance Evaluation - Performance 2005
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
jMarkov: an object-oriented framework for modeling and analyzing Markov chains and QBDs
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
Numerical analysis of M/G/1 type queueing systems with phase type transition structure
Journal of Computational and Applied Mathematics
Solving finite-buffer queues with Markovian arrivals
ACM SIGMETRICS Performance Evaluation Review
A conditional probability approach to M/G/1-like queues
Performance Evaluation
System-theoretical algorithmic solution to waiting times in semi-Markov queues
Performance Evaluation
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We introduce a new methodology for the exact analysis of M/G/1-type Markov processes. The methodology uses basic, well-known results for Markov chains by exploiting the structure of the repetitive portion of the chain and recasting the overall problem into the computation of the solution of a finite linear system. The methodology allows for the calculation of the aggregate probability of a finite set of classes of states from the state space, appropriately defined. Further, it allows for the computation of a set of measures of interest such as the system queue length or any of its higher moments. The proposed methodology is exact. Detailed experiments illustrate that the methodology is also numerically stable, and in many cases can yield significantly less expensive solutions when compared with other methods, as shown by detailed time and space complexity analysis.