M/G/1-Type Markov Processes: A Tutorial

Authors:
Alma Riska;Evgenia Smirni
Affiliations:
-;-
Venue:
Performance Evaluation of Complex Systems: Techniques and Tools, Performance 2002, Tutorial Lectures
Year:
2002

Citing 6
Cited 5

Stochastic complementation, uncoupling Markov chains, and the theory of nearly reducible systems

SIAM Review
Probability, stochastic processes, and queueing theory: the mathematics of computer performance modeling

Probability, stochastic processes, and queueing theory: the mathematics of computer performance modeling
Exact aggregate solutions for M/G/1-type Markov processes

SIGMETRICS '02 Proceedings of the 2002 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
The BMAP/G/1 QUEUE: A Tutorial

Performance Evaluation of Computer and Communication Systems, Joint Tutorial Papers of Performance '93 and Sigmetrics '93
MAMSolver: A Matrix Analytic Methods Tool

TOOLS '02 Proceedings of the 12th International Conference on Computer Performance Evaluation, Modelling Techniques and Tools
Theory, Volume 1, Queueing Systems

Theory, Volume 1, Queueing Systems

Bridging ETAQA and Ramaswami's formula for the solution of M/G/1-type processes

Performance Evaluation - Performance 2005
Modeling, analysis, measurement and experimentation with the Tangram-II integrated environment

valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
A conditional probability approach to M/G/1-like queues

Performance Evaluation
An Approximation Approach for the Deviation Matrix of Continuous-Time Markov Processes with Application to Markov Decision Theory

Operations Research
Exact analysis of the M/M/k/setup class of Markov chains via recursive renewal reward

Proceedings of the ACM SIGMETRICS/international conference on Measurement and modeling of computer systems

Quantified Score

Hi-index	0.00

Visualization

Abstract

M/G/1-type processes are commonly encountered when modeling modern complex computer and communication systems. In this tutorial, we present a detailed survey of existing solution methods for M/G/1-type processes, focusing on the matrix-analytic methodology. From first principles and using simple examples, we derive the fundamental matrix-analytic results and lay out recent advances. Finally, we give an overview of an existing, state-of-the-art software tool for the analysis of M/G/1-type processes.