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Moment matching algorithm
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Analysis of Multi-server Systems
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Contents
Analytical tools for multiserver systems
Subsections
Moment matching algorithm
Overview
Moment matching algorithms
Key idea
Summary of results
Characterizing phase type distributions
Key idea
Summary of results
Organization of this chapter
Brief tutorial on phase type distributions
Examples of PH distributions
Definition of PH distribution
Subclasses of PH distribution
Properties of PH distributions
State of the art in moment matching algorithms
Moment matching algorithms
Characterizing PH distributions
Characterizing phase type distributions
EC distribution
Concluding remarks
Simple closed form solution
Preliminaries
The
Simple
solution
Analyzing the number of phases required
Complete closed form solution
The
Complete
solution
Analyzing the number of phases required
Positive closed form solution
The
Positive
solution
Analyzing the number of phases required
Concluding remarks
Future directions
Dimensionality reduction of Markov chains
Overview
Analysis of priority M/M/2 queue via DR
Analysis of priority M/PH/2 queue via DR
RFB and GFB processes
Organization of this chapter
Brief tutorial on matrix analytic methods
Quasi-birth-and-death process
Examples of QBD processes
Definition of QBD process
Markovian arrival process
Examples of Markovian arrival processes
Definition of MAP
QBD process modeling MAP/PH/1/FCFS queue
Matrix analytic methods
Stationary probabilities
Translating stationary probabilities into performance measures
State of the art in the analysis of multidimensional Markov chains
Approaches using matrix analytic methods
Other approaches
FB, RFB, and GFB processes
Definition of FB process
Definition of RFB process
Examples of RFB processes
Size-based task assignment with cycle stealing under immediate dispatching
Preemptive priority queue
Definition of GFB process
Examples of GFB processes
Threshold-based policy for reducing switching costs in cycle stealing
Size-based task assignment with cycle stealing under central queue
Nonpreemptive priority queue
Threshold-based policies in Beneficiary-Donor model
Dimensionality reduction
Analysis of the birth-and-death FB process
Analysis of the FB process
Analysis of the RFB process
Analysis of the GFB process
Constructing a 1D Markov chain using an approximate background process
Approximations of dimensionality reduction
Dimensionality reduction with partial independence assumption
Dimensionality reduction with complete independence assumption
Computational complexity of DR, DR-PI, and DR-CI
Moments of inter-level passage times in QBD processes
Preliminaries
Example
Moments of passage time
Moments of passage time in repeating part
Extension to nonrepeating part
Generalization
Computing various performance measures
Distribution and moments of the number of jobs in the system
Distribution and moments of response time
Response time of high priority jobs
Response time of low priority jobs
Validation
Accuracy of dimensionality reduction
Running time of dimensionality reduction
Concluding remarks
Future directions
Takayuki Osogami 2005-07-19
