Contents

• List of Figures
• List of Tables
• Introduction
  • Motivation
  • Difficulty of performance analysis of multiserver systems
  • Road map
    • Synopsis of Part I: Analytical tools for multiserver systems
    • Synopsis of Part II: Performance analysis of multiserver systems
    • Synopsis of Part III: Further discussion and conclusion
  
  
• Analytical tools for multiserver systems
  • Moment matching algorithm
    • Overview
      • Moment matching algorithms
      • Characterizing phase type distributions
      • 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
    • Characterizing phase type distributions
    • EC distribution
    • Simple closed form solution
    • Complete closed form solution
    • Positive closed form solution
    • Concluding remarks
  • 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
      • Markovian arrival process
      • Matrix analytic methods
    • 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
      • Definition of GFB process
      • Examples of GFB processes
    • 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
      • Moments of passage time
      • Generalization
    • Computing various performance measures
      • Distribution and moments of the number of jobs in the system
      • Distribution and moments of response time
    • Validation
      • Accuracy of dimensionality reduction
      • Running time of dimensionality reduction
    • Concluding remarks
  
  
• Performance analysis of multiserver systems
  • Configuring multiserver systems with multiple priority classes
    • Introduction
    • State of the art in the optimal number of servers
    • How many servers are best in FCFS system?
    • How many servers are best in priority system?
    • New approximations for many priority classes
      • Motivation
      • Approximations for multiserver systems with multiple priority classes
      • Comparing DR-A with BB and MK-N
    • Concluding remarks
  • Improving traditional task assignment policies
    • Task assignment in server farms
    • State of the art in task assignment policies
    • Task assignment with cycle stealing
    • Performance of task assignment with cycle stealing
      • Summary of results
      • Stability
      • Mean response time
    • Concluding remarks
  • Reducing switching costs in cycle stealing
    • Motivation
    • Threshold based policy for reducing switching costs in cycle stealing
    • State of the art in cycle stealing
    • Results
      • Summary of results
      • Stability
      • Mean response time
    • Concluding remarks
  • Designing robust resource allocation policies
    • Introduction
      • Static and dynamic robustness
      • State of the art in resource allocation policies for the Beneficiary-Donor model
      • Summary of results
    • Static robustness and mean response time of single-threshold allocation policies
      • Single-threshold allocation policies: T1 and T2
      • Stability under single-threshold allocation policies
      • Mean response time of single-threshold allocation policies
      • Static robustness of single-threshold allocation policies
    • Static robustness and mean response time of multi-threshold allocation policies
      • T1T2 policy
      • The adaptive dual threshold (ADT) policy
    • Dynamic robustness of threshold based policies
    • Concluding remarks
  
  
• Further discussion and conclusion
  • Applications in contact center design
    • Motivation
    • Overview of contact center operation
    • Towards efficient contact center operation
      • Overview of contact center management
      • Capacity planning
      • Routing policy design
  • Conclusion
    • Analytical tools developed
    • Lessons learned in the analysis of multiserver systems
    • Future directions
  
  
• Bibliography
• Proofs
• Moment matching algorithm by Bobbio, Horváth, and Telek
• Properties of Markovian arrival processes